Exact Solutions for Bond and Option Prices with Systematic Jump Risk

REVIEW OF DERIVATIVES RESEARCH, Vol. 1 No. 1

Posted: 14 Apr 1998

See all articles by Sanjiv Ranjan Das

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business

Silverio Foresi

Goldman Sachs Group, Inc. - Quantitative Strategy Group

Abstract

A variety of realistic economic considerations make jump- diffusion models of interest rate dynamics an appealing modeling choice to price interest rate contingent claims. However, exact closed form solutions for bond prices when interest rates follow a mixed jump-diffusion process have proved very hard to derive. This paper puts forward two new models of interest rate dynamics which combine infrequent, discrete changes in the interest rate level, modeled as a jump process, with short lived, mean reverting shocks, modeled as a diffusion process. The two models differ in the way jumps affect the central tendency of interest rates; in one case shocks are temporary, in the other shocks are permanent. We derive exact closed form solutions for the price of a discount bond, and computationally tractable schemes to price bond options.

JEL Classification: G13, E43, G12

Suggested Citation

Das, Sanjiv Ranjan and Foresi, Silverio, Exact Solutions for Bond and Option Prices with Systematic Jump Risk. REVIEW OF DERIVATIVES RESEARCH, Vol. 1 No. 1, Available at SSRN: https://ssrn.com/abstract=7456

Sanjiv Ranjan Das (Contact Author)

Santa Clara University - Leavey School of Business ( email )

Department of Finance
316M Lucas Hall
Santa Clara, CA 95053
United States

HOME PAGE: http://srdas.github.io/

Silverio Foresi

Goldman Sachs Group, Inc. - Quantitative Strategy Group ( email )

32 Old Slip, 24th Floor
New York, NY 10005
United States
(212) 357-3508 (Phone)

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