June 28, 2014 for $VIX, great for $VIX, $VXX and volatility tracking.

November 3, 2013

Portfolioprobe's investment performance measurement vs calculation

Measurement as a call to action.

I said "measurement". My dialogist heard "calculation" but wanted "measurement". We went dizzy in the chase.

A calculation is what computers do.

A measurement is an assessment. It is a comparison with an ulterior motive.

I'm not going to weigh myself unless there is the possibility of a change in behavior. If there is no value of my weight that is going to affect the way that I act, then weighing is pointless -- the scale does the calculation but there is not actually a measurement.

Look at these on 4 schemes:

a performance statistic relative to a benchmark
a peer group
a performance statistic relative to no trading
random portfolios


October 29, 2013

Algorithmic predictions and portfolio management

We think the robot future is going to be more disruptive than many think, but we also suspect that actual data-crunching plays only a small part in the career of a successful analyst.

There is some time spent crafting a compelling narrative around some basic assumptions, and then an awful lot more spent repeating that story ad nauseam on the phone, in reports, and in person.

Not to mention the part about getting to know people at the companies they cover. Top of UK brokers' list of problems at the moment are regulatory plans to make them charge their clients directly (as opposed to their clients' customers) for introducing them to the management of companies.

But, even if it is just about the value of good ideas - if you have some really good algorithms for, say, indexing websites or trawling Twitter, why would you advertise and sell them?

The world's most successful hedge fund strategy is both the most secretive and the one that you could never invest in: Renaissance Technology's Medallion fund. The fund ignores the mainstream finance literature, preferring to scoop up experienced cryptographers and mathematicians required to sign intimidating non-compete clauses, and it is willing to trade signals in the noise that work even if it doesn't understand why.

April 16, 2013

Quant Start Quantitative-Finance-Reading-List

List by Michael Halls-Moore of

General Quant Finance Reading (Michael Lewis, Roger Lowenstein, Emanuel Derman).
Interview Preparation (Paul Wilmott, Mark Joshi)
Quantitative Trading ( Sheldon Natenberg, Nassim Nicholas Taleb, Barry Johnson, Euan Sinclair)
Mathematical Finance / financial engineering (John Hull, Salih Neftci)
Interest Rate Derivatives (Damiano Brigo, Fabio Mercurio)
C++ (Scott Meyers )
Python (Mark Lutz)
MATLAB ( Paolo Brandimarte)
R (Phil Spector, Norman Matloff, Paul Murrell)
Excel/VBA (Fabrice Douglas Rouah, Gregory Vainberg)

Quantstart's Quantitative-Finance-Reading-List

December 24, 2012

Financial crisis due to more than mortgages

This Mark Adelson article proposes the following deeper
causes beyond US mortgages: securities firms converting from partnerships to corporations, the 30-year trend of
deregulation, the quant movement, the spread of risk-taking culture through the financial
industry, and globalization.

October 25, 2012

Mandelbrot, "The Fractalist"

"I realized that mathematics cut off from the mysteries of the real world was not for me, so I took a different path," he writes. He wanted to play with what he calls "questions once reserved for poets and children."

He prized roughness and complication. "Think of color, pitch, loudness, heaviness and hotness," he once said. "Each is the topic of a branch of physics." He dedicated his life to studying roughness and irregularity through geometry, applying what he learned to biology, physics, finance and many other fields.

He was never easy to pin down. He hopscotched so frequently among disciplines and institutions -- I.B.M., Yale, Harvard -- that in his new memoir, "The Fractalist," he rather plaintively asks, "So where do I really belong?" The answer is: nearly everywhere.

As "The Fractalist" makes plain, Mandelbrot led a zigzag sort of life, rarely remaining in one place for long. He was born in Warsaw to a middle-class Lithuanian Jewish family that prized intellectual achievement. His mother was a dentist; his father worked in the clothing business. Both loved knowledge and ideas, and their relatives included many fiercely brainy men.

Continue reading "Mandelbrot, "The Fractalist" " »

July 12, 2012

reddit finance what are quant lifestyles like

reddit finance: What are quant lifestyles like ?

Posted in The Life and Quantfinance.

Buy side FI desk Mon-Thursday 12 hour days (8-8) Spend the day building trading/pricing models, test them, reporting functions done at night. A sample day Come in the office at 8am, eat breakfast at my desk and have coffee while catching up on news/market movements/big events fire up all the pricing and trading models, start checking the holdings, making sure we're positioned correctly. Start working on whatever piece of work I have to do, performance attribution on tons of issues to identify better "risk to reward" bets and other spreads that may be profitable. You'll spend your day creating models to do this. Confer with team about days movements (9am - 9:30 am), back to working on the models 12:30, have lunch maybe a quick workout too 13:30 check market, check daily p/l 13:40 back to working on models of the day ~16:00 confer with colleagues on potential trades/plays ~17:00 check days p/l, sign off on reports trade journals etc ~18:00 Conduct macro research/stress test/risk test, continue testing/refining models ~20:00 go home. Putting out random fires at anytime during the day: dealing with sell side sales guys (many of them are idiots), Chasing down unmatched trades, preparing presentations/client reports, Talking to clients Fridays 8-6 Would leave early on friday as I would fly somewhere new every weekend. 2.Quant trading for own book 6:00 am, wake up, hit the gym 7:00 check p/l 9:00 start working on research projects/ while keeping an eye on systems 15:00 stop research and go out and have fun :D Hours are very variable and you do the work whenever you want.... I'm considering going back to a "proper" job, but i'll make less money :(, however the structure of a workplace environment can be good, and I'd probably do something outside of trading so I can run my machines on the side.

Continue reading "reddit finance what are quant lifestyles like" »

June 27, 2012

JPM's London Whale trading var model change: material ?

