Pricing Exotic Discrete Variance Swaps under the 3/2-Stochastic Volatility Models |
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Authors: | Chi Hung Yuen Wendong Zheng Yue Kuen Kwok |
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Institution: | 1. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, Chinamaykwok@ust.hk;3. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China |
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Abstract: | AbstractWe consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor variance swaps, under the 3/2-stochastic volatility models (SVMs) with jumps in asset price. The class of SVMs that use a constant-elasticity-of-variance (CEV) process for the instantaneous variance exhibits good analytical tractability only when the CEV parameter takes just a few special values (namely 0, 1/2, 1 and 3/2). The popular Heston model corresponds to the choice of the CEV parameter to be 1/2. However, the stochastic volatility dynamics implied by the Heston model fails to capture some important empirical features of the market data. The choice of 3/2 for the CEV parameter in the SVM shows better agreement with empirical studies while it maintains a good level of analytical tractability. Using the partial integro-differential equation (PIDE) formulation, we manage to derive quasi-closed-form pricing formulas for the fair strike prices of various types of exotic discrete variance swaps with various weight processes and different return specifications under the 3/2-model. Pricing properties of these exotic discrete variance swaps with respect to various model parameters are explored. |
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Keywords: | Variance swaps gamma swaps corridor variance swaps 3/2-volatility model |
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