Option pricing under stochastic volatility for S & P 500 FTSE 100 index options

• Main Author: Lin, Nicole Yueh-Neng
• Published: University of Manchester 1999
• Subjects: 332.63
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.632541

This thesis examines option pricing under stochastic volatility for S&P 500 and FTSE 100 index options. The main contributions of the thesis are: (i) it provides empirical evidence of stochastic volatility in S&P 500 and FTSE 100 index returns; (ii) it explains empirically the impact of stochastic volatility on option pricing for index options; (iii) it tests whether option prices are consistent with the time series properties of the underlying asset price; and (iv) it investigates the magnitude and sign of volatility risk premlums. The empirical evidence shows that changes in S&P 500 and FTSE 100 index prices have distributions with fatter tails than the normal distribution and non-zero skewness. This leads to a consideration of non-normal distributions and possible explanations for deviations from normality. Of the possible explanations for the documented leptokurtosis in stock returns, stochastic volatility is generally regarded as the most likely candidate. The GARCH( 1,1 LTX model is shown to capture the volatile nature of our data well. A diffusion limit of the GARCH(1, 1 L TX process is the mean-reverting square root volatility process used in Heston's (1993) option pricing formula. This research considers Heston's (1993) stochastic volatility (SV) option pricing model as the empirical challenger to the Black-Scholes (BS) model, which assumes that the distribution of stock price changes is normally distributed with constant volatility. Insample pricing, out-of-sample forecasting, diagnosis of implied volatility curves, and internal consistency with the time series of implied volatilities and with the GARCH( 1,1 L TX process are examined to investigate the performance of the BS and SV models. We also conduct careful and detailed data screening for our empirical work. Our results reveal significant evidence of stochastic volatility implicit in option prices, and suggest that this phenomenon is essential to improving the performance of the BS model for index options. Nevertheless, internal consistency test results report inconsistency of both the BS and SV models with time-series data, indicating residual SV model misspecification for SPX and FTSE-I00 options. This has the important implication that stochastic volatility is a significant factor in option pricing but not the only factor affecting stock index option prices. Option pricing under stochastic volatility involves a preference issue since volatility is a nontraded asset. This research assumes that the volatility risk premium is proportional to the spot volatility level, which is internalised in the risk-neutral parameters. The actual volatility parameters can be recovered either from the time series of implied volatilities using option prices or from the GARCH( 1,1 L TX process using index returns. By comparing actual parameters with their risk-neutral counterparts, an estimate of the unit volatility risk premium can be thus obtained. Negative premiums for volatility risk are consistently observed in the SPX option market while there are mixed results for the S&P 500 index, FTSE 100 index and options markets. Nevertheless, the magnitudes of these estimates indicate that compensation for volatility risk is a significant component of the risk premiums in the S&P 500 and FTSE 100 index and option markets. However, the possibility of misspecification in the SV and GARCH(I,ILTX models should be kept in mind when explaining the magnitude and sign of risk premiums.