Sergey Levendorskiy (UT Austin, Economics)

"Optimal stopping in regime-switching models"

In the talk, a general framework for pricing of perpetual American and real options in regime-switching L\'evy models is presented. In each state of the Markov chain, which determines switches from one L\'evy process to another, the payoff stream is a monotone function of the L\'evy process labelled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The payoffs and riskless rates may depend on a state, which allows for jumps in prices at moment of switching. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains. We construct iteration procedures and prove that iterations converge to the solution of the optimization problem monotonically. The procedures are numerically efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. As first applications, we solve exit problems for a price-taking firm, and pricing problems for American options with infinite and finite time horizon. In the latter case, we use a modification of Carr's randomization procedure for regime-switching models.

The talk is based on 3 joint papers with Svetlana Boyarchenko:
1. "American Options in Regime-Switching Models"(September 6, 2006)
2. "Perpetual American Options in Regime-Switching Models" (September 5, 2006). 
3. "Exit Problems in Regime-Switching Models"