Hybrid Equity-Interest Rate Model with Stochastic Interest Rate and Volatility

Abstract

This paper presents an Equity-IR hybrid model that fits in the class of affine diffusion processes. In the absence of cash dividend payment, the moment generating function can be easily and rapidly computed. This allows for an efficient calibration of the model based on Vanilla European Options prices. In practice, cash dividend payments are common and are modeled via the piece-wise and escrowed approaches. We show how to compute Vanilla European Options prices efficiently in this case. The semi-analytical approximation pricing formulas obtained in the piece-wise approach are one of our primary results.In order to assess the semi-analytical pricing method, we compare the computed prices to those obtained via Monte Carlo simulation. Three discretization schemes are used: the two first ones, which have been introduced by Andersen, are the Quadratic Exponential (QE) and its extension with martingale correction QE-M. The last scheme is a new extension of the QE scheme denoted QE-I, that we introduced in order to allow the use of larger simulation time steps by comparison to QE and QE-M.