Abstract
In this paper, the authors study the distribution of the Vasicek model with mixed-exponential jumps and its applications in finance and insurance. With the aid of the piecewise deterministic Markov process theory and the martingale theory, the authors first obtain the explicit forms of the Laplace transforms for the distribution of the Vasicek model with mixed-exponential jumps and its integrated process. As some applications in finance and insurance, the pricing of the default-free zero-coupon bond and the European put option on the zero-coupon bond, and the moments of the aggregate accumulated claim amounts are discussed. The authors also provide some remarks and numerical calculations.
Highlights
Patie [4] generalized the Vasicek model and provided its applications in computing the Laplace transform of the price of a European call option
Vasicek [1] proposed the following classical Vasicek model which is defined by an equation of the form drt = α(β – rt) dt + σ dBt, (1.1)where α is the rate of mean reversion, β is the long-run level, σ is the volatility coefficient, and Bt is a standard Brownian motion.The Vasicek model is one of the earliest no-arbitrage interest rate models based upon the idea of mean reverting interest rates
5 Conclusion In this paper, we introduce the concept of Vasicek model with mixed-exponential jumps
Summary
Patie [4] generalized the Vasicek model and provided its applications in computing the Laplace transform of the price of a European call option. Beliaeva et al [24] discussed the pricing of American interest rate options under the Vasicek model with jumps. 2, we obtain the Laplace transforms for the Vasicek models with mixed-exponential jumps and their integrated processes.
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