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Risks 2016, 4(4), 51; doi:10.3390/risks4040051

Bayesian Option Pricing Framework with Stochastic Volatility for FX Data

1
Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
2
Discipline of Business Analytics, The University of Sydney, NSW 2006, Australia
*
Author to whom correspondence should be addressed.
Academic Editor: Qihe Tang
Received: 31 August 2016 / Revised: 3 December 2016 / Accepted: 9 December 2016 / Published: 16 December 2016
View Full-Text   |   Download PDF [554 KB, uploaded 16 December 2016]   |  

Abstract

The application of stochastic volatility (SV) models in the option pricing literature usually assumes that the market has sufficient option data to calibrate the model’s risk-neutral parameters. When option data are insufficient or unavailable, market practitioners must estimate the model from the historical returns of the underlying asset and then transform the resulting model into its risk-neutral equivalent. However, the likelihood function of an SV model can only be expressed in a high-dimensional integration, which makes the estimation a highly challenging task. The Bayesian approach has been the classical way to estimate SV models under the data-generating (physical) probability measure, but the transformation from the estimated physical dynamic into its risk-neutral counterpart has not been addressed. Inspired by the generalized autoregressive conditional heteroskedasticity (GARCH) option pricing approach by Duan in 1995, we propose an SV model that enables us to simultaneously and conveniently perform Bayesian inference and transformation into risk-neutral dynamics. Our model relaxes the normality assumption on innovations of both return and volatility processes, and our empirical study shows that the estimated option prices generate realistic implied volatility smile shapes. In addition, the volatility premium is almost flat across strike prices, so adding a few option data to the historical time series of the underlying asset can greatly improve the estimation of option prices. View Full-Text
Keywords: option pricing; volatility smile; Student-t; variance gamma; Markov chain Monte Carlo (MCMC) option pricing; volatility smile; Student-t; variance gamma; Markov chain Monte Carlo (MCMC)
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, Y.; Choy, S.T.B.; Wong, H.Y. Bayesian Option Pricing Framework with Stochastic Volatility for FX Data. Risks 2016, 4, 51.

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