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Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case. (English) Zbl 1281.91160

Summary: This study presents a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching. In comparison with all the previous studies in the literature, this research, which obtains closed-form exact solutions for variance and volatility swaps with discrete sampling times, serves several purposes. (1) It verifies the degree of validity of R. J. Elliott et al.’s continuous-sampling-time approximation for variance and volatility swaps of relatively short sampling periods [Appl. Math. Finance 14, No. 1, 41–62 (2007; Zbl 1281.91161)]. (2) It examines the effect of ignoring regime switching on pricing variance and volatility swaps. (3) It contributes to bridging the gap between S.-P. Zhu and G.-H. Lian’s approach [Math. Finance 21, No. 2, 233–256 (2011; Zbl 1214.91115)] and Elliott et al.’s framework. (4) Finally, it presents a semi-Monte-Carlo simulation for the pricing of other important realized variance based derivatives.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B70 Stochastic models in economics
91G60 Numerical methods (including Monte Carlo methods)
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