Typically, changes in value-at-risk models at banks are made by committees composed of managers who monitor risks and business heads who take them, according to risk management experts.

Banks in the United States are required to give investors periodic counts of their value-at-risk. The numbers are calculated and presented differently across companies, but in general are supposed to show a minimum amount that a portfolio could be expected to lose in each of a few days during a quarter.

What's most useful to investors is not so much the actual numbers, but how much they change, experts say.

JPMorgan first told investors on April 13 that the reading of risk at its CIO unit as of the end of March showed that the unit could lose at least $67 million in a single trading day, slightly less than the $69 million from the previous reading in December.

The report indicated steady risk management in the CIO's office, which was in contrast to press reports at the time that a London-based trader for JPMorgan was taking whale-sized positions.

But on May 10 when the bank suddenly disclosed the $2 billion-plus loss, it also revealed for the first time that the $67 million reading had been calculated with a new model. The prior model showed risk had actually spiked as the value-at-risk nearly doubled to $129 million.

Had the higher number been reported, said analyst Jason Goldberg of Barclays, "certainly, they would have been asked why the VaR doubled."

To bring a potential case against JPMorgan over its value-at-risk model change, the SEC will need to decide if the failure to disclose the model change was "material." In other words, would a reasonable investor see the information as significant?

Experts are divided on whether the understatement of risk by the bank will meet the SEC's legal test. It is unclear if investors would have seen the hike in risk-taking as something that could lead to a big trading loss.

Since the financial crisis, the SEC has faced a barrage of criticism for what some say is a failure to go after the top executives at the country's major banks.

Several legal experts say that the failure of JPMorgan to disclose changes to its value-at-risk modeling could actually present a prime opportunity to do just that.

"To make management sweat a little bit, the SEC's focus might well be on internal controls," said Charles Whitehead, a professor at Cornell Law School and former Wall Street executive.

Continue reading "JPM's London Whale trading var model change: material ?" »

June 9, 2012

SAS financial services modeling

The SAS financial services modeling group in San Diego, exploring ways they can take advantage of high-performance analytics and big data techniques to deliver more models, more quickly, and to more customers. This wasn't completely an academic exercise--the team in San Diego has added several new customers recently and have been looking for ways to boost productivity, so this is the perfect setup for our high-performance story. Perhaps you've seen Jim Davis' blog where he ponders what you can do with all the extra time savings that high-performance analytics offers ... provide service to more customers is one good idea!

June 3, 2012

Recover the trade, do not get stopped out

From offices on the 58th floor of the Chrysler Building in Midtown Manhattan, Mr. Weinstein runs a $5.5 billion hedge fund firm called Saba Capital Management. ("Saba" is Hebrew for "grandfatherly wisdom," a nod to his Israeli roots.) It was there, last autumn, that he noticed an aberration in the market for credit derivatives. He knew from experience what it was like to lose a lot of money at a big bank. Before starting Saba, he was responsible for a team that lost nearly $2 billion, in the depths of the financial crisis, at Deutsche Bank. Others lost even more. Last November, however, he saw that a certain index seemed to be trading out of line with the market it was supposed to track. He and his team pored through reams of data, trying to make sense of it.

It was his pick for the "best" investment idea of the moment. Mr. Weinstein recommended buying the Investment Grade Series 9 10-year Index CDS -- the same index that Mr. Iksil was shorting.

Continue reading "Recover the trade, do not get stopped out" »

April 12, 2012

Black Scholes formula in FX context

Derive the Black Scholes formula in FX context in a very simple way using measure change techniques. Of course, the final result can be used for all asset classes, though the derivation itself relies heavily on the symmetries prevailing in FX.

The idea goes back to a quantitative finance presentation held by Iain J. Clark where he did the derivation on just one slide. Here we repeat the derivation trying to fill in some technical details.

Continue reading "Black Scholes formula in FX context" »

December 31, 2011

Risk ratings, structured finance who's who

The departures of Ms. Tillman and Ms. Rose come as S&P President Doug Peterson works to forge a new identity for the firm and restore a reputation tarnished by the crisis. The former Citigroup Inc. banker has sought to enhance the firm's internal controls while championing analysts' independence.

Some former S&P analysts say those changes, some under way since Mr. Peterson took over in September, have been slow going. They say many of their one-time colleagues who oversaw the ratings on complex mortgage-linked deals have remained at the firm since 2008--despite calls from investors, regulators and lawmakers for wholesale changes to the way S&P and the other major rating firms do business.

An S&P spokesman declined to comment.

Despite the backlash, S&P and rivals Moody's Investors Service and Fitch Ratings remain the dominant players in the business of ratings everything for corporate and sovereign debt to asset-backed securities.

The Justice Department and the Securities and Exchange Commission are investigating S&P's crisis-era ratings on mortgage-linked deals, people familiar with the matter have said. Former S&P employees who have been questioned as part of the probe say that Justice Department investigators have expressed consternation that so many of the managers who oversaw the ratings on mortgage-linked securities remain at the firm, making it difficult for them to speak with a broad group of former analysts.

A Justice Department spokeswoman declined to comment.

Mr. Peterson succeeded Deven Sharma in September. S&P replaced its chief credit officer, Mark Adelson, in early December. Mr. Adelson was hired by Mr. Sharma in May 2008 and given the mandate to make it harder for debt-issuers to earn a triple-A from the firm. Mr. Adelson was moved to a "senior research fellow" position, considered by former and current S&P employees to be a demotion. At the time Mr. Adelson had declined to comment.

The firm also announced earlier this month that David Jacob, who succeeded Ms. Rose as S&P's structured finance chief, would step down at the end of the year.

