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Seoul Journal of Economics
[ Article ]
Seoul Journal of Economics - Vol. 15, No. 4, pp.499-528
ISSN: 1225-0279 (Print)
Print publication date 30 Nov 2002
Received 02 Sep 2002 Revised 20 Oct 2003

Pricing Call Options under Stochastic Volatilities

Chang Mo Ahn ; D. Chinhyung Cho
Professor, College of Business Administration, Sejong University, 98 Kunja-Dong, Kwangjin-Ku, Seoul, 143-747, Korea, Tel: +82-2-3408-3166 cmahn@sejong.ac.kr
Professor, College of Business Administration, Sejong University, 98 Kunja-Dong, Kwangjin-Ku, Seoul, 143-179, Korea, Tel: +82-2-3408-3171 david@sejong.ac.kr

JEL Classification: G12

Abstract

This paper derives a closed-form solution for the European call option price when the volatility of the underlying stock returns is governed by a diffusion process. The model uses the continuity property of a diffusion process and the martingale approach to valuation of assets under no arbitrage. The pricing formula differs from the Black-Scholes formula in that it needs a volatility adjustment. The volatility movement is allowed to be contemporaneously correlated with the stock price movement.

Keywords:

Continuity, Diffusion, Martingale, No arbitrage, Stochastic volatilities

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