Abstract
The valuation and hedging of defaultable game options is studied in a hazard process model of credit risk. A convenient pricing formula with respect to a reference filteration is derived. A connection of arbitrage prices with a suitable notion of hedging is obtained. The main result shows that the arbitrage prices are the minimal superhedging prices with sigma martingale cost under a risk neutral measure.
Highlights
The goal of this work is to analyze valuation and hedging of defaultable contracts with game option features within a hazard process model of credit risk
In Bielecki et al 3, we formally defined a defaultable game option, that is, a financial contract that can be seen as an intermediate case between a general mathematical concept of a game option and much more specific convertible bond with credit risk
Building on results of Kifer 8 and Kallsen and Kuhn 6, we showed that the study of an arbitrage price of a defaultable game option can be reduced to the study of the value process of the related Dynkin game under some risk-neutral measure Q for the primary market model
Summary
The goal of this work is to analyze valuation and hedging of defaultable contracts with game option features within a hazard process model of credit risk. Building on results of Kifer 8 and Kallsen and Kuhn 6 , we showed that the study of an arbitrage price of a defaultable game option can be reduced to the study of the value process of the related Dynkin game under some risk-neutral measure Q for the primary market model. It should be acknowledged that structural models, with their sound economic background, are better suited for inference of reliable debt information, such as: risk-neutral default probabilities or the present value of the firm’s debt, from the equities, which are the most liquid among all financial instruments The structure of these models, as rich as it may be and which can include a list of factors such as stock, spreads, default status, and credit events never rich enough to yield consistent prices for a full set of CDS spreads and/or implied volatilities of related options. As we aim to specify models for pricing and hedging contracts with optional features such as convertible bonds , we favor the reduced-form approach in the sequel
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