9 books and some lectures

I was recently invited to give a talk to postgraduate Masters and PhD students in Computational Finance and Machine Learning at both King’s College and University College at the University of London. The students asked if there were any books and lectures that I could recommend to those aspiring to have a career in risk management. While there are many excellent sources of information, I think the following 9 books should provide a good background. I could not have afforded some of these when I was a student living on the minimum wage and so suggest looking for them in your library first. Also some second hand bookshops are very reasonably priced and former students may be willing to give away their books freely. I have also included my thoughts on some lectures and articles I have found useful. Anyone should feel free to add a book that made the light bulb go on for them, to help the students currently working to get on the job ladder.

Some lectures: I have attended several external presentations. I am not convinced that they are always value for money. I think the articles in the Financial Times, New York Times and Wall Street Journal are of much greater value. Some of the talks that helped me think through issues early in my career, even where I might have disagreed, are as follows. Though I don’t know if these are still available on the internet, they are worth searching for. 

Structuring, Pricing and Hedging Complicated Barrier Options (Pricing and hedging Exotic options) - Vadim Linetsky 

I found this to be an interesting presentation, but that is probably due to the mathematical bias. A barrier option's delta is discontinuous at the barrier, thus creating hedging problems. To hedge barrier options, dealers usually establish positions in a series of standard vanilla options which provide a good hedge for a wide range of underlying prices. However, when the underlying nears the barrier level, these static hedges need to be rebalanced, which results in a flurry of trading activity in vanilla options. This, in turn, results in further trading activity in the underlying asset as dealers who sold vanilla options to hedgers of knock-out options need to dynamically hedge their exposure. This increases market volatility around popular barrier levels and increases the cost of hedging barrier options.

A good example of the problems created by the discrete nature of barrier options was given: a group of hedge funds purchased from a well-known broker-dealer and other dealers $500 million of barrier (up-and-in) puts on Venezuelan bonds with strike of 45 cents on the dollar. In order for the puts to be activated, underlying bonds should have traded above the barrier set at 51 cents at some time prior to the puts' maturity. An obvious conflict of interest between the counterparties, the funds who needed to drive the prices higher to trigger the barrier and the dealers who needed the prices to stay below the barrier to avoid the liability, resulted in a fierce battle to control Venezuelan bond prices. At one point during the crash, the screen flashed a “bid” price of 51 1/8, indicating a willing buyer at that price. Shortly afterwards, however, Euro Brokers flashed “error” on its screens, negating that particular transaction. At that point, whether or not the knock-in options had been triggered was academic: the puts' 45 exercise price was far below the market, meaning that they could not be exercised at a profit. A few days later, however, it mattered a great deal: Mexico devalued its peso, torpedoing emerging-market bonds. A short while later, Venezuelan par bonds had plunged 24% to about 38.75 cents on the dollar. Suddenly the knock-ins were potentially very valuable, if they had, in fact, been activated. But had they? This was a subject of debate. The main broker-dealer vehemently disagreed. The 51 1/8 bid that had flickered on the screen “was one of two things: Either someone made a mistake, or it was an attempt at manipulation”, according to the Wall Street Journal.

Motivated by risk management problems with barriers, Vadim introduces a family of path-dependent options: step options, parametrised by a finite knock-out/in rate, r. For a down-and-out step option, its payoff at expiration is the payoff of an otherwise identical vanilla option discounted by a so-called knock-out factor exp(-rT), where T is the total time during the life of the contract the price of the underlying is lower than the specified barrier level.

Selecting Optimum Interest Rate Pricing Models for Particular Products and Applications - Farshid Jamshidian

Prior to attending this presentation, I had read a couple of papers by Jamshidian, who has a very methodical rigorous approach and a Harvard mathematics Ph.D to boot. He struck me as a very authoritative speaker who understood his subject very well but gave the impression he suffered from little contact with practitioners. His basic premise was that a different approach is required to the no-arbitrage condition to understand LIBOR and swap markets as compared to, say, traditional term structure models such as Vasicek, CIR, BDT, HJM: neither the risk-neutral measure nor the instantaneous interest rate play a significant role. He introduces a so-called “Market Model”; see Jamshidian, 1997, Finance and Stochastics 1, pp 293-330. 

