On Computational Finance

Wrong-Way Risk in CVA

2011-10-17T13:48:00.001+01:00

Counterpartyrisk

Itis a combination of credit risk (default of the counterparty) andmarket risk (uncertain potential value of the derivative contract atthe time point when a credit event happens). Counterparty risktypically arises from a broad class of financial products:

Over-The-Counter (non-exchange) derivatives, such as:

interest rate swaps and swaptions
foreign exchange (FX) forwards and options
credit default swaps

Securities financing transactions:
- repo and reverse repo agreements
- securities borrowing and lending

Credit Exposure

Theterm exposure defines the loss we incur in the event of acounterparty default. Exposure is characterized by the fact that apositive value of a financial instrument corresponds to a claim on adefaulted counterparty that we might lose, whereas in the case ofnegative value, when our counterparty defaults we will still have topay them back the amount.

PricingCounterparty Risk

Intuitivelythe risk-free price of a contract must be different from a risky(counterparty mightdefault) contract. The price of a riskyderivative could be thought as the risk-free price less thecomponentcorrecting for the counterparty risk:

P_risky = P_{risk free} − CVA

Thelatter component is called (Counterparty) Credit Valuation Adjustment(CVA).

Credit ValuationAdjustment

Saythat time T is the maturity of a derivative between aderivatives dealer and one of counterparties and v(t) is itsvalue at time t (this is usually non-deterministic if tis future time!). If we assume that v(t) is independent of thedefault time, then CVA can be expressed as:

where q(t) is the probability of default at time t andR is the % of contract value that can be recovered afterdefault. The max(v(t),0) accounts only for situations when thecounterparty owes us money, and is called exposure at time t.

Wrong-Way risk

Wrong-wayrisk is defined by International Swaps and Derivatives Association(ISDA) as the risk that occurs when “exposure to a counterparty isadversely correlated with the credit quality of that counterparty”.In short it arises when default risk and credit exposure increasetogether.

Saythat the derivative value v(t) is dependent on some underlyingasset value x(t,w), where w is a generated scenario.Then the CVA formulation with wrong way risk changes into:

where the two functions q and v have their randomcomponents (dW₁ and dW₂if driven by Brownian motions) correlated with some parameter \rho.The structure of q has quite some freedom depending on how wemodel the default probability. V is product-dependent and is asum of product values if we consider a portfolio.

LiteratureOverview:

I have skimmed through a list of papers and looked up available bookson the Wrong-Way Risk topic and related ones.

Jon Gregory book covers most of fundamental, financial issues,definitions, concepts related to CVA and wrong-way risk. D.Brigobooks cover in-depth the mathematical modelling parts with somesmaller sections on Monte Carlo simulation of those models. He alsodoes cover (in complicated manner, but in great depth) thecalibration problem of both interest-rates and credit models. Thereare some books I don't have access to yet and can just judge from thetable of contents such as Pykhtin book on Credit Risk Modelling.

The papers on wrong-way risk can be split into two categories:valuing CVA per product and CVA on portfolio level. The former ismainly covered by D.Brigo and the latter by mixed groups of academicsand finance professionals. While Brigo articles are again writtenwith depth (motivation, modelling, calibration, tests) other articleswere sketchy in parts (missing motivations for models, unclearcalibration). As my research will probably be regardingportfolio-level CVA, this might be a good opportunity. Except thepaper “Effective modelling of wrong way risk”, which is rathercomplicated, reasonably rigorous and uses multi-factor models formodelling credit and exposure dependence, the others mostly assumeGaussian distributions for both (hence correlating the two factorsbecomes trivial). In each of the papers, the authors made eitherreal-data or simulation based testing of Wrong-Way risk effects onCVA and CVA sensitivities, drawing practically the same (intuitive)conclusion that W-W risk matters a lot. Coming back to the “Effectivemodelling of wrong way risk” paper: this paper covered not only CVA& wrong way risk modelling with a linear multi-factor model, butalso gave some intuition how the model works together with the Baselregulatory requirements.

