European Option Pricing Using Trinomial Method with Dividend

Abstract

The accurate valuation of European options is a primary challenge in quantitative finance, particulary when dividend payment influence the underlying stock price. Convetional option pricing models often overlook the dividend variable or face computational complexities that reduce the accuracy and stability of the result. This study aims to determine the value of Eropean-style options using the trinomial method with dividend payments. The trinomial method with dividend was applied to five stock with the same period and expiration date. Based on the Mean Absolute Percentage Error (MAPE) calculation, it can be concluded that the trinomial model used to predict option prices has varying levels of accuracy. The result show the MAPE values for a 2.25 month dividend as follows: AAPL at 27.11% for calls and 25.86% for puts; MSFT at 10.03% for calls and 4.57% for puts; AON at 7.56% for calls and 6.52% for puts; IBM at 24.96% for calls and 15.22% for puts; and META at 17.46% for calls and 28.59% for puts. Meanshile, the MAPE calvulation for a 3 month dividend yielded: AAPL at 27.13% for call and 25.86% for puts; MSFT at 10.03% for calls and 4.57% for puts; AON at 7.94% for calls and 7.69% for puts; IBM at 24.96% for calls and 15.22% for puts; and META at 17.46% for calls and 28.59% for puts. Oevrall, the calculations show aggregate MAPE values of 17.42% for calls and 16.15% for puts (2.25 month dividend), and 17.50% for calls and 16.39% for puts (3 month dividend). This indicates that the trinomial model, which accounts for distributions, produces values thah approximate actual option prices.