118 Frequently Asked Questions In Quantitative Finance
wrong than other assumptions you are making, such as
what future volatility will be.
Of course, the definition of closed form is to some
extent in the eye of the beholder. If an option can be
priced in terms of an infinite sum of hypergeometric
functions does that count? Some Asian options can be
priced that way. Or what about a closed form involving
a subtle integration in the complex plane that must
ultimately be done numerically? That is the Heston
stochastic volatility model.
If closed form is so appreciated, is it worth spending
much time seeking them out? Probably not. There are
always new products being invented and new pricing
models being devised, but they are unlikely to be of
the simple type that can be solved explicitly. Chances
are that either you will have to solve these numerically,
or approximate them by something not too dissimilar.
Approximations such as Black ’76 are probably your
best chance of finding closed-form solutions for new
products these days.
References and Further Reading
Black F 1976 The pricing of commodity contracts.Journal of
Financial Economics 3 167–79
Haug, EG 2003 Know your weapon, Parts 1 and 2.Wilmott
magazine, May and July
Haug, EG 2006The complete Guide to Option Pricing Formulas.
McGraw-Hill
Lewis, A 2000Option Valuation under Stochastic Volatility.
Finance Press