The general intuition is that there are rigorous models per product,but sketchy and not well tested ones in a portfolio setting. Authorsshow that Wrong-Way correlations have a strong effect on CVA, butdon't precisely show how well can these correlations be defined(which model is better, a linear, deterministic/ stochastic,pros/cons) and while they mention that using complicated model mightbe troublesome due to lack of data for calibration, nothing explicitis shown. On top of the above – none of the papers mentioncomputational issues, except some recommendations for usingQuasi-Monte-Carlo and importance sampling if this is feasible withinthe modelling framework.

Main literature:

Author	Paper/Book Title	Notes
Jon Gregory	Book: Counterparty credit risk	A full book on CCR, CVA and Wrong-Way risk, mostly verbal arguments with a couple of simplistic examples for modelling. (Taken from Yonita)
D.Brigo	Interest Rate Models; With Smile Inflation and Credit	Very in-depth book on credit and interest-rates modelling. Includes CVA. I have my own copy of the book.
D.Brigo	Credit Models and the Crisis	Correlations, Copula models; I don't have access to the book yet.
D.Brigo	Credit risk Frontiers	New (2011) book on Credit Modelling, CVA. Don't have access to it yet.
Michael Pykhtin	Book: Counterparty Credit Risk Modelling	A collection of papers related to regulatory and pricing issues regarding CVA and probably some parts on wrong-way risk (don't have access to it yet)
D. Brigo	Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting	Includes Wrong-way risk correlations, collateral management rules.
D. Brigo, I. Bakkar.	Accurate counterparty risk valuation for energy-commodities swaps. Energy Risk. March 2009 issue	CVA on Oil Commodity contracts + correlations
D. Brigo and M. Masetti.	Risk Neutral Pricing of Counterparty Risk. In: Pykhtin, M. (Editor), Counterparty Credit Risk Modelling: Risk Management, Pricing and Regulation.	CVA on Equity with correlations present covered
Damiano Brigo; Andrea Pallavicini	Counterparty risk and Contingent CDS valuation under correlation between interest-rates and default	CIR++ model for credit , calibration topic covered.
D. Brigo, A. Pallavicini and V. Papatheodorou	Bilateral counterparty risk valuation for Interest rate products: Impact of volatilities and correlations.	G2++ model for interest-rates; CVA for IR (vanilla & exotics) with correlations modelling (analytical formulas)
John Hull and Alan White	CVA and Wrong Way Risk	Simple model with numerical results, Greeks of CVA, effects on collateral and simulated empirical tests of wrong-way risk effect in different cases.
Juan Carlos, Juan Antonia, dan Rosen, David Saunders	Effective modelling of wrong way risk	Detailed paper on allocation methods for counterparty risk capital, Basel II requirements and ways of matching them (alpha multiplier, full wrong-way risk modelling and so on)
Christopher C. Finger	Toward a better estimation of wrong-way credit exposure	Old 1999 paper. Not reviewed yet.
Riverside Risk Advisers	Quantifying Right-Way and Wrong-Way Risk	Simple model with correlated Gaussians.
SunGard Adaptiv	Wrong-Way Risk	Introductory white paper on definitions, motivation.

Business Startup To Do List:

2010-01-19T13:48:00.000Z

Boosting Business With a Facebook Fan Page

ALGO TRADING page 3

2010-01-19T12:55:00.001Z

How to Learn Algorithmic Trading: Part 3

2010 January 12

by quantivity

Third in a series on learning quantitative / algorithmic trading, this post focuses on financial modeling and analysis, assuming understanding of financial mathematics from Part 2 and overview of quantitative trading from Part 1. After digesting these, readers should be capable of both building interesting systematic trading systems and understanding microstructure dynamics that drive modern market making (sell side) and large block trading (buy side).

