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

Alessandra Aimi,Lorenzo Diazzi,Chiara Guardasoni

doi:10.3390/axioms7020040

Alessandra Aimi, Lorenzo Diazzi + Show 1 more

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https://doi.org/10.3390/axioms7020040

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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® code is made available here.

Highlights

The pricing of continuously-monitored Asian options is a relevant task from both a mathematical and a financial point of view.Asian options are quite common derivatives because they provide protection against strong price fluctuations in volatile markets and reduce the possibilities of price manipulations
Some of which are displayed in the following, have been obtained by the MATLAB R codes implementing the algorithms of SABO, FD1 and FD2 described in Sections 4.1, 4.2.1 and 4.2.2, respectively
Looking at Example 1, the values of a call option with an up-and-out barrier obtained by SABO

Summary

Introduction

The pricing of continuously-monitored Asian options is a relevant task from both a mathematical and a financial point of view.Asian options are quite common derivatives because they provide protection against strong price fluctuations in volatile markets and reduce the possibilities of price manipulations. The pricing of continuously-monitored Asian options is a relevant task from both a mathematical and a financial point of view. Asian option depends on the average price of the underlying asset that is less volatile than the asset price itself. Asian options are less valuable than their vanilla European counterparts because an option on a lower volatility asset is worth less. It is more difficult to deal with Asian options than vanilla options because their price depends on the average value assumed by the underlying asset during the option’s life, requiring some mathematical effort in order to describe the dynamics of the average under consideration. Asian options are equipped with a continuously-monitored geometric average [1]

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