Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatilities

Anatoliy Swishchuk

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Market Dynamics and Volatility

Abstract

A new probabilistic approach is proposed to study variance and volatility swaps for financial markets with underlying asset and variance that follow the Heston (1993) model. We also study covariance and correlation swaps for the financial markets. As an application, we provide a numerical example using S&P60 Canada Index to price swap on the volatility.

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References

1973The Pricing of Options and Corporate Liabilities 1986Generalized autoregressive conditional heteroskedasticity 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 2005Theory of rational option pricing 2016“Options, Futures, and Other Derivatives”1987Stochastic Differential Equations: An Introduction with Applications.1987The Pricing of Options on Assets with Stochastic Volatilities

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2012Option Pricing in Multivariate Stochastic Volatility Models of OU Type 2017Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index 2012New solvable stochastic volatility models for pricing volatility derivatives 2007Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets

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