Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case

Abstract

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 Elliott et al.'s [Appl. Math. Finance, 2007, 14(1), 41–62] continuous-sampling-time approximation for variance and volatility swaps of relatively short sampling periods. (2) It examines the effect of ignoring regime switching on pricing variance and volatility swaps. (3) It contributes to bridging the gap between Zhu and Lian's [Math. Finance, 2011, 21(2), 233–256] approach 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.

Keywords:

• Variance swaps
• Regime switching
• Stochastic volatility
• Characteristic function

JEL Classification :

• C6
• G1
• G13

Notes

†http://cfe.cboe.com/Products/Spec_VT.aspx

‡http://www.euronext.com/fic/000/010/990/109901.ppt

†The notation in their paper has been converted into our notation.