We analyze pricing and portfolio optimization problems in defaultable regime switching markets. We contribute to both of these problems by obtaining novel characterizations of option prices and optimal portfolio strategies under regime-switching . Using our option price representation, we develop a novel efficient method to price claims which may depend on the full path of the underlying Markov chain. This is done via a change of probability measure and a short-time asymptotic expansion of the claim's price in terms of the Laplace transforms of the symmetric Dirichlet distribution . The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path-dependent claims that we term self-decomposable  as well as the important class of vulnerable call and put options on a stock. In the portfolio optimization context, we obtain explicit constructions of value functions and investment strategies for investors with Constant Relative Risk Aversion (CRRA) utilities, built on the Hamilton-Jacobi-Bellman (HJB) framework developed in Capponi and Figueroa-Lopez (2011). We give a precise characterization of the investment strategies in terms of corporate bond returns, forward rates, and expected recovery at default, and illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economical analysis .
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time Markov process. As a result of this representation, along with a short-time asymptotic expansion of the claim's price process, we develop an efficient method for pricing claims whose payoffs may depend on the full path of the underlying Markov chain . The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path-dependent claims that we term self-decomposable , as well as the important class of vulnerable call and put options on a stock. We provide a detailed error analysis and illustrate the accuracy and computational complexity of our method on several market traded instruments, such as defaultable bond prices, barrier options, and vulnerable call options. Using again our Poisson series representation, we show differentiability in time of the pre-default price function of European vulnerable claims, which enables us to rigorously deduce Feynman-Kac representations for the pre-default pricing function and new semimartingale representations for the price process of the vulnerable claim under both risk-neutral and objective probability measures .
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We analyze pricing and portfolio optimization problems in defaultable regime switching markets. We contribute to both of these problems by obtaining novel characterizations of option prices and optimal portfolio strategies under
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a
R
. Using our option price representation, we develop a novel efficient method to price claims which may depend on the full path of the underlying Markov chain. This is done via a change of probability measure and
market driven by an underlying continuous- time Markov process. As a result of this representation, along with
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in terms of the Laplace transforms of the symmetric Dirichlet distribution
process, we develop an efficient method for pricing claims whose payoffs may depend on the full path of the underlying Markov chain
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,
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In the portfolio optimization context, we obtain explicit constructions of value functions and investment strategies for investors with Constant Relative Risk Aversion (CRRA) utilities, built on the Hamilton-Jacobi-Bellman (HJB) framework developed in Capponi and Figueroa-Lopez (2011). We give a precise characterization of the investment strategies in terms of corporate bond returns, forward rates, and expected recovery at default, and illustrate the dependence of the optimal strategies on time, losses given default, and risk aversion level of the investor through a detailed economical analysis
We provide a detailed error analysis and illustrate the accuracy and computational complexity of our method on several market traded instruments, such as defaultable bond prices, barrier options, and vulnerable call options. Using again our Poisson series representation, we show differentiability in time of the pre-default price function of European vulnerable claims, which enables us to rigorously deduce Feynman-Kac representations for the pre-default pricing function and new semimartingale representations for the price process of the vulnerable claim under both risk-neutral and objective probability measures