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Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatility. Anatoliy Swishchuk Department of Mathematics & Statistics, York University, Toronto, ON, Canada Seminar-April 15, 2004 Department of Statistics, University of Toronto. Outline. Introduction
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Modeling of Variance and Volatility Swapsfor Financial Markets with Stochastic Volatility Anatoliy Swishchuk Department of Mathematics & Statistics, York University, Toronto, ON, Canada Seminar-April 15, 2004 Department of Statistics, University of Toronto
Outline • Introduction • Stochastic Volatility Model: Heston (1993) Model • Solution of the Volatility Equation • Property of the Solution • Variance and Volatility Swaps • Calculation of Expectation and Variance • Covariance and Correlation Swaps • Numerical Example: S&P60 Canada Index
Introduction • Cox, Ingersoll &Ross (CIR) (1985)-stochastic variance model; • Heston (1993)-asset price has variance that follows a CIR model; • Brockhaus & Long (2000)-calculation expectation and variance for volatility swap using analytical approach; • He & Wang (RBC Financial Group) (2002)-proposed deterministic volatility for variance and volatility swaps: Query Note for the 6th IPSW PIMS, Vancouver, UBC, May 2002
Calculation of E[V] and Var[V] in Discrete Case (sketch) (continuation)
Statistics on Log-Returns of S&P60 Canada Index for 5 years (1997-2002)
Generating Different Input Variables for the Volatility Swap Model