Forward Measures in a Ho and Lee Jump Diffusion Model

28 Pages Posted: 23 May 2001

See all articles by David B. Colwell

David B. Colwell

UNSW Australia Business School, School of Banking and Finance; Financial Research Network (FIRN)

Solene Arcus

UNSW Australia Business School, School of Banking and Finance

Abstract

Empirical studies have shown that macroeconomic announcements result in large jumps in the short-term interest rate process. For this reason, finding a tractable option pricing model for jump diffusion models is of considerable interest. In this paper, we consider a model that could be described as a (continuous-time) Ho and Lee model with jumps. We first derive forward measures for this process using the Heath-Jarrow-Morton methodology. It is well known that in a jump diffusion model there are many equivalent martingale measures. We thus make two different assumptions regarding the pricing measure: (i) first we assume that the distribution of jumps is time-independent under the equilibrium spot measure; (ii) then we assume that the distribution of jumps is time-independent under the equilibrium forward measure. We show that only the second assumption leads to option prices that can be explicitly calculated. Using this assumption we derive the price of European options on bonds. The resulting formulas are extensions of the Ho and Lee model and have analogies to the Bates (1991) equity option pricing model in which the market price of jump risk results in a sort of dividend yield that depends on the jump parameters.

JEL Classification: E43, G13

Suggested Citation

Colwell, David B. and Arcus, Solene, Forward Measures in a Ho and Lee Jump Diffusion Model. EFMA 2001 Lugano Meetings, Available at SSRN: https://ssrn.com/abstract=271069 or http://dx.doi.org/10.2139/ssrn.271069

David B. Colwell (Contact Author)

UNSW Australia Business School, School of Banking and Finance ( email )

Sydney, NSW 2052
Australia
+61 (2) 9385 5851 (Phone)
+61 (2) 9385 6347 (Fax)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Solene Arcus

UNSW Australia Business School, School of Banking and Finance

Sydney, NSW 2052
Australia

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