Continue reading "Risk ratings, structured finance who's who" »

April 9, 2011

QuantNet for Quant Finance

QuantNet is portal from education and recruiting in quant finance.

Example 1: the coming glut of financial engineers:

Financial trading has transformed over the past 30 years. In the early '80s, the people drawn to trading had a passion for markets, but few had the academic pedigree that's a prerequisite today. Many had only a high school education, but the markets were straightforward enough that a basic understanding of option theory and CAPM sufficed. When derivatives markets exploded in size, both in terms of equity trading and footloose liquid capital, complexity increased by an order of magnitude. Traders with a technical background who had been there from the start were able to capture "monopoly profits" since a failure to understand the technical nuances of the business was a barrier to entry for many prospective quants. Academics and engineers were in short supply, and therefore were hot commodities.
Today, however, the situation looks much different. Where advanced training in quantitative finance was once the exception, there is a growing army with advanced credentials. Black-Scholes and Ito's Lemma used to be hallmarks of an expert in quant finance; now they're part of the MBA curriculum and even some undergraduate math programs. Interest rate derivatives and the Gaussian copula for credit and mortgage derivatives were similarly standardized.
[ Via BI/Clusterstock ]

Example 2: Understanding the Difference Between Risk Taking, Risk Management and Risk Control:

Since the full magnitude of the recent financial crisis has become clear, a great deal has been written about how risk management failed us. We hear of purported death knells for quantitative financial modeling, cries of "back-to-basics" and even reports of civil war brewing between the quants and the managers. Commentators highlight spectacular blow-ups and mind-bending tales of management ineffectiveness, outsized hubris and plain ineptitude. And then, of course, there is always the requisite finger pointing towards those institutions that, either through intellectual and strategic prowess or via sheer brazen luck, came out smelling of banknotes and roses. We all love the drama - it's the ultimate in reality TV and in the context of our self-obsessed culture, it really drives home the maxim that truth is stranger than fiction.

Now that the dust has settled, the question remains: was it risk management and quantitative modeling that failed the people, or was it the people who were supposed to be implementing risk management strategies and leveraging quantitative finance that failed the people?

January 2, 2010

Growth vs Value, year-over-year

Let's slice the market another way. Growth stocks outperformed value stocks last year. Investment newsletters often argue that this means growth stocks are likely to do so in 2010 as well. Though not every adviser agrees on how to define these two types of stocks, researchers generally rely on the ratio of price to book value per share. Stocks with the highest ratios are deemed growth stocks, while those with the lowest ratios are considered value stocks.

Using these definitions, the finance professors Eugene F. Fama of the University of Chicago and Kenneth R. French of Dartmouth have calculated the returns of both categories back to 1926. But their database shows no correlation in performance from one year to the next for either class. That means that, while growth stocks this year may very well continue to lead the market, whether they do so won't be determined by their 2009 performance.

There are good reasons for these findings, according to Lawrence G. Tint, chairman of Quantal International, a firm that conducts risk modeling for institutional investors. Mr. Tint said that if the market's return in one year were a predictor of its return the next year, "investors would rush in on Jan. 1 to buy or sell, depending on the direction of the anticipated movement."

"We can be comforted by the fact that reasonably efficient markets always base their level on anticipated future returns," he added, "and do not include history in the calculation."

Continue reading "Growth vs Value, year-over-year" »

April 20, 2009

Elements of this intellectual hubris, Brooks

Calling bottom? When David Brooks writes about the Gaussian copula function, can a quanfinance resurgence be far behind?

Many writers have described elements of this intellectual hubris. Amar Bhidé has described the fallacy of diversification. Bankers thought that if they bundled slices of many assets into giant packages then they didn't have to perform due diligence on each one. In Wired, Felix Salmon described the false lure of the Gaussian copula function, the formula that gave finance whizzes the illusion that they could accurately calculate risks. Benoit Mandelbrot and Nassim Taleb have explained why extreme events are much more likely to disrupt financial markets than most bankers understood.

February 5, 2009

Black Swan Formation

The amusing certitude technical analysts place on trading price and volume in equities markets reaches a new high: the black swan formation.


Continue reading "Black Swan Formation" »

January 25, 2009

If your ideas is so good, why aren't you rich already ?

If this works then why are you telling us about it and not doing it yourself?
There are many responses, including Wilmott's response:

1. I don't have the ability to do it myself, this is my marketing pitch, want to back me?

2. Ideas are cheap, I know which ones are good or bad but not everyone can tell the difference

3. Do you know all the barriers to entry? $1million in lawyers fees to set up a fund, months of software writing, years of knocking on doors trying to raise money. Forget it!

4. This is a great idea, but I've got better

5. I don't want to spend the rest of my life doing this, even if it is profitable, variety is the spice of life

6. I did, and now I've retired or, more simply, I've got enough money already

7. My lawyer/doctor/wife says I mustn't

Continue reading "If your ideas is so good, why aren't you rich already ?" »

January 7, 2009

VAR in 2009

The NYT has a deeper look at quantitative financial risk:

Risk Mismanagement
Published: January 4, 2009
Were the measures used to evaluate Wall Street trades flawed? Or was the mistake ignoring them?

The End of the Financial World as We Know It
Published: January 4, 2009
We have a brief chance to cure ourselves. But first we need to ask: of what?

How to Repair a Broken Financial World
Published: January 4, 2009
There are obvious changes in the financial system to be made, to prevent some version of what has happened from happening all over again.

Continue reading "VAR in 2009" »

January 4, 2009

Falkenstein: Finding Alpha

Falkenblog (and aka Hedgefund Guy on Mahalanobis) is a frequent read, and if the book is as consistently interesting, it will be recommended.

