PT - JOURNAL ARTICLE
AU - Navas, Javier F.
TI - Correct Calculation of Volatility in a Jump-Diffusion Model
AID - 10.3905/jod.2003.319217
DP - 2003 Nov 30
TA - The Journal of Derivatives
PG - 66--72
VI - 11
IP - 2
4099 - http://jod.iijournals.com/content/11/2/66.short
4100 - http://jod.iijournals.com/content/11/2/66.full
AB - The jump-diffusion model as an extension of the Black-Scholes pure logarithmic diffusion process was first introduced by Merton and others in the 1970s. The underlying asset follows a regular diffusion, but occasionally experiences a large discrete jump of random size, whose arrival is governed by a Poisson process. To estimate the volatility parameters for a jump-diffusion process, it is important to take into account the impact of both random jump arrival and also the uncertainty over the size of a jump if it should occur. In this article, Navas points out that the influence of jump size uncertainty on stock volatility was left out by a number of the early, and some not-so-early, investigators. The effect on theoretical option values is not huge, but also not negligible, as the results presented here show.