Analytically pricing variance and volatility swaps under a Markov-modulated model with liquidity risks |
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Institution: | 1. Department of Business Administration, Konkuk University, Gwangjin‐gu, Seoul 05029, Republic of Korea;2. Department of Finance, Dong-A University, 225, Gudeok-ro, Seo-gu, Busan 49236, Republic of Korea;1. School of Economics, Jinan University, Guangzhou 510630, China;2. School of Business Administration, South China University of Technology, Guangzhou 510640, China;1. College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China;2. School of Business Administration, Northeastern University, Shenyang 110169, China |
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Abstract: | This paper determines strike prices of discretely sampled variance/volatility swaps taking into account stochastic liquidity risks and the switching of economic conditions. We adopt nonlinear regime switching volatility to reflect how asset prices are affected by economic cycles, and market prices of assets are discounted according to the level of market liquidity. We then establish a risk-neutral measure under regime switching Esscher transform, so that analytical valuation of variance/volatility swaps can be completed based on the closed-form forward characteristic function. The limiting behavior of discretely sampled variance/volatility swaps is also considered through the investigation of pricing continuously sampled variance/volatility swaps. Finally, based on the results from numerical implementation, we confirm that the new model is very flexible in reflecting different influence associated with common real market observations. |
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Keywords: | Variance/volatility swaps Stochastic liquidity Regime switching Forward characteristic function Nonlinearity |
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