Hedging Claims with Feedback Jumps in the Price Process
نویسندگان
چکیده
We study a hedging and pricing problem of a model where the price process of a risky asset has jumps with instantaneous feedback from the most recent asset price. We model these jumps with a doubly stochastic Poisson process with an intensity function depending on the current price. We find a closed form expression of the local risk minimization strategy using Föllmer and Schweizer decomposition and Feynman-Kac type integrodifferential equation. The possibility that the jumps depend on the most recent price is new for this type of model.
منابع مشابه
Robustness of quadratic hedging strategies in finance via Fourier transforms
In this paper we investigate the consequences of the choice of the model to partial hedging in incomplete markets in finance. In fact we consider two models for the stock price process. The first model is a geometric Lévy process in which the small jumps might have infinite activity. The second model is a geometric Lévy process where the small jumps are truncated or replaced by a Brownian motio...
متن کاملOption Pricing in the Presence of Operational Risk
In this paper we distinguish between operational risks depending on whether the operational risk naturally arises in the context of model risk. As the pricing model exposes itself to operational errors whenever it updates and improves its investment model and other related parameters. In this case, it is no longer optimal to implement the best model. Generally, an option is exercised in a jump-...
متن کاملBackward Stochastic Differential Equation on Hedging American Contingent Claims
We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation, and obtain the upper hedging price ...
متن کاملStatic Hedging of Standard Options
We consider the hedging of options when the price of the underlying asset is always exposed to the possibility of jumps of random size. Working in a single factor Markovian setting, we derive a new spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this portfolio of shorter-term options, the portfolio weights do not vary with the under...
متن کاملHedging of Contingent Claims in Incomplete Markets
This report surveys important results in the literature on the problem of hedging contingent claims in incomplete markets. Consider a probability space (Ω,F , P ) and let X be a stochastic process describing the fluctuation of the stock price. Given a contingent claim H, the problem is to find an “optimal” admissible trading strategy, which is a dynamic porfolio of stock and bond (with fixed pr...
متن کامل