Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab^® codes)

Abstract

A Semi-Analytical method for pricing of Barrier Options (SABO) is presented. The method is based on the foundations of Boundary Integral Methods which is recast here for the application to barrier option pricing in the Black-Scholes model with time-dependent interest rate, volatility and dividend yield. The validity of the numerical method is illustrated by several numerical examples and comparisons.

Numerical pricing of geometric asian options with barriers

“…SABO is the acronym of semianalytical method for pricing of barrier options, and it has been introduced for European options both in Black‐Scholes and in Heston and Bates frameworks. For geometric Asian option, a formal and deep argumentation was described in the work of Aimi and Guardasoni, and it proceeds as follows.…”

“…Semianalytical method for pricing of barrier options has been recently introduced for the computation of European barrier options within various differential models in other works . This new approach, based on boundary element method, turns out to be stable and efficient, especially when the differential problem is defined in an unbounded domain and the data is assigned on a limited boundary (which is the case of the “barrier options”).…”

“…2 Barrier options are largely exchanged as they are good products for hedging and investment and they are cheaper than vanilla options, but, for Asian options, we found in literature only the analysis of the work of Atkinson and Kazantzaki, 3 which provides rigorous bounds in the arithmetic mean case.Semianalytical method for pricing of barrier options has been recently introduced for the computation of European barrier options within various differential models in other works. [4][5][6] This new approach, based on boundary element method, 7,8 turns out to be stable and efficient, especially when the differential problem is defined in an unbounded domain and the data is assigned on a limited boundary (which is the case of the "barrier options"). The method is particularly advantageous for its high accuracy, for the implicit satisfaction of the far-field behavior of the solution, and for the low discretization costs.…”

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

“…asymptotic conditions of vanilla option , {(S, A) : S = 0 ∨ A → −∞ ∨ A → +∞}, (7) with the final condition:…”

“…In this context, SABO is a Semi-Analytical method conceived of for the pricing of Barrier Options, and its milestones are resumed in Section 4.1. It is quite a general method, applicable also to fixed strike payoffs [4,5], put options [6], time-dependent parameters [7] and double barriers [8].…”