Finding Alpha: The Search for Alpha When Risk and Return Break Down (Wiley Finance) by Eric Falkenstein (Hardcover - Jun 29, 2009)

December 28, 2008

Irony of diversification

Imagine you are stranded on a desert island. For fresh water, there are three natural springs, but it is possible one or more have been poisoned. To minimize your risk, what is your optimal strategy for drinking from the springs? You might:

  • select one of the three springs at random and drink exclusively from it
  • select two of the springs at random and drink exclusively from them, or
  • drink from all three springs.

Your best strategy is to drink from just one spring. Yet, according to a certain financial theory, the optimal strategy is the diversified approach of drinking from all three springs.

Continue reading "Irony of diversification" »

November 26, 2008

D-man on derivatives

Cash is the ultimate financial derivative, according to Emanuel Derman.

One airy invention is the PIK (payment-in-kind) bond, a loan that pays its promised interest in additional bonds of the same kind, as opposed to solid cash. It sounds insubstantial, a barely disguised pyramid scheme in which you make your promised payments each time with further promises of payment, each at least as chancy as a subprime CDO. But think about the dollar: deposit it in the bank for a year and you get more dollars at the end. What is paper money but a PIK, an early derivatives contract? To trust it you have to trust the country that provide its value, and the same is true of payment in kind. Used wisely, maybe payment in kind can serve as hallmark of trust in the financial supply chain too.

October 23, 2008

Rambunctious Quant

RAMBUNCTIOUS QUANT, new quantitative content.

September 9, 2008

Josh Rosner, Graham Fisher: leverage amplifies losses

As Josh Rosner, an expert on mortgage securities at Graham Fisher in New York noted in a research piece last week, the leverage used to put such securities pools together can amplify losses. For example, a 4 percent loss in a mortgage-backed security held by collateralized debt obligations can turn into almost a 40 percent loss to the holder of the C.D.O. itself.

Continue reading "Josh Rosner, Graham Fisher: leverage amplifies losses" »

September 8, 2008

Option Volatility & Pricing: Advanced Trading Strategies and Techniques, Sheldon Natenberg

Option Volatility & Pricing: Advanced Trading Strategies and Techniques
, second edition (1994, Hardcover) by Sheldon Natenberg.

Natenberg not only takes great pains to explain the concept of volatility, in addition to other inputs into an option pricing model, but clearly shows that option pricing isn't the exact science many seem to believe, for the simple reason that we never know if our volatility estimate is correct.

July 21, 2007

ABX Mortgage Index

A way to measure the effects of problems in the sub-prime mortgage
sector is to look at Credit Default Swaps (CDS). Remember that these
CDS contracts effectively work as a kind of insurance policy for banks
or other holders of bad mortgages. If the mortgage goes bad, then
the seller of the CDS must pay the bank for the lost mortgage payments
(alternatively ... if the mortgage stays good then the seller makes a lot
of money).

The index that measures the CDS market for home equity is called
the ABX.HE index. The sub-variation of this index that refers to risky
sub-prime loans is called the ABX.HE BBB index.
Markit's ABX catalog.

Continue reading "ABX Mortgage Index" »

July 15, 2007

Bond Market Association, Securities Industry and Financial Markets

SIFMA, the Securities Industry and Financial Markets Association
represents the industry (eponymously)..

Born of the merger between The Securities Industry Association and
The Bond Market Association, SIFMA is a 'single powerful voice'.

Example publication: Mortgage Prepayment Projection Tables,
PSA Median, CPR average, etc.

More in Quant Finance, mortgage.

June 7, 2007

Interest rate risk (IRR)

Interest Rate Risk - Models Similarities and differences

By comparing three different approaches to interest rate modelling, namely
* spot,
* forward and
* market models,
Han Lee of Commerzbank Securities finds that each has a different method
of constructing the effective volatility function, which determines its use.
Han H Lee is head of fixed-income derivatives research at Commerzbank
Securities in London.

See also Basel on Interest Rae risk, OCC / Treasury on interest rate risk,
and the FDIC on interest rate risk management.

June 1, 2007

Epicurean Dealmaker

epicureandealmaker on fat tails.
Derivatives: Transfering risk or reducing risk ?

May 30, 2007

Interest-rate term-structure pricing models: Riccardo Rebonato

Review Paper. Interest-rate term-structure pricing models: a review
Riccardo Rebonato

Interest-rate term structure modelling from the early short-rate-based
models to the current developments; use models for pricing complex
derivatives or for relative-value option trading. Therefore, relative-pricing
models are given a greater emphasis than equilibrium models.

The current state of modelling owes a lot to how models have
historically developed in the industry, and stresses the importance
of 'technological' developments (such as faster computers or more
efficient Monte Carlo techniques) in guiding the direction of theoretical

The importance of the joint practices of vega hedging and daily
model-recalibration is analysed in detail. The relevance of market
incompleteness and of the possible informational inefficiency of
derivatives markets for calibration and pricing is also discussed.

Continue reading "Interest-rate term-structure pricing models: Riccardo Rebonato" »

May 24, 2007

Accrued Interest

Accrued Interest aka accruedint, smart about finance and economics.
Why Home Depot should borrow more.

May 3, 2007

Effect of Mortgage Refinancing on Interest-Rate Volatility, Duarte

Effect of Mortgage Refinancing on Interest-Rate Volatility
and not vice versa, by Duarte at UW.

