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Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Aug 20
CVA (credit value adjustment) is a hot topic, thanks to the financial crisis.  It is the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk. Check Wikipedia for its detail definition.

A paper "CVA and Wrong-Way Risk" by John Hull and Alan White published in the Financial Analysts Journal uses Monte Carlo simulation to demonstrate the CVA calculation via a simple model.
This paper proposes a simple model for incorporating wrong-way and right-way risk into CVA (credit value adjustment) calculations. These are the calculations, involving Monte Carlo simulation, made by a dealer to determine the reduction in the value of its derivatives portfolio because of the possibility of a counterparty default. The model assumes a relationship between the hazard rate of the counterparty and variables whose values can be generated as part of the Monte Carlo simulation. Numerical results for portfolios of 25 instruments dependent on five underlying market variables are presented. The paper finds that wrong-way and right-way risk have a significant effect on the Greek letters of CVA as well as on CVA itself. It also finds that the percentage effect depends on the collateral arrangements.

Article, Working paper.
Aug 16
A very nice paper by Knaup and Wagner (2012) published in Management Science. Enjoy it.

We propose a new method for measuring the quality of banks' credit portfolios. This method makes use of information embedded in bank share prices by exploiting differences in their sensitivity to credit default swap spreads of borrowers of varying quality. The method allows us to derive a credit risk indicator (CRI). This indicator represents the perceived share of high-risk exposures in a bank's portfolio and can be used as a risk weight for computing regulatory capital requirements. We estimate CRIs for the 150 largest U.S. bank holding companies. We find that their CRIs are able to forecast bank failures and share price performances during the crisis of 2007–2009, even after controlling for a variety of traditional asset quality and general risk proxies.

Article, Working paper
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Apr 24
There is a large debate on whether we should blame the Black Scholes model for the credit crisis, for example, Guardian publishes an article "The mathematical equation that caused the banks to crash" discussing the issue that the Black-Scholes equation was the mathematical justification for the trading that plunged the world's banks into catastrophe.

Should we? I don't think so, the black scholes is just a weapon, it is the person who use it improperly should be blamed instead. This infographic is a simple defense of the Black Scholes model.
a defense of black scholes model
Mar 30
This article is a guest post by Dr Timothy Johnson.

In the aftermath of the Credit Crisis it became popular to blame quants and mathematics for the Credit Crisis. In November, 2008, a former French prime minister, Michel Rocard, wrote in Le Monde that “mathematicians are guilty (unwittingly) of crimes against humanity”. More seriously, the following March, the UK’s financial regulator, the Financial Services Authority published the Turner Review on the causes and cures of the crisis where it identified one of the causes as a “misplaced reliance in sophisticated mathematics”. Wired wrote about The Formula That Killed Wall Street and the FT followed up on the Wired report.

As the dust settled, The Financial Crisis Inquiry Comission Report gave a more thoughtful analysis. They mentioned maths and quants, but only in passing. Their conclusion was that there had been a “systemic breakdown in accountability and ethics”, which had resulted in lax regulation and excessive borrowing.

In one respect the FCIC conclusions are positive for mathematicians, the Crisis wasn’t their fault. On the other hand, if the problems were rooted in ethics, then surely maths has no role in preventing future Crisis. Maths is just another tool, like a spread sheet or double entry bookkeeping. This is pretty depressing for the heirs of Newton, Euler, Riemann, Poincaré and Kolmogorov.

The mathematical study of probability is usually thought to have begun in the mid-sixteenth century, with Cardano’s Liber de Ludo Alea (‘Book on Games of Chance’), where there is the first explicit statement that the chance of rolling a six on a fair dice is 1 in 6. Shortly after making this statement, Cardano makes the perceptive observation that
These facts contribute a great deal to understanding but hardly anything to practical play.1

Cardano’s work was ignored for centuries, the problem was, despite Cardano’s status as a mathematician, his ‘Book on Games of Chance’ didn’t fit in to what modern mathematicians regard as proper mathematics. The fact is that Cardano did not see his work on probability as principally a mathematical work, but as an investigation of the ethics of gambling, a point made recently by the mathematician David Bellhouse2.
Feb 28
Dr. Donald R. van Deventer is the Chairman and Chief Executive Officer of Kamakura Corporation, the world's leading provider of risk management solutions. His primary financial consulting and research interests involve the practical application of leading Kamakura Corporationedge financial theory to solve critical financial risk management problems. He was elected to the 50 member RISK Magazine Hall of Fame in 2002. Dr. Donald R. van Deventer has served on the editorial board of the Journal of Credit Risk since 2005, and has written numerous papers and several books covering a wide range of risk management.  

Tell us a little background info about yourself. Where are you from? What’s your education background?

I grew up in Los Angeles and was a double major at Occidental College in mathematics and economics.  I went to Harvard University and earned my Ph.D. in business economics in 1977.  The business economics program is a joint program of the Department of Economics and the Harvard Business School.

You had worked for a few financial institutions before founding your own company, what are the advantage and disadvantage of working in a risk solution provider over in the risk management group of a big financial firm, especially for a junior?

If one has the chance to work for a very innovative firm like Kamakura, there’s the challenge and the pleasure of making the state of the art better every day.  Within large financial institutions, a junior risk analyst is often trapped using an old fashioned legacy risk system purchased years before from a mediocre vendor.  That’s bad for one’s career for two reasons.  First, you don’t learn state of the art risk management and you run the risk of turning into a risk dinosaur at a young age. Second, if the firm is not using best practice risk management, the odds of failure are high even at a large bank as we’ve seen in the last five years.

A lot of people blame Copula or Black-Scholes formula for the current financial crisis, what’s your opinion on this debate?

My partner Prof. Robert Jarrow has a nice paper on the misuse of financial models and a video on the front page of the Kamakura web site www.kamakuraco.com on exactly this topic.  Black and Scholes certainly shouldn’t be blamed if an analyst uses the Black model (which assumes interest rates are constant) to price interest rate options.  The incorrect usage of financial models is astonishingly widespread.
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