Hyperbolic Normal Stochastic Volatility Model

Journal of Futures Markets, 39(2):186-204, 2019

26 Pages Posted: 23 Jan 2018 Last revised: 11 Jan 2019

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University - HSBC School of Business

Chenru Liu

Peking University - HSBC Business School; Stanford University, School of Engineering, Management Science & Engineering, Students

Byoung Ki Seo

Ulsan National Institute of Science and Technology

Date Written: September 7, 2018

Abstract

For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution -- a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

Keywords: Stochastic Volatility, SABR Model, Bougerol's Identity, Johnson's SU Distribution

JEL Classification: C15, C52, G13

Suggested Citation

Choi, Jaehyuk and Liu, Chenru and Seo, Byoung Ki, Hyperbolic Normal Stochastic Volatility Model (September 7, 2018). Journal of Futures Markets, 39(2):186-204, 2019. Available at SSRN: https://ssrn.com/abstract=3068836 or http://dx.doi.org/10.2139/ssrn.3068836

Jaehyuk Choi (Contact Author)

Peking University - HSBC School of Business ( email )

University Town
Shenzhen, Guangdong 518055
China

HOME PAGE: http://www.jaehyukchoi.net/phbs_en

Chenru Liu

Peking University - HSBC Business School ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Stanford University, School of Engineering, Management Science & Engineering, Students ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Byoung Ki Seo

Ulsan National Institute of Science and Technology ( email )

50 UNIST-gil
Ulju-gun
Ulsan, 44919
Korea, Republic of (South Korea)
+82-52-217-3150 (Phone)

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