Rough stochastic elasticity of variance and option pricing

Jiling Cao; Jeong Hoon Kim; See Woo Kim; Wenjun Zhang

doi:10.1016/j.frl.2019.101381

Rough stochastic elasticity of variance and option pricing

Jiling Cao, Jeong Hoon Kim, See Woo Kim, Wenjun Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

This study is concerned with the elasticity of variance for risky assets. We show that the elasticity of variance for S&P500 exhibits short-range correlations. By using asymptotic and martingale methods, we obtain a semi-analytical expression for the option price in the two-scale regime where the constant elasticity of variance is perturbed by a smooth and bounded function of a rapid fractional Ornstein–Uhlenbeck process with Hurst exponent within [Formula presented]. The associated implied volatility is presented and discussed. As a result, the scope of Markov stochastic elasticity of variance model is extended to a non-Markov case.

Original language	English
Article number	101381
Journal	Finance Research Letters
Volume	37
DOIs	https://doi.org/10.1016/j.frl.2019.101381
Publication status	Published - 2020 Nov

Bibliographical note

Funding Information:
The authors would like to thank José Da Fonseca for valuable discussions and suggestions on empirical studies on elasticity of variance. The author J.-H. Kim was supported by the National Research Foundation of Korea ( NRF-2017R1A2B4003226 ). Appendix A

Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Finance

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10.1016/j.frl.2019.101381

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abstract = "This study is concerned with the elasticity of variance for risky assets. We show that the elasticity of variance for S&P500 exhibits short-range correlations. By using asymptotic and martingale methods, we obtain a semi-analytical expression for the option price in the two-scale regime where the constant elasticity of variance is perturbed by a smooth and bounded function of a rapid fractional Ornstein–Uhlenbeck process with Hurst exponent within [Formula presented]. The associated implied volatility is presented and discussed. As a result, the scope of Markov stochastic elasticity of variance model is extended to a non-Markov case.",

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AU - Cao, Jiling

AU - Kim, Jeong Hoon

AU - Kim, See Woo

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N2 - This study is concerned with the elasticity of variance for risky assets. We show that the elasticity of variance for S&P500 exhibits short-range correlations. By using asymptotic and martingale methods, we obtain a semi-analytical expression for the option price in the two-scale regime where the constant elasticity of variance is perturbed by a smooth and bounded function of a rapid fractional Ornstein–Uhlenbeck process with Hurst exponent within [Formula presented]. The associated implied volatility is presented and discussed. As a result, the scope of Markov stochastic elasticity of variance model is extended to a non-Markov case.

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Rough stochastic elasticity of variance and option pricing

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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