Determining the price of option contracts is a crucial aspect of financial markets, particularly for investors aiming to manage risk and make informed investment decisions. In this study, the price of an Asian call option is calculated using the Monte Carlo Stratified Sampling method based on the stock price data of Tesla, Inc. (TSLA) from January 2021 to December 2023. This method has been proven to reduce variance compared to the Standard Monte Carlo simulation, leading to faster price convergence and more efficient results. The parameters used in the simulation include the initial stock price  (S_0), number of simulations (N), maturity time  (T)dividend = 0, risk-free rate (r), strike price ( K), and volatility

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 (?) (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.
 
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Measuring performance solely by relying on returns is probably not enough, it is important to consider both returns and risks. Some measurement methods that consider both of these factors are the Sharpe Ratio index, Treynor Ratio, Jensen Alpha, and Information Ratio. Risk analysis using Value at Risk Monte Carlo simulation is also important to determine the potential for extreme risks. The purpose of this study is to provide a good understanding of the performance and risk of mutual fund investments. Based on the performance results, Schroder is the most superior mutual fund, with the highest Information Ratio, Sharpe Ratio, and Jensen Ratio, indicating that they are able to generate good returns considering the risks taken. However, Schroder also has the highest VaR, meaning it has the potential for large losses in the worst market conditions. On the other hand, MNC is at the bottom in almost all performance methods, indicating poor performance with low returns and lower risks.