This month sees the 30th anniversary of the Black-Scholes model, published originally in the Journal of Political Economy. Developed by Robert Merton and Myron Scholes in collaboration with Fischer Black, its importance and impact on the financial markets has been tremendous and it has formed the basis for most derivatives-pricing systems.However, it is now time to move on from the Black-Scholes approach to pricing options.
Otherwise, there is a danger that the model's numerous acknowledged limitations will fatally harm the very markets it played such a important role in developing.
The professional market has long been aware of the problems with Black-Scholes and its derivations, particularly when pricing non-vanilla options.
However, these models, collectively referred to as Black-Scholes pricing, continue to underpin most option systems.
A big flaw is their assumption that everything but the spot rate of the underlying product is constant through the life of the option, which is evidently not true, as volatility, such as interest and dividend rates, can change frequently.
Black-Scholes also ignores important transaction costs, such as crossing the bid/offer spread when re-hedging, as well as the different natures of liquid versus illiquid markets.
Over the past 30 years as liquidity improved in options markets, it became abundantly clear that Black-Scholes prices often differ substantially from the market price. At best, the Black-Scholes price, known as theoretical value, can only be considered as a good approximation of the true market price.
There is often a large discrepancy between theoretical value and the market price, including for standard vanilla options. Looking specifically at foreign exchange, this can be as much as 0.5% even in liquid currency pairs such as dollar/yen. For every $10m ([euro]8.5m) traded - a modest amount in the interbank market - a portfolio's value could be out by $50,000.
The problem is worse in emerging market currencies, where the hedging of exposure is probably more important. The discrepancy between theoretical value and the market price in these currencies can be as much as 2%.
Not surprisingly, greater problems can occur when pricing exotic options. One reason is that unlike with vanilla options, it is not possible to adjust the Black-Scholes price through the volatility input; other risk aspects of the option have to be taken into consideration.
In short, users of systems reliant on a Black-Scholes type model cannot be sure they are consistently producing the true market value. …