Thanks to awwthor, quant.this, Josh Ulrich, Gappy, and Bjørn for their comments and recommendations on the original post. As with the preceding two posts, the following is intended to inform retail quantitative trading with a bias to equity, exchange-traded derivatives, and FX.
Begin with standard introductory financial time series asset dynamics, volatility, and forecast modeling:

Analysis of Financial Time Series, by Tsay: standard applied time series text for financial econometrics
Market Models: A Guide to Financial Data Analysis, by Alexander: excellent introduction to financial modeling and forecast
Asset Price Dynamics, Volatility, and Prediction, by Taylor: classic text on financial modeling and forecast

Proceed to modern portfolio theory and financial engineering:

Modern Portfolio Theory and Investment Analysis, by Elton et al.: standard text on modern portfolio theory
Options, Futures and Other Derivatives, by Hull: standard reference for introductory financial engineering
Active Portfolio Management, by Grinold & Kahn: standard introduction to quantitative portfolio management by the BGI guys who invented it
Principles of Financial Engineering, by Neftci: intermediate financial engineering

Continue on to volatility for options and correlation / dispersion for arb:

Volatility and Correlation, by Rebonato: excellent coverage of volatility and correlation
Volatility Trading, by Sinclair: volatility arbitrage by a retail practitioner
Volatility Surface, by Gatheral: theoretical coverage of vol models, by well-known researcher
Options as a Strategic Investment, by McMillan: classic introductory text on derivative hedging and volatility trading
Option Volatility & Pricing, by Natenberg: dated practitioner introduction to volatility trading

Finally, delve into high-frequency & market microstructure to enjoy foundations of modern buy and sell sides:

Trading and Exchanges: Market Microstructure for Practitioners, by Harris: practitioner introduction to stylized financial microstructure effects
An Introduction to High-Frequency Finance, by Dacorogna et al.: theoretical and dated practitioner introduction to HF, with emphasis on FX
Empirical Market Microstructure, by Hasbrouck: intermediate equity market microstructure, with coverage of standard theoretical models
Microstructure Approach to Exchange Rates, by Lyons: intermediate FX market microstructure, covering both theory and empirical models (bit dated)
Market Microstructure Theory, by O’Hara: classic introduction to microstructure theory; now dated
Optimal Trading Strategies, by Kissell and Glantz: practitioner introduction to market impact and optimal execution

From here, readers can happily delve into the journal literature.

Books to read

2010-01-19T12:54:00.000Z

Liar's Poker: Rising Through the Wreckage on Wall Street (Paperback)

http://www.amazon.com/gp/product/0140143459/102-5134678-4651360?n=283155

The Predictors: How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street (Paperback)

http://www.amazon.com/gp/product/0805057579/102-5134678-4651360?n=283155

ALGO TRADING page 2

2010-01-19T12:51:00.001Z

How to Learn Algorithmic Trading: Part 2

from Quantivity by quantivity

Excellent readership and thoughtful comments on the original How to Learn Algorithmic Trading have motivated two follow-up posts on learning quantitative / algorithmic trading (while retrospectively revising the original to improve consistency). This Part focuses on the cross-discipline foundations of financial mathematics, whose knowledge is generally assumed by practitioners and financial modeling literature. The subsequent, Part 3, focuses on modern financial modeling and analysis.
Depending on reader interest, this topic may warrant a future series of posts to delve into seminal literature in selected trading disciplines, such as suggested by etrading on the Penn-Lehman Automated Trading Project.

Thanks to awwthor, quant.this, Josh Ulrich, Gappy, and Bjørn for their comments and recommendations. As with the original post, the following is intended to inform retail quantitative trading with a bias to equity, exchange-traded derivatives, and FX.
To begin, start with solid theoretical econometrics, with emphasis on time series, and meet regression (assuming solid background in linear and matrix algebra):

Time Series Analysis, by Hamilton: classic text on time series econometrics
Econometric Analysis, by Greene: classic text on theoretical econometrics

Next, dive into filtering and wavelets and meet Fourier:

Wavelet Methods for Time Series Analysis, by Percival and Walden: standard theoretical text on wavelets
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, by Gençay, Selçuk, and Whitcher: applied filtering and wavelets for finance and economics

Explore modern statistical / machine learning and meet reinforcement and (un)supervision, descendant of original Turing / von Neumann “AI” tradition:

Artificial Intelligence: A Modern Approach, by Russell and Norvig: standard introduction to classic AI
The Elements of Statistical Learning, by Hastie, Tibshirani, and Friedman: standard intermediate statistical learning
Pattern Recognition and Machine Learning, by Bishop: intermediate classification and learning
Pattern Classification, by Duda: standard introductory classification

