Functional of the Diffusion Path of a Two-State Markov-Chain Model for Option Pricing
15 Pages Posted: 27 Mar 2013
Date Written: March 26, 2013
This paper studies the functional of the path of a diffusion in which volatility switches between two states: high and low. For this two-state Markov-chain model, we derive a closed-form expression for the distribution function for the time spent in the high volatility state by guessing the form of, and calculating the coefficients in, the solution to a pair of integral equations.
Keywords: Markov-chain, diffusion, volatility, density
JEL Classification: C61, G11, G12, G13
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