Optimal Stopping, Free Boundary, and American Option in a Jump-Diffusion Model
نویسنده
چکیده
This paper considers the American put option valuation in a jumpdiffusion model and relates this optimal-stopping problem to a parabolic integrodifferential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its counterpart European price and the early exercise premium. Compared with the Black–Scholes (BS) [5] model, this premium has an additional term due to the presence of jumps. We prove the continuity of the free boundary and also give one estimate near maturity, generalizing a recent result of Barles et al. [3] for the BS model. Finally, we study the effect of the market price of jump risk and the intensity of jumps on the American put option price and its critical stock price.
منابع مشابه
Free Boundary Problems and Perpetual American Strangles
We consider the perpetual American strangles in the geometric jump-diffusion models. We assume further that the jump distribution is a mixture of exponential distributions. To solve the corresponding optimal stopping problem for this option, by using the approach in [5], we derive a system of equations that is equivalent to the associated free boundary problem with smooth pasting condition. We ...
متن کاملPerpetual barrier options in jump-diffusion models∗
We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial irregular optimal stopping problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The obtained...
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 کاملO ct 2 00 7 Remarks on the American Put Option for Jump Diffusions ∗ †
We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...
متن کامل2 8 A ug 2 00 7 Remarks on the American Put Option for Jump Diffusions ∗ †
We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...
متن کامل