The pricing of options on assets with stochastic volatilities. (English) Zbl 1126.91369

Hull, John; White, Alan

Shephard, Neil (ed.), Stochastic volatility. Selected readings. Oxford: Oxford University Press (ISBN 0-19-925720-5/pbk; 0-19-925719-1/hbk). Advanced Texts in Econometrics, 109-129 (2005).

Summary: One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.
For the entire collection see [Zbl 1076.60005].

MSC:

91G20

Derivative securities (option pricing, hedging, etc.)

Keywords:

European call; series form; numerical solutions; Black-Scholes price