Pricing gold options under Markov-modulated jump-diffusion processes

Abstract

In this study, we empirically investigate the properties of gold returns, and the European gold options are priced when the underlying gold price dynamics are driven by Markov-modulated jump-diffusion processes. Specifically, the jump events are captured by a compound Poisson process with a log-normal jump size, and the regime-switching intensity rate is governed by a continuous-time finite-state Markov chain. Under an incomplete market setting, we study the valuation of European gold options using the method of Esscher transform. The estimated results and numerical examples are provided.

Keywords:

• gold price
• European gold option
• Markov-modulated jump-diffusion process
• Esscher transform

JEL Classification:

• C51
• G12

Notes

¹  The tested data are from Datastream and cover the period from 4 January 2005 to 31 December 2010.

²  The option data are from Bloomberg. These data correspond to the gold prices and cover the period between 24 January 2011 and 15 April 2011 (expiration date). There are a total of 60 observations for each call option contract.