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

Mukarram Attari

Journal of Financial and Quantitative Analysis, 1999, vol. 34, issue 3, 293-322

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 size jumps. 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, stochastic volatility jump-diffusion, and Gamma process option prices can be obtained as limiting cases. The methodology is also applied to obtain the prices of options on stocks. Finally, the paper shows how portfolios to hedge derivative securities can be built.

Date: 1999
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