Application of Conditional Monte Carlo Simulation in Determining European Option Contract Pricing (Case Study on Toyota Motor Corporation (TM) Stock)

Abstract

When making investment decisions, it is crucial for investors to consider various risks that may arise, both in the short and long term. One method to measure risk is through volatility. Volatility represents a statistical measurement of the degree of price variation over a specific period, expressed as volatility (σ) (Aklimawati & Wahyudi, 2013). This study aims to discuss the pricing of European option contracts using Conditional Monte Carlo simulation and the Black-Scholes method. The data used in this study is secondary data obtained from Yahoo Finance. The data consists of quantitative information, namely the monthly closing prices of Toyota Motor Corporation (TM) stock, spanning 5 years from July 1, 2019, to July 1, 2024, yielding 60 data points. In this research, the pricing of European call option contracts was calculated using Conditional Monte Carlo simulation and the Black-Scholes method. The study concludes that European option contract pricing can be determined using two methods: Conditional Monte Carlo simulation and the Black-Scholes method. Conditional Monte Carlo simulation can be employed to calculate European option prices in a structured manner, utilizing stochastic volatility estimated through the Ordinary Least Squares (OLS) method. The two methods yield differing option prices; Conditional Monte Carlo simulation produces lower option price estimates with relatively lower error values compared to the Black-Scholes method at every strike price. The lower estimates from Conditional Monte Carlo simulation are due to its consideration of stochastic changes in volatility, whereas the Black-Scholes method results in higher prices due to its assumption of constant volatility. The comparison demonstrates that Conditional Monte Carlo simulation provides cheaper price estimates under market conditions with non-constant volatility, despite requiring higher computational time compared to the Black-Scholes method.

,