Pricing China 50 ETF Calls with BSM and Monte Carlo Simulation
Summary
The article outlines a Monte Carlo approach to pricing European calls on the China 50 ETF under the Black-Scholes-Merton framework. It divides the life of the option into time steps, simulates the underlying price with normally distributed shocks, calculates each path’s payoff at expiry, and discounts the average payoff at the risk-free rate. Volatility is estimated from historical log returns and annualized. The article presents the method as a starting point for option strategy research, while omitting a full derivation of BSM and the simulation method.
The reported model values differ considerably from observed closing prices. The author attributes this gap to the finite number of simulations, simplifying BSM assumptions, and the volatility estimate, and suggests improving the volatility calculation. Historical volatility alone may not reflect market-implied expectations, so the example is not a reliable standalone quote or evidence of a profitable trading strategy. No detailed numerical results or validation procedure are included.
Key ideas
- The method simulates underlying prices under BSM dynamics and averages discounted European call payoffs.
- It estimates annualized volatility from historical log returns.
- The article reports substantial differences between simulated estimates and market closing prices.
- Finite simulation samples, model assumptions, and volatility estimation limit pricing accuracy.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.