THE BINO-TRINOMIAL TREE MODEL FOR PRICING BARRIER OPTIONS AND THEIR APPLICATIONS - Aulia Rahayu, Rima
One of the most popular types of exotic options is the barrier option. The barrier option is of particular interest because there is a limit that must be reached to activate the option. This limit can be used as a reference for investors to minimize losses that may occur. In addition, the price offered for the barrier option is relatively cheaper than the vanilla option. There are various methods for determining the price of barrier options, including numerical methods and analytical methods. Because not all types of barrier options can be solved using analytical methods, the alternative is using numerical methods. Some common types of numerical methods are Monte Carlo methods, finite difference methods, and lattice methods. Obtaining accurate results using the Monte Carlo method requires quite a lot of simulations. Then the finite difference method always requires a Partial Differential Equation (PDP), while not all types of barrier options have PDP. So in this case the lattice method is the choice to determine the price of the barrier option. Commonly used lattice methods include the binomial tree model and the trinomial tree. In the binomial tree model, the resulting error is relatively large due to distributional errors and non-linearity errors. With the additional flexibility (stretch parameters) introduced by Ritchken to the trinomial tree structure, the non-linearity error can be overcome. This happens because the node layer on the stock price can touch the barrier right. However, because there are more nodes generated than the binomial tree model, the computational model will be heavier. In this case, another alternative model was used proposed by Dai and Lyuu (2010) in their research entitled "The Bino-Trinomial Tree: A Simple Model For Efficient and Accurate Option Pricing". By combining the trinomial tree structure in the first step and then the other step in the form of a binomial tree, this model is named Bino-Trinomial Tree (BTT). In this study, a computational technique was added to align the calculation results at each node, namely in the form of rounding the value of the stock price to the nearest integer ("round") when calculating the option price in the backward phase. With these computational techniques the BTT model can generate efficient and effective option barrier prices. Because the BTT tree structure is less than the trinomial tree structure, the BTT model is superior to the trinomial tree model in terms of calculation time. In addition, the flexible structure of the BTT model makes it easy to apply to various types of barriers such as single barriers, double barriers, and shifting barriers. To the best of our knowledge, there is no literature to overcome the window barrier option using the BTT model. Where this window barrier is a special type of partial barrier that can provide investors with a hedging experience with a more flexible structure. So we use the BTT model to solve it, which is then compared with the Trinomial Kamrad-Ritchken (K-R) model. As an implementation because the barrier shifts are one of the features of Employee Stock Options (OSK), where the barrier in OSK is known as a psychological barrier, so we use the BTT model to calculate OSK prices, which are then compared with the Hull-White and K-R Trinomial models. In this case, the BTT model is still one of the most efficient and effective lattice models. In addition, the BTT model can also overcome the phenomenon that as the maturity date approaches, an employee will lower his psychological barrier. Because OSK is generally valid for a long time and if an employee lowers his psychological barrier, the price of OSK obtained will be cheaper. This study also presents an analysis of the parameter sensitivity to OSK.