Pricing Continuously Monitored Barrier Options Under the Sabr Model: A Closed-Form Approximation

26 Pages Posted: 20 Dec 2017

See all articles by Nian Yang

Nian Yang

Nanjing University - School of Business

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China.

Zhenyu Cui

Stevens Institute of Technology - School of Business

Date Written: December 8, 2017

Abstract

The stochastic alpha beta rho (SABR) model introduced by Hagan et al. (2002) is widely used in both fixed income and the foreign exchange (FX) markets. Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets. In this paper, we develop closed-form formulas to approximate various types of barrier option prices (down-and-out/in, up-and-out/in) under the SABR model. We first derive an approximate formula for the survival density. The barrier option price is the one-dimensional integral of its payoff function and the survival density, which can be easily implemented and quickly evaluated. The approximation error of the survival density is also analyzed. To the best of our knowledge, it is the first time that analytical (approximate) formulas for the survival density and the barrier option prices for the SABR model are derived. Numerical experiments demonstrate the validity and efficiency of these formulas.

Keywords: SABR model, continuously monitored barrier options, survival density, closed-form approximation, stochastic volatility

JEL Classification: C63, G12, G13, G23

Suggested Citation

Yang, Nian and Liu, Yanchu and Cui, Zhenyu, Pricing Continuously Monitored Barrier Options Under the Sabr Model: A Closed-Form Approximation (December 8, 2017). Available at SSRN: https://ssrn.com/abstract=3089039 or http://dx.doi.org/10.2139/ssrn.3089039

Nian Yang

Nanjing University - School of Business ( email )

Nanjing
China

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China. ( email )

Haizhu District,
Guangzhou, China.
Guangzhou, Guangdong 510275
China

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

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