Pricing Ftse 100 Index Options Under Stochastic Volatility
Lancaster University Management School, Department of Accounting and Finance Working Paper No. 99/018
30 Pages Posted: 9 Dec 1999
Results from the ARCH/GARCH literature and studies of implied volatility clearly show that volatility changes over time. This paper investigates the improvement in pricing of FTSE 100 index options from taking into account stochastic volatility. The major tool for this analysis is Heston?s (1993) stochastic volatility option pricing formula, which allows for systematic volatility risk and arbitrary correlation between underlying returns and volatility. The relation between actual and implied volatilities is also investigated using the approach of Bates (1996). The results reveal significant evidence of stochastic volatility implicit in option prices, suggesting that this phenomenon is essential to improving the performance of the Black-Scholes model for FTSE 100 index options. Given the assumption that the volatility risk premium is proportional to the spot volatility level, the compensation for volatility risk, in absolute terms, is significant. However, from the standpoint of internal consistency, the study finds that the estimated volatility of the time series of implied instantaneous variances is less than the variability of variance implicit in index option contracts. This indicates the presence of residual model misspecification.
JEL Classification: C32, G13
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