Monte Carlo method for evaluating cryptocurrency options

This thesis explores the implementation and effectiveness of Monte Carlo simulations to model future Bitcoin (BTC) option prices under both normal and extreme market conditions. The study employs various simulation approaches, including historical daily returns, Geometric Brownian Motion (GBM), and a modified GBM with dynamic drift. By analysing the impact of extreme events on the accuracy of these models, the research aims to provide a nuanced understanding of Bitcoin price dynamics and their implications for financial modelling. The results indicate that while incorporating dynamic drift into GBM improves the accuracy of simulated option prices, significant discrepancies remain due to the heavy-tailed nature of Bitcoin returns and the reliance on historical volatility. The study underscores the need for more sophisticated models to better capture the full scope of Bitcoin price movements, suggesting future research directions in financial modelling and option pricing