Next Article in Journal
Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
Next Article in Special Issue
Change Point Estimation in Panel Data without Boundary Issue
Previous Article in Journal
Compositions of Conditional Risk Measures and Solvency Capital
Previous Article in Special Issue
Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models
Article Menu

Export Article

Open AccessArticle
Risks 2016, 4(4), 51;

Bayesian Option Pricing Framework with Stochastic Volatility for FX Data

Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
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
Full-Text   |   PDF [554 KB, uploaded 16 December 2016]   |  


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)

Figure 1

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).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top