Continue reading "Effect of Mortgage Refinancing on Interest-Rate Volatility, Duarte" »

January 15, 2007

All About Alpha

AllAboutAlpha, example:
value premium, value pricing.

return = alpha + beta * (market return)

January 7, 2007

Nassim Nicholas Taleb, fooled by randomness

Nassim Nicholas Taleb, Fooled By Randomness (and black swans), with

Black Swan discussion: MeFi, Telergraph

December 8, 2006

Option Adjusted Spreads: The OAS Trilogy

Trilogy by Andrew Davidson and Co (AdCo)
1. Active Passive Decomposition
2. Prepay risk and option adjusted valuation concept
3. prOAS Valuation model with refinancing and turnover risk

August 7, 2006

TBMA Mortgage Prepayment Projection Tables

TBMA Mortgage Prepayment Projection Tables: Questions and Answers

TBMA = The Bond Market Association.

Continue reading "TBMA Mortgage Prepayment Projection Tables" »

August 6, 2006

Hedging beyond duration and convexity

Hedging beyond duration and convexity.

By considering a representation using a Fourier-like harmonic,
empirical evidence that such a series provides our hedging
strategy on a mortgage-backed security (MBS) with the first
four principal components of yield curve.

Continue reading "Hedging beyond duration and convexity" »

July 16, 2006

Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?

An Empirical Test of a Two-Factor Mortgage Valuation Model:
How Much Do House Prices Matter?

Mortgage-backed securities, with their relative structural simplicity
and their lack of recovery rate uncertainty if default occurs, are
particularly suitable for developing and testing risky debt valuation
models. A two-factor structural mortgage pricing model in which
rational mortgage-holders endogenously choose when to prepay
and default subject to
i. explicit frictions (transaction costs) payable when terminating
their mortgages,
ii. exogenous background terminations, and
iii. a credit related impact of the loan-to-value ratio (LTV) on

We estimate the model using pool-level mortgage termination data
for Freddie Mac Participation Certificates, and find that the effect of
the house price factor on the results is both statistically and
economically significant. Out-of-sample estimates of MBS prices
produce option adjusted spreads of between 5 and 25 basis
points, well within quoted values for these securities.

Chris Downing, Richard Stanton, and Nancy E. Wallace,
An Empirical Test of a Two-Factor Mortgage Valuation Model:
How Much Do House Prices Matter
(link to 406 K, PDF file)

Chris Downing, Federal Reserve Board, Washington, DC
Richard Stanton, Haas School of Business, University of California, Berkeley
Nancy E. Wallace, Haas School of Business, University of California, Berkeley

Continue reading "Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?" »

July 12, 2006

Mortgage Valuation and Optimal Refinancing, Pliska

An equilibrium valuation of fixed-rate mortgage contracts in
discrete time -- the mortgagor’s prepayment behavior
described by intensity process and with exogenous mortgage
rates, the value of the contract is derived in an explicit form
that can be interpreted as the principal balance plus the
value of a certain swap.

A nonlinear equation for what the mortgage rate in a
competitive market, and thus mortgage rates are endogenous
and depend upon the mortgagor’s prepayment behavior.

The complementary problem, where mortgage rates are
exogenous and the mortgagor seeks the optimal refinancing
strategy, is then solved via a Markov decision chain.

Finally, the equilibrium problem, where the mortgagor
is a representative agent in the economy who seeks the
optimal refinancing strategy and where the mortgage
rates are endogenous, is developed, solved, and analysed.

Mortgage Valuation and Optimal Refinancing, Stanley R. Pliska:
shorter and longer versions.

Continue reading "Mortgage Valuation and Optimal Refinancing, Pliska" »

July 5, 2006

Kalotay's option theory

Andrew Kalotay research on mortgage theory.
Valuation and optimal exercise of options, calling and refunding.

Previously: Option-Theoretic Prepayment Model for Mortgages by
Fabozzi , Kalotay and Yang.

June 30, 2006

JFI (Journal of Fized Income)

Journal of Fized Income (JFI) by Institutional Investor.

Fixed Income Analysts Society (FIASI);
Fixed Income Securities: Tools for Today's Markets, Second Edition by Bruce Tuckman;
The Handbook of Fixed Income Securities, Edited by Frank Fabozzi.

June 13, 2006

The Complexities of Mortgage Options (Prendergast)

Mortgage option prices behave quite differently than the prices of
options on underlying securities that do not exhibit significant
convexity. As a result, the intuition of many market participants
about option risk characteristics does not typically apply to
mortgage options.

The risk characteristics of these options: negative convexity of
the underlying mortgage and the positive gamma of the option
impact call option convexity in opposing directions. As a result,
call option convexity can be either positive or negative,
depending on the interest rate scenario and option specification.

On the other hand, a mortgage put option is always positively convex.
A quantitative understanding of these risk characteristics is critical
for money managers and broker/dealers who use mortgage options.

The Complexities of Mortgage Options
Prendergast, Joseph R.
March 2003

June 8, 2006

Wilmotters' Quant Quantitative Finance notes

Paul Wilmott, Emanuel Derman and Domicic Dominic Connor (DCDC)
write Wilmotters: Paul, Emanuel, Dominic.

June 3, 2006

hp 12c

HP 12c calculator goes platinum. Joy for CFA.

May 26, 2006

House Price CAPM

Cointegration and Error Correction Mechanism Approaches:
Estimating a Capital Asset Pricing Model (CAPM) for House
Price Index Returns with SAS

Many researchers erroneously use the framework of linear
regression models to analyze time series data when predicting
changes over time or when extrapolating from present conditions
to future conditions. Caution is needed when interpreting the results
of these regression models. Granger and Newbold (1974) discovered
the existence of ‘spurious regressions’ that can occur when the
variables in a regression are nonstationary. While these regressions
appear to look good in terms of having a high R2 and significant
t-statistics, the results are meaningless. Both analysis and modeling
of time series data require knowledge about the mathematical model
of the process.

