A spectral approach to pricing of forward starting options

Zhigang Tong ,Dongping Hou ,Jianhua Guan

doi:10.28919/mfl/4036

Abstract

We propose a new class of models for pricing forward starting options. We assume that the asset price is a nonlinear function of a CIR process, time changed by a composition of a Levy subordinator and an absolutely ´ continuous process. The new models introduce the nonlinearity in both drift and diffusion components of the underlying process and can capture jumps and stochastic volatility in a flexible way. By employing the spectral expansion technique, we are able to derive the analytical formulas for the forward starting option prices. We also implement a specific model numerically and test its sensitivity to some of the key parameters of the model.

Highlights

The forward starting options are options that start at a specified future date with an expiration date set further in the future
We assume that the asset price is a nonlinear function of a CIR process, time changed by a composition of a Levy subordinator and an absolutely continuous process
Y (t) = X(T (t)), where T is a time change process. To introduce both jumps and stochastic volatility into the asset price, we model the time change process T by composing a Levy subordinator and an absolutely continuous time change process as follows: (2.4)

Summary

Introduction

The forward starting options are options that start at a specified future date with an expiration date set further in the future. Kruse and Nogel [15] adopt Heston’s stochastic volatility model by integrating the option pricing formula with respect to the conditional density of the variance value at strike determination date Their quasi-analytical pricing formulas involve the numerical solution of a two-dimensional integration problem. Zhang and Geng [35] provide an efficient method for pricing forward starting options under stochastic volatility model with double exponential jumps. We relax the strong assumptions of the AJD models and propose a non-affine model with stochastic volatility and jumps for pricing forward starting options. 5, we analyze the effect of the parameters of the model on the option prices through specific numerical examples

Model framework

Spectral expansion method for the TC-CIR-CEV model

Valuation of forward starting options

Numerical Analysis

Conclusion