The Pricing of Options on Assets with Stochastic Volatilities

Authors

  • JOHN HULL,

  • ALAN WHITE

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    • Both authors from Faculty of Administrative Studies, York University. The authors would like to thank Phelim P. Boyle, Michael Brennan, Herbert Johnson, Stephen Ross, Eduardo Schwartz, and an anonymous referee for helpful comments on earlier drafts of this paper. This research was funded by the Financial Research Foundation of Canada.


ABSTRACT

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.

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