Delta hedging in discrete time under stochastic interest rate

Abstract

We propose a methodology based on the Laplace transform to compute the variance of the hedging error due to time discretization for financial derivatives when the interest rate is stochastic. Our approach can be applied to any affine model for asset prices and to a very general class of hedging strategies, including Delta hedging. We apply it in a two-dimensional market model, obtained by combining the models of Black-Scholes and Vasicek, where we compare a strategy that correctly takes into account the variability of interest rates to one that erroneously assumes that they are deterministic. We show that the differences between the two strategies can be very significant. The factors with stronger influence are the ratio between the standard deviations of the equity and that of the interest rate, and their correlation. The methodology is also applied to study the Delta hedging strategy for an interest rate option in the Cox-Ingersoll and Ross model, measuring the variance of the hedging error as a function of the frequency of the rebalancing dates. We compare the results obtained to those coming from a classical Monte Carlo simulation.

A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options

“…To transform the tfBS-PDE (10) and for the convenience of numerical implementation, we consider the following change of variables Using the Landau ( [37]) transformation of the asset price variable ( x = ln S b f ) serves to ensure that x = 0 whenever S = b( ) , which help in transforming the free boundary conditions to fixed boundary conditions. Using this transformation, the free boundary S = b( ) is then transformed to a fixed boundary x = 0 .…”

“…As such, a number of revised models have been suggested, leading to the development of more sophisticated models, those which are well suited in explaining unusual markets dynamics. A few examples of these revised models are but not limited to regime-switching and jump diffusion models [4][5][6], stochastic volatility models [7][8][9], and stochastic interest rates models [10][11][12] just to mention but a few.…”

ε-monotone Fourier methods for optimal stochastic control in finance

“…These optimal stochastic problems arise in many important financial applications. This includes problems such as asset allocation (Li and Ng, 2000;Huang, 2010;Forsyth and Vetzal, 2017;Cong and Oosterlee, 2016), pricing of variable annuities (Bauer et al, 2008;Dai et al, 2008;Ignatieva et al, 2018;Alonso-Garcia et al, 2018;Huang et al, 2017), and hedging in discrete time (Remillard and Rubenthaler, 2013;Angelini and Herzel, 2014) to name just a few.…”