This paper introduces a methodology that utilizes the power
of the SAS DATA STEP, and PROC X12
and REG procedures. The DATA STEP uses the SAS LAG and
DIF functions to manipulate the data and create an additional
set of variables including Home Price Index Returns (HPI_R1), first
differenced, and lagged first differenced. PROC X12 seasonally
adjusts the time series. Resulting variables are manipulated
further (1) to create additional variables that are tested for
stationarity, (2) to develop a cointegration model, and (3) to
develop an error correction mechanism modeled to determine
the short-run deviations from long-run equilibrium. The relevancy
of each variable created in the data step to time series analysis is
discussed. Of particular interest is the coefficient of the error
correction term that can be modeled in an error correction mechanism
to determine the speed at which the series returns to equilibrium. The
main finding is that Metropolitan Statistical Areas (MSAs) with very
slow shortrun acceleration paths to the equilibrium have higher
returns and risk associated with house price returns than
MSAs with very rapid speed-of-adjustment coefficients.

-- Ismail Mohamed and Theresa R. DiVenti, PDF.

May 16, 2006

The Quant / Richard Booth

THE QUANT by Richard Booth: about the intersections of law, business, finance,
economics, and statistics. A law Professor.

October 31, 2005

Fooled by Randomness 2005

One of the best conference programs for quantitative risk
analysis: Fooled by Randomness 2005. text, PDF.

October 19, 2005

Credit Risk Models II: Structural Models. (Elizalde)

Credit Risk Models II: Structural Models
July 2005

The structural approach for modelling credit risk considers both
the case of a single firm and the case with default dependences
between firms.

In the single firm case, we review the Merton (1974) model and
first passage models, based on Black & Cox (1976), examining
their main characteristics and extensions. The issue of estimating
structural models is also addressed, covering the different ways
proposed in the literature.

The issue of estimating structural models is also addressed,
covering the different ways proposed in the literature.

Secondly, we model default dependences among firms, which account
for two types of default correlations: cyclical default correlation
and contagion effects. We close with a brief mention of factor models.

The paper guides readers throught the literature, providing a
comprehensive list of references and, along the way, suggesting
different possible extensions for its future development.


Continue reading "Credit Risk Models II: Structural Models. (Elizalde)" »

September 10, 2005

Volatility vs Liquidity

Traditionally, economists have thought that big up-and-down
fluctuations in returns indicated risky investments, so many hedge
fund investors have hoped to see a pattern of smooth and even returns.

Andrew Lo quickly saw that lots of hedge funds were posting returns
that were just too smooth to be realistic. Digging deeper, he found
that funds with hard-to-appraise, illiquid investments - like real
estate or esoteric interest rate swaps - showed returns that were
particularly even. In those cases, he concluded, managers had no way
to measure their fluctuations, and simply assumed that their value was
going up steadily. The problem, unfortunately, is that those are
exactly the kinds of investments that can be subject to big losses in
a crisis. In 1998, investors retreated en masse from such investments.

Mr. Lo came to a disturbing conclusion: that smooth returns,
far from proving that hedge funds are safe, may be a warning
sign for the industry.

Continue reading "Volatility vs Liquidity" »

August 27, 2005

Non-Gaussian Panel Time Series Model Decomposing Default Risk

We model 1980--2003 rating and cohort specific cumulative default
frequencies. The data is decomposed into systematic and firm-specific
risk components. We have to cope with

(i) the shared exposure of each cohort and rating class to the same
systematic risk factor;

(ii) strongly non-Gaussian features of the individual time series;

(iii) possible dynamics of the unobserved common risk factor;

(iv) changing default probabilities per rating cohort over time
(ageing effects), and

(v) missing observations. We propose a non-Gaussian multivariate state
space model that simultaneously deals with all of this issues.

The model is estimated using importance sampling techniques.

Continue reading "Non-Gaussian Panel Time Series Model Decomposing Default Risk" »

August 26, 2005

Macroeconomic determinants of the yield curve

Macroeconomic variables besides inflation and real activity drive the
yield curve in the framework of no-arbitrage affine term structure
models. We construct model-based projection of all the latent factors
onto the observable macro factors, which are real activity and

As a result, the factors are decomposed into the “macro” part: a
linear function of the macro variables and their lags; and the truly
novel part which is orthogonal to the entire history of the macro
variables. We are able to relate the unexplained part of the short
rate to such measures of liquidity as the AAA credit spread and MZM
growth rate. The unexplained part of the slope is highly correlated
with the budget deficit.

Continue reading "Macroeconomic determinants of the yield curve" »

August 21, 2005

Efficient Calibration for Libor Market Models

LMM Calibrator Estimation of volatility and correlation parameters in
the sense of (Brigo and Mercurio 2001), (Brigo and Morini 2004) and
(Brigo, Mercurio, and Morini 2005)

  1. Estimate volatilities from Caps/Floors
  2. Rescale volatilities to the needed Libor maturity
  3. Extract correlation parameters from swaption volatilities

Alternative strategies and implementation issues, Thomas Weber, .

See also Interest rate modelling, Brigo, Mercurio, Pelsser.

July 27, 2005

Correlation-dependent Credit Structural Model

In 1976 Black and Cox proposed a structural model where an obligor
defaults when the value of its assets hits a certain barrier. In 2001
Zhou showed how the model can be extended to two obligors whose assets
are correlated. In this paper we show how the model can be extended to
a large number of different obligors. The correlations between the
assets of the obligors are determined by one or more factors.

We examine the dynamics for credit spreads implied by the model and
explore how the model price tranches of collateralized debt
obligations (CDOs). We compare the model with the widely used Gaussian
copula model of survival time and test how well the model fits market
data on the prices of CDO tranches.

We consider two extensions of the model. The first reflects empirical
research showing that default correlations are positively dependent on
default rates. The second reflects empirical research showing that
recovery rates are negatively dependent on default rates.