Review operations research and meet duality, with focus on mathematical optimization (not to be confused with computer science “programming”); thanks to Gappy, since my references pre-date many of these:

Linear and Nonlinear Programming, by Luenberger: standard introduction to optimization
Nonlinear Programming, by Bazaraa et al.: standard non-linear optimization
Convex Optimization, by Boyd and Vandenberghe: standard convex optimization (generalization of linear methods, including LP, OLS, etc.), including approximation, fitting, and estimation

Finally, for those interested in options and vol, review modern stochastic calculus and meet Itō (presuming working knowledge of measure theory and stochastic processes):

Financial Calculus, by Baxter and Rennie: pleasant intuitive introduction
Stochastic Calculus for Finance I, by Shreve: gentle introduction via binomial
Stochastic Calculus for Finance II, by Shreve: gentle continuous-time introduction

Continue on to Part 3 to dive into modern financial modeling and analysis.

Books list

2010-01-19T12:48:00.002Z

Trade Your Way to Financial Freedom, by Tharp: standard retail overview, ignoring the ridiculous title
Mathematics of Money Management, by Vince: standard retail introduction to money management
Intermarket Trading Strategies, by Katsanos: random mix of trading strategies
Advanced Trading Rules, by Acar and Satchell: survey of trading strategies
Applied Quantitative Methods for Trading and Investment, by Dunis et al: survey of trading strategies (including a hint of Burgess statarb)

NIPS*2009 Online Papers

2010-01-19T12:33:00.000Z

The papers below appear in Advances in Neural Information Processing Systems 22 edited by Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams and A. Culotta, (2009).

http://books.nips.cc/nips22.html

IMDB movie search and API:

2010-01-19T12:31:00.001Z

Power Tool:
http://www.imdb.com/list

Power API's
http://www.imdb.com/interfaces

A Decent List of Quant Trading Firms

2009-12-01T14:31:00.001Z

A Decent List of Quant Trading Firms

from Max Dama on Automated Trading by Max Dama

This could be useful for finding a job or just Googling out of curiousity. This is a secretive industry so it can be hard to tell which firms are important.

From Nuclear Phynance:

Banks -
Goldman Sachs
Morgan Stanley (PDT or ETL)
Barclays
Deutsche
JP Morgan

Hedge Funds -
Two Sigma
Millennium / World Quant
Renaissance
HBK
Citadel
IV Capital
Tower Research
Knight
Blue Crest
Winton Capital
GSA Capital
Etc.

Prop -
CTC (Chicago Trading Company)
Fox River Partners
Jump Trading
Spot Trading
GETCO
Sun Trading
Matlock Capital
Ronin Capital
Allston Trading
Chopper Trading
Tradelink
Etc.

It would be great to extend this list, please leave a comment with additions.

Excellent source of historical equity & forex data !!!!

2009-12-01T14:05:00.000Z

http://www.dukascopy.com/swiss/english/data_feed/csv_data_export/?ibref=1062

history back to 5 years !!!!

Muziic for LINUX !!!!

2009-10-19T16:53:00.002+01:00

Nice alternative from debian:
MiniTube:
http://flavio.tordini.org/minitube

Quant/Trader reading list

2009-10-08T00:22:00.002+01:00

Options, Futures and other Derivatives
by John C. Hull
Option & Volatility and Pricing
by Sheldon Natenberg
Inventing Money
by Nicolas Dunbar
When Genius Failed - Rise and Fall of LTCM
by Roger Lowenstein
Dynamic Hedging
by Nassim Nicolas Taleb
Fooled by Randomness
by Nassim Nicolas Taleb
Black Swan
by Nassim Nicolas Taleb
Bringing Down the House
by Ben Mezrich
Smartest Guys in the Room
by McLean
My Life As a Quant
Emanuel Derman
Liar's Poker
Michael Lewis
Visual Display of Quantitative Information
by Edward Tufte
The Pragmatic Programmer
by Andrew Hunt
Design Patterns
by Erich Gamma
The Mythical Manmonth
by Frederick P. Brooks
Refactoring
by Martin Fowler
Peopleware:Productive Projects and Teams
by Tom DeMarco
Microserf
by Douglas Coupland
Code
by G. W. Knows

