Quantitative Pricing of Complex Convertible Bonds Based on The Geometric Brownian Motion Model Via Monte Carlo Simulation

Abstract

Convertible bonds are crucial derivatives in quantitative finance. Their complex terms like automatic redemption and barrier prices, coupled with stocks’ dynamic pricing features, pose precise pricing challenges. Traditional analytical methods struggle to capture the interactions among multiple factors. Thus, this study develops a quantitative pricing framework for complex convertible bonds by integrating the geometric Brownian motion (GBM) model with Monte Carlo simulation. Using Tesla’s closing prices from January 6, 2020, to January 11, 2022, as the sample, this article estimated the GBM parameters (drift rate is 0.4428 and volatility is 1.2866) via log returns. Finally, this paper simulated 10,000 future one-year stock price paths and retained 4,895 valid paths after normal distribution filtering. Based on risk-neutral pricing theory, this paper priced a 13.25% p.a. USD Autocallable Barrier Reverse Convertible issued by Credit Suisse London Branch (face value USD 5,000). The theoretical price was USD 3,593.87, and repeated simulations show the price stabilizes above USD 3,500. Risk analysis reveals that 72.54% of valid paths indicate a stock price decline after one year, and 37.4% of valid paths trigger barrier clauses (consistent with 2022-2023 actual trends), validating the framework’s feasibility.