Full-fledged SABR through Markov Chains

13 Pages Posted: 14 Mar 2019

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Duy Nguyen

Marist College - Department of Mathematics

Date Written: February 23, 2019

Abstract

We present a general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form matrix expressions for European options are derived. We also propose a recursive risk-neutral valuation technique for pricing discretely monitored path-dependent options, and use it to price Bermudan and barrier options. In addition, we provide single Laplace transform formula for discretely monitored arithmetic Asian options. Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.

Keywords: SABR model, Markov chain, exotic options, calibration

JEL Classification: C58, G13, G17

Suggested Citation

Cui, Zhenyu and Kirkby, Justin and Nguyen, Duy, Full-fledged SABR through Markov Chains (February 23, 2019). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3340657 or http://dx.doi.org/10.2139/ssrn.3340657

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

Justin Kirkby

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

Duy Nguyen

Marist College - Department of Mathematics ( email )

NY
United States

HOME PAGE: http://sites.google.com/site/nducduy/

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