Continuity Correction for Barrier Options in Jump-Diffusion Models

Continuity Correction for Barrier Options in Jump-Diffusion Models

Perpetual 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...

A Continuity Correction for Discrete Barrier Options

The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring in...

Hedging of Options in Jump-Diffusion Markets with Correlated Assets

We consider the hedging problem in a jump-diffusion market with correlated assets. For this purpose, we employ the locally risk-minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. ‎This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk-minimizing portfolio. ‎...

Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution. © 2009 Elsevier B.V. All rights reserved.