Pricing and hedging options with GARCH-stable proxy volatilities

Sharif Mozumder, M. Humayun Kabir and Michael Dempsey

Applied Economics, 2018, vol. 50, issue 56, 6034-6046

Abstract: This article considers modelling nonnormality in return with stable Paretian (SP) innovations in generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) volatility dynamics. The forecasted volatilities from these dynamics have been used as a proxy to the volatility parameter of the Black–Scholes (BS) model. The performance of these proxy-BS models has been compared with the performance of the BS model of constant volatility. Using a cross section of S&P500 options data, we find that EGARCH volatility forecast with SP innovations is an excellent proxy to BS constant volatility in terms of pricing. We find improved performance of hedging for an illustrative option portfolio. We also find better performance of spectral risk measure (SRM) than value-at-risk (VaR) and expected shortfall (ES) in estimating option portfolio risk in case of the proxy-BS models under SP innovations.Abbreviation: generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH)

Date: 2018
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DOI: 10.1080/00036846.2018.1488057

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