Effective Use of Correlation and Instantaneous Volatility for Exotic Interest Rate Derivatives - Ricardo Rebonato

Discussion centered on the limitations of simple two factor interest rate models. He said that empirical correlations between forward rates and the relative prices of caps and swaptions both imply a downward sloping correlation curve - perhaps a decaying exponential would be a good approximation. He then showed that you can't achieve this form with less than about 5 factors. 2 factors imply a flat correlation curve at the origin. If you're pricing correlation dependent structures a 2 factor is not likely to be very good (although much better than 1 factor of course). In practice we try to use a model of the spread or whatever; what do we do? A 5 factor is of course not a realistic option. He had a very neat idea - consider principal components as a Fourier series.

Forecasting Volatility and Correlation using Econometrics and Recursive Partitioning with Application to Index Enhancement and Portfolio Rebalancing - Brian Bielinski

A good speaker though I still don't know what a recursive partitioning is after this talk. He and the audience got a little entangled by some statistical questions and I wondered whether the process being presented might have been a little mechanical. Focus was on equity portfolios and main points were:

GARCH volatility - pretty good estimate of volatility, can incorporate mean reversion.

GARCH skew - can estimate distributions of underlying assets in future.

His conclusion was - Use a statistical estimator to estimate volatility but use GARCH to forecast. I was three months into my first risk management job and was thinking what would you use a volatility estimate for except as implied volatility i.e. a forecast? 

New Research: Asset Allocation with Derivatives - Prof Dilip Madan

Lots of economics jargon and many acronyms and pedagogical in parts. The basic idea revolves around explaining the positions taken in derivative securities and their underlying assets using optimal wealth profiles and “proprietary: probability density functions: not really my area but many in the audience showed much interest. 

A New Class of (Almost) Positive Interest Rate Models - Sunil Gandhi

A somewhat misleading title: not really any recent developments in the talk. A review of simple ideas about risk and (more interestingly) some heuristic approaches to modelling abnormal-ish aspects such as fat tails. No breakthroughs or anything mind-blowing; although I agree with the assertion that simple models should be used wherever possible, and that naive estimates of historic parameters, when used carefully, are not significantly worse than “best” estimates. 

A Unified Theory of Volatility - Bruno Dupire

Dupire is a giant in the industry. The nineteenth time he had presented this material, apparently. It is good stuff, especially to see how one can move from the implied volatility surface (vols for options of strike K and maturity T), to the local volatility surface (vols for (limiting) calendar spreads with strike K and maturities T and T+ dT). This represents the continuous time analogue to building trees with the vol at each node being a function of underlying and time at each node chosen such that the prices of all options match the market. One can in theory lock-in these local or “instantaneous forward” vols by the appropriate trade in calendar and butterfly spreads. There is an associated stochastic volatility model in which this vol structure is embedded. Straightforward pictures can be drawn, showing the sensitivities of options positions to changes in the vol surface. The theory is elegant, but of limited practical use since we need to take many second derivatives of smoothed surfaces. 

Applying Alternative Mathematical Analysis for Measuring Forecasting and Hedging Correlation Risk - Vincent Gesser

An academic talk that revealed one of the standard flaws of much of academic finance: claims for one or another model based on retrospective fitting to limited data. The empirical phenomena studied is well known enough: the vol skew for options (such that OTM puts are overpriced relative to OTM calls). As an academic exercise, fitting models to data and seeing if they replicate aspects of the data is OK; however, from a practical viewpoint few are going to adopt a model as being better in any predictive sense based on such an approach. Vincent gave retrospective explanations about how one could have traded using such models – though he pointed that this scheme would have resulted in over 50% of capital being wiped out on four or five occasions. He then used historically generated parameters to value options by several methods (not including whole yield curve methods as far as I could make out) and found that they were all different from the market values (based on implied vol). He then said that the least different values were the best models.

Derivative Price Modelling - David Murphy

Probably among the best talks. Entertaining and relevant: main emphasis on how modelling techniques can be badly misused. He made cases (some more convincing than others) against previous uses of genetic algorithms, neural networks, and chaos theory in finance. It certainly seems true that people attempt to adopt such technologies simply because they think others are, without realizing the flaws, or, as I had thought back then, simply the nonsensical nature of what they are doing: e.g. building a model with more parameters/neurones/etc than data points. Such a model just stores the data. He described a method of valuing American structures by Monte Carlo. If you value an American option by Monte Carlo at each point assuming that the rest of the path is known (perfect foresight) you get an upper bound. For a given time T-1 stock price, he lets the expected time T option value be the average of time T option prices corresponding to a number of neighbouring stock prices. This gives a better upper bound that appears to converge very quickly. He claims that it works in more dimensions (i.e. for more complex problems, e.g. American call on the maximum of two stocks) and is much quicker than other (PDE or lattice) methods. The hard part is the choice of neighbourhood.