Journal
MATHEMATICS AND FINANCIAL ECONOMICS
Volume 15, Issue 2, Pages 381-396Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s11579-020-00281-y
Keywords
Stochastic volatility; Stochastic long-term mean; Closed-form; European options; Risk management; Empirical studies
Categories
Funding
- National Natural Science Foundation of China [11601189]
- Research Base of Humanities and Social Sciences outside Jiangsu Universities Research Center of Southern Jiangsu Capital Market [2017ZSJD020]
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This paper introduces a new stochastic volatility model with a stochastic long-term mean to better describe the term structure of implied volatility and variance swap curve. Through numerical comparison and empirical study, it is shown that the new model can lead to more accurate option prices compared to the Heston model.
Based upon the fact that a constant long-term mean could not provide a good description of the term structure of the implied volatility and variance swap curve, as suggested by Byelkina and Levin (in: Sixth world congress of the Bachelier Finance Society, Toronto, 2010) and Forde and Jacquier (Appl Math Finance 17(3):241-259, 2010), this paper presents a new stochastic volatility model, by assuming the long-term mean of the volatility in the Heston model be stochastic. An important feature of our model is that it still preserves the essential advantage of the Heston model, i.e., the analytic tractability, because a closed-form pricing formula for European options can be derived, which could not only facilitate the risk management process but also help save plenty of time in terms of model calibration. The effect of the newly introduced stochastic long-term mean is demonstrated through the numerical comparison with the Heston model. It is also shown that the current model can overall lead to more accurate option prices than the Heston model, through a carefully designed empirical study.
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