Pricing of Variance and Volatility Swaps with Semi-Markov Volatilities

Anatoliy Swishchuk
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Anatoliy Swishchuk: University of Calgary, Canada

Chapter 13 in Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities, 2013, pp 173-187 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThe following sections are included:IntroductionMartingale Characterization of Semi-Markov ProcessesMarkov Renewal and Semi-Markov ProcessesJump Measure for Semi-Markov ProcessMartingale Characterization of Semi-Markov ProcessesMinimal Risk-Neutral (Martingale) Measure for Stock Price with Semi-Markov Stochastic VolatilityCurrent Life Stochastic Volatility Driven by Semi-Markov Process (Current Life Semi-Markov Volatility)Minimal Martingale MeasurePricing of Variance Swaps for Stochastic Volatility Driven by a Semi-Markov ProcessExample of Variance Swap for Stochastic Volatility Driven by Two-State Continuous-Time Markov ChainPricing of Volatility Swaps for Stochastic Volatility Driven by a Semi-Markov ProcessVolatility SwapPricing of Volatility SwapDiscussions of Some ExtensionsLocal Current Stochastic Volatility Driven by a Semi-Markov Process (Local Current Semi-Markov Volatility)Local Stochastic Volatility Driven by a Semi-Markov Process (Local Semi-Markov Volatility)Dupire Formula for Semi-Markov Local VolatilityRisk-Minimizing Strategies (or Portfolios) and Residual RiskSummaryBibliography

Keywords: Stochastic Volatilities; Variance; Volatility; Covariance; Correlation Swaps; Change of Time; Option Pricing; Stochastic Volatilities with Delay; Multi-Factor Stochastic Volatilities Models; Regime-Switching Stochastic Volatilities; Levy-Based Stochastic Volatilities with Delay; COGARCH Stochastic Volatility; Stochastic Volatility Driven by Fractional Brownian Motion; Delayed Heston Model; Semi-Markov Stochastic Volatilities; Energy Markets; Forward and Futures in Energy Markets (search for similar items in EconPapers)
Date: 2013
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