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The Pricing of Options on Assets with Stochastic Volatilities
Author(s) -
HULL JOHN,
WHITE ALAN
Publication year - 1987
Publication title -
the journal of finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 18.151
H-Index - 299
eISSN - 1540-6261
pISSN - 0022-1082
DOI - 10.1111/j.1540-6261.1987.tb02568.x
Subject(s) - stochastic volatility , call option , economics , stock price , volatility (finance) , implied volatility , valuation of options , financial economics , black–scholes model , econometrics , volatility smile , strike price , series (stratigraphy) , paleontology , biology
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.