Efficient Lattice Method for Valuing of Options with Barrier in a Regime Switching Model

Youngchul Han,Geonwoo Kim

doi:10.1155/2016/2474305

Youngchul Han, Geonwoo Kim

Open Access

https://doi.org/10.1155/2016/2474305

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Abstract

We propose an efficient lattice method for valuation of options with barrier in a regime switching model. Specifically, we extend the trinomial tree method of Yuen and Yang (2010) by calculating the local average of prices near a node of the lattice. The proposed method reduces oscillations of the lattice method for pricing barrier options and improves the convergence speed. Finally, computational results for the valuation of options with barrier show that the proposed method with interpolation is more efficient than the other tree methods.

Highlights

Barrier options are most popular options among the exotic options
We study all types of barrier options including the European type and the American type
It is possible to extend multistate regime switching model ) are calculated using the local averages with regime switching (LARS) and LARSI (LARS-type) methods, and the accuracy and efficiency of LARS-type method for valuing options with barrier are shown by comparing with the results given in [12, 16]

Summary

Introduction

Barrier options are most popular options among the exotic options. The barrier options are the contingent claims whose payoffs depend on the relationship between the specified barriers and the path of the underlying asset. Many researchers have used the regime switching model which leads to transition of volatilities of the underlying assets for valuation of various options. Bollen [14] first introduced a lattice method for valuation of options with a single underlying asset in regime switching model. Liu and Zhao [15] extended the method of Lin [6] to options with two underlying assets which follow the regime switching model. Yuen and Yang [16] developed a trinomial tree method for valuation of options in a regime switching model. We propose the efficient lattice methods for pricing options including American type options in a regime switching model.

Trinomial Tree Method for the Regime Switching Model

Numerical Methods

Numerical Results

Concluding Remark