Best Cities to work and live for Finance Professionals

2009-08-31T20:24:00.001+01:00

http://www.investopedia.com/articles/financialcareers/top-10-financial-career-cities.asp

Nice Overview of tax heavens

2009-08-31T20:12:00.002+01:00

http://www.investopedia.com/articles/tax/09/tax-havens.asp

Fix for Ubuntu Nvidia 9600GT bug

2009-07-30T19:10:00.001+01:00

Bug sound usually like "graphics adapter not sound", when gdm is loading, the screen is flashing several times and then xorg crashes, gives option to go for low resolution mode.

Solution:
It is probably a bug in gdm link.

To solve it add line GdmXserverTimeout=20 in /etc/gdm/gdm.conf to [daemon] section. You can also use other display manager, for example slim.

Fundamentals of Commodity Pricing

2009-07-30T10:48:00.003+01:00

General Ideas:
http://www.oxfordfutures.com/futures-education/futures-fundamentals/futures-fundamentals.htm
More on Commodity Spreads:
http://futures.tradingcharts.com/learning/commodity_spreads.html
Fundamental Analysis of Commodities market
http://commodities.about.com/od/researchcommodities/a/fundamental.htm
Nice Article on Oil pricing
http://seekingalpha.com/article/91920-oil-and-commodities-pricing-fundamentals-bubble-or-manipulation
Website with news on comodities, technicals and fundamentals
http://www.cfdtrading.com/category/oil-gold/oil-gold-fundamentals/

Website to look at:
http://seekingalpha.com/

Chicago Board of Trade:
http://www.cmegroup.com/

Book to search for:

Commodity Fundamentals: How To Trade the Precious Metals, Energy, Grain, and Tropical Commodity Markets (Wiley Trading) (Hardcover)

Auto Regressive models for Time series

2009-07-30T10:44:00.002+01:00

Ubuntu links to have a look at

2009-07-29T09:18:00.003+01:00

10 Things to do After Installing Ubuntu Linux

2009-07-29T09:17:00.000+01:00

http://ubuntulinuxhelp.com/10-things-to-do-after-installing-ubuntu-linux/

Top 25 Ubuntu programs

2009-07-29T09:16:00.001+01:00

http://www.examiner.com/x-18153-Knoxville-Technology-Examiner~y2009m7d26-Top-25Ubuntu-Programs

Ubuntu System Admin Class: Command Line Basics

2009-07-29T09:09:00.000+01:00

Read and learn it here

Tweak Your Ubuntu System With Ubuntu Tweak

2009-07-29T09:03:00.000+01:00

It is never easy to tweak your Ubuntu system unless you use some graphical tool like Ubuntu Tweak. It lets you tweak your system in an easy and safe way, otherwise you will have to play with configuration files and it could lead to system crash.

More here
It is currently supported in Gnome desktop environment only and provides you many useful desktop and system tweak options. You can easily tweak the hidden settings, cleanup the unneeded packages, install up-to-date versions of applications, and do much more with it. Lets explore how we can install and use it in Ubuntu.

How to watch online TV from US in europe

2009-07-28T20:43:00.001+01:00

http://lifehacker.com/5318593/ip-hider-accesses-hulu-other-us+only-content-from-outside-the-us

Superb info links for Wi-Fi hacking

2009-07-28T20:42:00.000+01:00

Awesome tutorials - will try some time :)

Stylish Free website builder (trial)

2009-07-28T20:41:00.000+01:00

http://testsite117.moonfruit.com/#

Matlab GPU programming

2009-07-28T17:54:00.002+01:00

After some googling to find useful tutorials on Matlab and CUDA programming i came up with a few nice links:

2009-07-28T17:53:00.001+01:00

From now on i'll try to make some use of my blog and post usefull things i discover for my own reference

World of Debt

2008-10-23T14:06:00.001+01:00

After watching Zeitgeist 2 (movie), i have decided to research more on the topic discussed.

A nice website to look at:
http://www.webofdebt.com