Discontinuous Interest Rate Processes: An Equilibrium Model for Bond Option Prices

33 Pages Posted: 14 Nov 1996

Date Written: November 1996

Abstract

This paper obtains equilibrium interest rate option prices for discontinuous short-term interest rate processes. The prices are first obtained for a general distribution of jump sizes using a process with a number of fixed sized jumps. The option price is the expectation, over the number and timing of jumps, of the option price given the number and timing of the jumps. This is similar in form to Merton's jump-diffusion option pricing formula for stock options. The differences are that (i) this paper does not need the assumption that jump risk is not priced and (ii) the timing of the jumps is also important. The pricing formulas are then used to obtain option prices when the jump distribution is known to be one of the continuous distributions. The commonly used jump-diffusion and stochastic volatility diffusion option prices can be obtained as limiting cases. The paper shows how portfolios to hedge derivative securities can be built.

JEL Classification: G12, G13

Suggested Citation

Attari, Mukarram, Discontinuous Interest Rate Processes: An Equilibrium Model for Bond Option Prices (November 1996). Available at SSRN: https://ssrn.com/abstract=633 or http://dx.doi.org/10.2139/ssrn.633

Mukarram Attari (Contact Author)

CRA International, Incorporated ( email )

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Washington, DC 20004
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617-425-3336 (Phone)

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