Pricing of the American Put Under Lévy Processes

Abstract

Abstract. We consider the American put with the finite time horizon, T , assuming that under a chosen equivalent martingale measure stock returns follow a regular Lévy process of exponential type. We formulate the free boundary value problem for the price of the American put, and develop the non-Gaussian analog of the method of lines and Carr's randomization method used in the Gaussian option pricing theory. The result is the (discretized) early exercise boundary and prices of the American put for all strikes and maturities from 0 to T . In the case of exponential jump-diffusion processes, a simple efficient pricing scheme is constructed.

Analysis of the Optimal Exercise Boundary of American Options for Jump Diffusions

“…This behavior of the free boundary was also observed by Levendorskiȋ [2004] and Lamberton and Mikou [2008] in the exponential Lévy models. The purpose of our paper is to extend the regularity results of the free boundary to the case where (1.5) is not satisfied.…”

Regularity of the obstacle problem for a fractional power of the laplace operator

“…For non perpetual options, a parabolic version of this problem is considered. A very readable explanation of these models can be found in the book of Cont and Tankov [6] (See also [10] and [11]). Usually the models are in one dimension, and although general payoffs functions are considered, the case when ϕ = (K − e x ) + (the American put) is of special interest.…”

Efficient Option Pricing Under Levy Processes, with CVA and FVA

“…Unfortunately, apart from a few special cases (such as the hyper-exponential Lévy processes [35,53,54]), no explicit formulas for φ ± q (ξ ) are known. Instead, one must use the integral formulas recalled in Section 4.2.…”