A new high-order compact scheme for American options under jump-diffusion processes

摘要

Jump-diffusion option pricing models have the ability to fit various implied volatility patterns observed in market option prices. In the partial differential equations framework, pricing an American put when the underlying follows a jump process requires the solution of a partial integro-differential equation. For this problem, second-order finite difference discretisations have been commonly employed. This work develops a new scheme which is based on a high-order compact discretisation of the spatial terms of the equation and a fourth-order time integration scheme. We demonstrate that the scheme is highly accurate for at-the-money American options and oscillation-free greeks are computed.