article Open AccessTop 1% cited
The Pricing of Options on Assets with Stochastic Volatilities
The Journal of Finance · 1987 · Vol. 42(2) · pp. 281–300
John Hull✉Alan White(Wild Sheep Foundation)
Abstract
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.
Stochastic processes and financial applicationsFinancial Markets and Investment StrategiesCapital Investment and Risk AnalysisStochastic volatilityCall optionEconomicsStock priceVolatility (finance)Implied volatilityValuation of optionsFinancial economicsBlack–Scholes modelEconometrics
Citations
3,855
FWCI
25.25
field-weighted impact
References
14
Percentile
100%
vs. same field & year
Citations per year
Cited by
Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models
The Review of Economic Studies · 1998 · 2,310 citations
Variance Risk Premiums
Review of Financial Studies · 2008 · 1,381 citations
Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2001 · 1,876 citations
Measuring and Testing the Impact of News on Volatility
The Journal of Finance · 1993 · 3,678 citations
Stock Price Distributions with Stochastic Volatility: An Analytic Approach
Review of Financial Studies · 1991 · 1,547 citations
Delta-Hedged Gains and the Negative Market Volatility Risk Premium
Review of Financial Studies · 2003 · 987 citations
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
Review of Financial Studies · 1993 · 9,005 citations
Pricing Interest-Rate-Derivative Securities
Review of Financial Studies · 1990 · 2,232 citations
References
The valuation of options for alternative stochastic processes
Journal of Financial Economics · 1976 · 3,020 citations
The Pricing of Options and Corporate Liabilities
Journal of Political Economy · 1973 · 29,215 citations
Option pricing when underlying stock returns are discontinuous
Journal of Financial Economics · 1976 · 6,048 citations
Related articles
The Pricing of Options on Assets with Stochastic Volatilities
The Journal of Finance · 1987 · 3,855 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.