Efficient BEM-Based Algorithm for Pricing Floating Strike Asian Barrier Options (with MATLAB® Code)

Abstract

This paper aims to illustrate how SABO (Semi-Analytical method for Barrier Option pricing) is easily applicable for pricing floating strike Asian barrier options with a continuous geometric average. Recently, this method has been applied in the Black-Scholes framework to European vanilla barrier options with constant and time-dependent parameters or barriers and to geometric Asian barrier options with a fixed strike price. The greater efficiency of SABO with respect to classical finite difference methods is clearly evident in numerical simulations. For the first time, a user-friendly MATLAB R code is made available here.

Multi-Asset Barrier Options Pricing by Collocation BEM (with Matlab® Code)

“…Then, the resulting domain Ω is partitioned as shown in Figure 1 in order to approximate the option value by a Finite Element Method. However, if we are interested in the computation of the option value only at a desired point (S 1 , S 2 ) of the domain, it may certainly be convenient to apply the strategy already tested for various kind of options (based on one asset only) under several dynamics [2][3][4][5]16,17] and that we called SABO.…”

“…The consideration of two dimensional partial differential problems can be suggested for several reasons: the desire to complicate the model to get closer to reality (such as, for example, introducing the dependence of option value on a stochastic volatility variable [3]) or the evaluation of options that depend not only on the asset value. In this last direction we have already approached Asian options whose payoff depends on the average of asset values [4,5] giving rise to a degenerate PDE based on two independent variables: the asset value and the average.…”

“…The discussion in the following sections can be developed in the general dimension n [13]; however, for the sake of clarity and to simplify numerics, we will detail it considering two underlying assets S 1 , S 2 only. Hence, the convenience and reliability of SABO will be highlighted with proofs and numerical examples for a two assets framework, and, in continuity with the previous article in this journal [4], we have inserted in Appendix A a ready to use Matlab ® code.…”

Advanced Numerical Methods in Applied Sciences

“…The numerical solution of Black-Scholes-type partial differential equations is studied in [9], where the authors provide a numerical method, and a related Matlab R code, for pricing some kinds of Asian options.…”

A closed-form approximation for pricing geometric Istanbul options

“…For the geometric Asian option (GAO), the pricing formula is known in closed-form (see Kemna and Vorst (1990) for the call and Angus (1999) for more examples of payoffs). Recently, the GAOs with barrier have been studied by Aimi and Guardasoni (2017) and Aimi et al (2018). The price of this type of options has no closed-form expression and is increasingly the subject of financial research.…”