Risk Latte - Napoleon on Wall Street: Advent of the Stochastic Volatility Models

Napoleon on Wall Street: Advent of the Stochastic Volatility Models

Rahul Bhattacharya
August 20, 2012

They say in Finance the road from academia or a university to the trading desk of a bank is quite short. Within a couple of years any breakthrough research in quantitative finance within a university gets translated onto a viable financial product or an ingredient in manufacturing of that product. In 1993, Steven Heston of Yale University published his seminal paper on Stochastic Volatility. However, in this case, this piece of mathematics had to wait a decade before Napoleon could re-introduce it to the world.

In 2002, Goldman Sachs introduced the Napoleon options, a kind of reverse cliquet options. To the best of our knowledge, the product was developed by Goldman's team in the City of London and was first introduced to the institutional investors in Europe. Of course, very soon, a lot of large banks in the City had come out with similar structures as the Napoleon option. It is rumored that the payoff of the product resembled the hat of Emperor Napoleon and hence the quants who came up with the product named it Napoleon options.

In latter part of 2002, Goldman Sachs won practically every singletrade. This baffled many market observers, most of all the salespersons within Goldman. Quite soon, however, the bank realized that it had screwed up its quantitative models using which the product was priced.By early 2003 the bank was sitting on large positions in the volatility market and it tried very hard to hedge out its positions.

In short, it seems that Goldman's model had heavily underpriced the Napoleon options and hence there were lots of takers for the product. Some trader or investor somewhere, possibly on the buy side, as is always the case, was smarter than the quant on the sell side who was manufacturing the product. Of course, the full extent of Goldman’s woes was never ever known and most traders and quants in the City were unaware of the extent to which the volatility pricing model had broken down.

Between 2002 and 2004 the market for the reverse cliquets heated up in Europe and trading in this class of product amongst large banks in the City, especially the French banks, and the institutional investors rose significantly. Napoleon option was at the centre of many large reverse cliquet deals and many European dealers started quoting the price of these products in the market. By 2004, however, cracks had started appearing and many dealers realized that they had substantially misjudged the risks associated with reverse cliquets in general and Napoleon options in particular. The dramatic decline in short term equity volatility in 2003 from 40% to 15% startedhurtingthose traders who had failed to fully factor in hedging costs in trades that were written in 2002 and 2003. Yet, despite this many large European banks and derivatives houses such as NIBC Petercam Derivatives, BNP Paribas, SocieteGenerale and Credit Suisse First Boston kept on aggressively trading in reverse cliquets and Napoleon options.

In the meantime, Goldman Sachs kept on unwinding positions starting middle of 2003. The bank had finally realized that it not accurately factored in the costs of hedging the volatility of volatility (vvol) in Napoleon option products.

Introduction of the Napoleon option by Goldman Sachs and its subsequent realization that the quantitative models it had used to price the product led, for the first time, to the thinking by most quants on the trading desks on both sides of the Atlantic that something was missing as far as the volatility models that were being used in pricing financial derivatives were concerned. Even though stochastic volatility model was introduced by Hull and White in late 1980s and Heston’s seminal paper on stochastic volatility had come out in 1993, and a few banks had toyed with the idea, it wasn’t until the occurrence of this mis-pricing episode of the Napoleon options in 2002 that practitioners really took the stochastic volatility model seriously.

Napoleon was the first to illustrate that "local volatility" models and some other models such as the "independent increment technique" were inaccurate to value financial products which depended on forward (volatility) skews and in more ways than one, this product was responsible for formally introducing the "stochastic volatility" models on the Street.

Further Reading
Reverse cliquets: end of the road, Christopher Jeffery, Risk.net, 2004
The Volatility Surface, Jim Gatheral, John Wiley & Sons, 2006

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