Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models

TL;DR

This paper analyzes pricing methods for volatility swaps, variance swaps, and VIX futures using stochastic volatility and jump diffusion models, employing approximation techniques and empirical calibration with S&P 500 data.

Contribution

It introduces a comprehensive approach combining convexity correction and Laplace transform methods for pricing, and evaluates the impact of jumps through empirical analysis.

Findings

Jump inclusion affects volatility derivative prices

Convexity correction improves pricing accuracy

Model calibration aligns with historical data

Abstract

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.