Modeling and Pricing of Swaps for Local Stochastic Volatilities with Delay and Jumps

Abstract

The valuation of the variance swaps for local stochastic volatility with delay and jumps is discussed in this paper. We provide some analytical closed forms for the expectation of the realized variance for the stochastic volatility with delay and jumps. Besides, we also present a lower bound for delay as a measure of risk. We also discuss the approaches for calculating of other swaps such as volatility, covariance, correlation swaps. As applications of our analytical solutions, a numerical example using S&P60 Canada Index (1998-2002) and S&P500 Index (1990-1993) are then provided to price variance swaps with delay and jumps.

Keywords: local stochastic volatility, delay, jumps, variance swaps, S&P60 Canada Index, S&P500 Index

JEL Classification: C32