Bond and option pricing for interest rate model with clustering effects

Xin Zhang, Jie Xiong and Yang Shen

Quantitative Finance, 2018, vol. 18, issue 6, 969-981

Abstract: This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:18:y:2018:i:6:p:969-981

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DOI: 10.1080/14697688.2017.1388534

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