Abstract
Using an integral equation associated with generalized backward Kolmogorov's equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of jump-diffusions with Markovian switching. The results are used to find the expectation of first passage time of some financial models.
Highlights
Owing to the increasing demands on regime-switching diffusions in financial engineering and wireless communications, much attention has been drawn to switching jump diffusion processes
One of the early efforts of using such hybrid models for financial applications can be traced back to 1, 2, in which both the appreciation rate and the volatility of a stock depend on a continuous Markov chain
In a stock market, the regimes can be roughly divided into two states, bull market and bear market
Summary
Owing to the increasing demands on regime-switching diffusions in financial engineering and wireless communications, much attention has been drawn to switching jump diffusion processes. One of the early efforts of using such hybrid models for financial applications can be traced back to 1, 2 , in which both the appreciation rate and the volatility of a stock depend on a continuous Markov chain. The introduction of such models makes it possible to describe stochastic volatility in a relatively simpler manner. Adopting a Markov regime-switching model is an easy way to capture all the cyclical features of the drift and volatility of asset return depending on market environment. The results are used to find the expectation of first passage time of some financial models
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