Stochastic Modeling and Efficient Simulation of Brent Crude Option Prices
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Khulkhachiev Savr
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This study analyzes Brent crude oil call option pricing by integrating the Black–Scholes analytical model with Monte Carlo simulation enhanced by a control variate. Historical daily closing prices of Brent crude from July 2007 to December 2024 (Yahoo! Finance) are used to calibrate asset dynamics. The Black–Scholes formula provides a theoretical option price under the assumption of constant volatility. The Monte Carlo simulation generates numerous stochastic price paths under a Geometric Brownian Motion model, yielding an initial option price estimate of $10.66 (with mean simulated oil price $73.31 and volatility $28.71 at one year). By using the Black–Scholes value ($10.16) as a control variate, the Monte Carlo estimate is adjusted to $10.16, effectively reducing variance. These results demonstrate that combining analytical and numerical methods yields robust option price estimates and better captures market uncertainty.
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Authors
Khulkhachiev Savr
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References:
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