Preliminary remarks on option pricing and dynamic hedging (original) (raw)
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Option Pricing And Hedging For Stock Prices With Discrete Jumps And Stochastic Intensity Rate
anson.ucdavis.edu
We show that it is possible to avoid the discrepancies of continuous path models for stock prices and still be able to hedge options if one uses birth and death models. One needs the stock and another market traded derivative to hedge an option in this setting. However, unlike in continuous models, the number of extra traded derivatives required for hedging does not go up with the introduction of stochastic intensity. We derive the results explicitly when the intensity rate follows a two state Markov process and outline ways of generalizing this to other models for the evolution of the intensity rate. We establish the risk-neutral measure and describe the algorithm for inverting option prices to get values of the unknown parameters in the model. We show that one needs to use filtering equations for updating parameter values and present those equations for the general case.
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