Analytically pricing volatility swaps under stochastic volatility

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:288

Article

Zhu, Song-Ping¹  Lian, Guang-Hua² 

[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia

[2] Univ S Australia, Sch Commerce, Adelaide, SA 5001, Australia

关键词: Volatility swaps;    Heston model;    Stochastic volatility;    Characteristic function;   

DOI  :  10.1016/j.cam.2015.04.036

来源: Elsevier

【 摘 要 】

Papers focusing on analytically pricing discretely-sampled volatility swaps are rare in literature, mainly due to the inherent difficulty associated with the nonlinearity in the pay-off function. In this paper, we present a closed-form exact solution for the pricing of discretely-sampled volatility swaps, under the framework of Heston (1993) stochastic volatility model, based on the definition of the so-called average of realized volatility. By working out such a closed-form exact solution for discretely-sampled volatility swaps, this work represents a substantial progress in the field of pricing volatility swaps, as it has: (1) significantly reduced the computational time in obtaining numerical values for the discretely-sampled volatility swaps; (2) improved the computational accuracy of discretely-sampled volatility swaps, comparing with the continuous sampling approximation, especially when the time interval between sampling points is large; (3) enabled all the hedging ratios of a volatility swap to be analytically derived. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free