Continue reading "Correlation-dependent Credit Structural Model" »

July 25, 2005

Optimal Recursive Refinancing and the Valuation of Mortgage-Backed Securities (Longstaff)

The optimal recursive refinancing problem where a borrower minimizes
his lifetime mortgage costs by repeatedly refinancing when rates
drop. Key factors affecting the optimal decision are the cost of
refinancing and the possibility that the mortgagor may have to
refinance at a premium rate because of his credit.

The optimal recursive strategy often results in prepayment being
delayed significantly relative to traditional models. Furthermore,
mortgage values can exceed par by much more than the cost of
refinancing. Applying the recursive model to an extensive sample of
mortgage-backed security prices, we find that the implied credit
spreads that match these prices closely parallel borrowers’ actual
spreads at the origination of the mortgage. These results suggest
that optimal recursive models may provide a promising alternative
to the reduced-form prepayment models widely used in practice.

Francis A. Longstaff, Anderson School of Management.

Continue reading "Optimal Recursive Refinancing and the Valuation of Mortgage-Backed Securities (Longstaff)" »

July 23, 2005

Modelling Dependence with Copulas for Risk Management

Modelling of dependence is one of the most rucial issues in risk
management. Whereas classically independence was equated to linear
correlation, more recently, mainly due to extremal market moves,
the limitations of the linear correlation concept were strongly felt.

In order to stress test dependence in a financial or insurance
portfolio, the notion of copula offers a versatile tool.

* Basic properties of copulas,
* The underlying simulation and numerical issues,
* Use of copula based techniques in integrated risk management.


July 22, 2005

Dependence Modelling in Risk Management

* Simulation of dependent risks,
* Statistical estimation of correlation in the static case,
* Dependence and correlation in a dynamically changing environment
* Extremes for heavy-tailed random vectors and multivariate stochastic processes.

Crucial to questions of risk aggregation, the project aims to
establish the fundamentals of dependence and correlation modelling.

July 21, 2005

Asset prices by Enricode Giorgi

Default models and asset pricing models at Enricode Giorgi's resource,
some with correlated defaults.

July 15, 2005

OAS measure of yield

OAS measure of yield has been introduced to accurately price callable
bonds but is also used now as a measure for bullets' yield.

1. For bullets, it is more accurate than yield to maturity (YTM) as

a. You use implied forward rates instead of the yield to maturity as
a reinvestment rate.

b. You discount using the zero cpn curve instead of the YTM
Even more, you calibrate your forward rates so that the PV of yor
coupons match the market values.

2. For callable bonds and MBS, the YTM measure also assumes holding
till maturity which is obviously inaccurate so the OAS uses binomial
tree which takes into account the contingency of the future coupons.

The OAS is a constant spread to the whole discount curve you use
( e.g. treasury) which would result in a PV equal to the market price.

Continue reading "OAS measure of yield" »

June 7, 2005

Kay Giesecke Credit Modeller at Cornell OR

Kay Giesecke (of Cornell's School of Operations Research and Industrial Engineering)
research interests (Credit Risk, Default Correlation, Credit Derivatives, Systemic Risk)
match his research.

June 3, 2005

Handbook of Fixed Income Securities (Fabozzi)

The Handbook of Fixed Income Securities
Edited by Frank Fabozzi

Hardcover: 1500 pages
Publisher: McGraw-Hill; 7 edition (April 1, 2005)
ISBN: 0071440992

Part 1. Background.
1. Overview of the Types and Features of Fixed Income Securities.
2. Risks Associated with Investing in Fixed Income Securities.
3. A Review of the Time Value of Money.
4. Bond Pricing and Return Measures.
5. Measuring Interest Rate Risk.
6. The Sturcture of Interest Rates.
7. Bond Market Indexes.

Part 2. Government and Private Debt Obligations.
8. U.S. Treasury and Agency Securities.
9. Municipal Bonds.
10. Private Money Market Instruments.
11. Corporate Bonds.
12. Medium-Term Notes.
13. Inflation-Indexed Bonds (Tips).
14. Floating-Rate Securities.
15. Nonconvertible Preferred Stock.
16. International Bond Markets and Instruments.
17. Brady Bonds.
18. Stable Value Investments.

Part 3. Credit Analysis.
19. Credit Analysis for Corporate Bonds.
20. Credit Considerations in Evaluating High-yield Bonds.
21. Investing in 11 and Other Distressed Companies.
22. Guidelines in the Credit Analysis of General Obligation and Revenue Municipal Bonds.
23. High-Yield Analysis of Emerging Markets Debt.

Part 4. Mortgage-Backed and Asset-Backed Securities.
24. Mortgages and Overview of Mortgage-Backed Securities.
25. Mortgage Pass-Throughs.
26. Collateralized Mortgage Obligations.
27. Nonagency CMOs.
28. Commercial Mortgage-Backed Securities.
29. Securities Backed by Automobile Loans.
30. Securities Backed by Closed-End Home Equity Loans.
31. Securities Backed by Manufactured Housing Loans.
32. Securities Backed by Credit Card Receivables.

Part 5. Fixed Income Analytics and Modeling.
33. Characteristics of and Strategies with Callable Securities.
34. Valuation of Bonds with Embedded Options.
35. Valuation of CMOs.
36. Fixed Income Risk Modeling.
37. OAS and Effective Duration.
38. Evaluation Amortizing ABS. A Primer on Static Spread.

