Statistical Methods in Finance 2016

Dec 18 - 22, 2016


Barndorff-Nielsen and Shephard model, its generalization, and implementation in pricing various swaps

by Indranil Sen Gupta

In this presentation, a class of generalized Barndorff-Nielsen and Shephard model will be investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets will be studied in terms of equivalent martingale measures (EMM). Various structure preserving subclasses of EMMs will be derived. It will be shown that such models can be effectively used for arbitrage free pricing of volatility, variance, and covariance swaps. One of the major challenges in arbitrage free pricing of swap is to obtain an accurate pricing expression which can be used with good computational accuracy. In this presentation various approximate expressions will be obtained for the pricing of volatility, variance, and covariance swaps. It will be shown that with the approximate formulas obtained from the Barndorff-Nielsen and Shephard model the error estimation in fitting the delivery price is much less than the existing models with comparable parameters.