Part 6. Portfolio Management.
39. Bond Management. Past, Current, and Future.
40. The Active Decisions in the Selection of Passive Management and Performance Bogeys.
41. Managing Indexed and Enhanced Indexed Bond Portfolios.
42. Global Corporate Bond Portfolio Management.
43. Management of a High-Yield Bond Portfolio.
44. Bond Immunization. An Asset/Liability Optimization Strategy.
45. Dedicated Bond Portfolios.
46. Managing Market Risk Proactively at Long-Term Investment Funds.
47. Improving Insurance company Portfolio Returns.
48. International Bond Investing and Portfolio Management.
49. International Fixed Income Investing. Theory and Practice.

Part 7. Equity-Linked Securities and Their Valuation.
50. Convertible Securities and Their Investment Characterics.
51. Convertible Securities and Their Valuation.

Part 8. Derivative Instruments and Their Portfolio Management Applications.
52. Introduction to Interest-Rate Futures and Options Contracts.
53. Pricing Futures and Portfolio Applications.
54. Treasury Bond Futures Mechanics and Basis Valuation.
55. The Basics of Interest-Rate Options.
56. Controlling Interest Rate Risk and Futures and Options.
57. Interest-Rate Swaps.
58. Interest-Rate Caps and Floors and Compound Options.

June 2, 2005

Fixed Income Securities: Tools for Today's Markets (Tuckman)

Fixed Income Securities: Tools for Today's Markets,
Second Edition by Bruce Tuckman.

# Bond Prices, Discount Factors, and Arbitrage.
# Bond Prices, Spot Rates, and Forward Rates.
# Yield to Maturity.
# Generalizations and Curve Fitting.

# One-Factor Measures of Sensitivity.
# Measures of Price Sensitivity Based on Parallel Yield Shifts.
# Key Rate and Bucket Exposures.
# Regression-Based Hedging.

# The Science of Term Structure Models.
# The Short-Rate Process and the Shape of the Term Structure.
# The Art of Term Structure Models: Drift.
# The Art of Term Structure Models: Volatility and Distribution.
# Multi-Factor Term Structure Models.
# Trading with Term Structure Models.

# Repo.
# Forward Markets.
# Eurodollar and Fed Fund Futures.
# Interest Rate Swaps.
# Fixed Income Options.
# Note and Bond Futures.
# Mortgage-Backed Securities.

May 31, 2005

Derivatives Portal

Derivatives Portal risk and finance papers, journals, books, conferences.
More background than trade press touts.


May 18, 2005


financialbulls by JW O'Brien looks at financial engineering
and risk management in real life.

April 26, 2005

Residential Mortgage Termination and Severity, De Franco

Modeling Residential Mortgage Termination and Severity
Using Loan Level Data

Three essays on modeling residential mortgages.

Chapter 1 presents and estimates a new model of loss given
default using a new dataset of prime and subprime mortgages. The
model combines option theory proxies with information on the loan
contract and the cash flow position of the borrower. The results
suggest that severity on subprime and adjustable rate mortgages are
similar to losses on fixed rate prime loans, but that investor owned
properties have significantly higher losses than owner occupied
houses. The results also suggest systemic overappraisals on refinanced

Chapter 2 uses option pricing methodology to value the prepayment and
default options associated with a residential mortgage, if house
prices are mean reverting.

Numerical solutions compare the results from the mean reverting house
price model to the results from a model where house prices follow a
geometric Brownian motion process.

The main contributions are:

(1) the value of the implicit rent (service flow) is derived as a
function of the house price process instead of assumed to be constant,
as in prior research;

(2) the mean reverting model has additional factors that may help
forecast mortgage termination; and

(3) the house price process is shown to have a significant effect on
the value of a mortgage over a wide range of parameter values.

Chapter 3 presents a modeling framework for residential mortgages that
has separate models for each loan payment status (Current, 30 Days
Late, 60 Days Late, 90+ Days Late, in Foreclosure, in REO, or Paid
Off). It is shown that several classes of traditional mortgage
prepayment and default models are restricted forms of this model, and
that the restrictions are rejected empirically.

Continue reading "Residential Mortgage Termination and Severity, De Franco" »

April 24, 2005

Option-Theoretic Prepayment Model for Mortgages: Fabozzi , Kalotay and Yang

A new approach for modeling the prepayments of a mortgage pool
shows how to value mortgage pools and agency mortgage-backed
securities. A notion of refinancing efficiency describes the
full spectrum of refinancing behavior.

The approach has two distinguishing features:

(1) The primary focus is on understanding the market value of a
mortgage, in contrast with standard models that strive (often
unsuccessfully) to predict future cash flows, and

(2) we use two separate yield curves, one for discounting mortgage
cash flows and the other for MBS cash flows.

An Option-Theoretic Prepayment Model for Mortgages and Mortgage-
Backed Securities

To appear in International Journal of Theoretical and Applied Finance
Dec 2004, jrg 7, nr 8, december 2004, pages 949-978.

March 27, 2005

Riskmetrics journals

Riskmetrics journals and old (1999-2002) Working Papers.

March 7, 2005

FIASI ads Three New Hall-of-Famers

In 2003 November, the Fixed Income Analysts Society tipped its hat to
three leading lights in the fixed-income arena, inducting Frank J.
Fabozzi, Abner D. Goldstine and Oldrich A. Vasicek into its Hall of
Fame. The eighth annual awards ceremony recognized the trio for their
contributions to the advancement of fixed-income analysis and
portfolio management. Previous Hall of Famers include Martin
Leibowitz, Fischer Black, John C. Bogle and William H. Gross.

Fabozzi, of course, is a name on everyone’s lips. He single-handedly
created and stocked a library of books on fixed-income education
where nothing of the kind existed, helping school many thousands of
individuals in the theory and business of the debt markets. Goldstine
is an innovator in the creation of bond portfolios for investors.
Vasicek is a fixed-income modeler who opened up new avenues in
interest rate derivatives and credit modeling.

Nina Mehta, Financial Engineering News.