Authors: Farid Soroush
The valuation of financial derivatives, particularly options, has long been a topic of interest in finance. Among the various methods developed for option pricing, the Monte Carlo simulation stands out due to its versatility and capability to model complex financial instruments. In this article, we apply the Monte Carlo method to price European options using two prominent models: the Geometric Brownian Motion (GBM) and the Heston model. While the GBM model assumes constant volatility and offers simplicity, it often falls short in capturing real market dynamics. Conversely, the Heston model introduces stochastic volatility, providing a more nuanced representation of market behaviors. Leveraging the computational efficiency of C++, our simulations reveal distinct price paths for each model. The GBM paths exhibit smooth trajectories, while the Heston paths are more varied, reflecting its allowance for stochastic volatility. Statistical analyses further underscore a significant difference in the final stock prices generated by the two models. The Heston model's prices display a broader distribution, capturing the model's inherent variability. Additionally, autocorrelation analyses suggest a more intricate autoregressive structure for the Heston model. In conclusion, while the GBM model provides simplicity and predictability, the Heston model offers a richer, albeit more complex, representation, especially in volatile market scenarios. This article offers a comparative study of the GBM and Heston models, shedding light on their utility under varying market conditions.
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[v1] 2023-08-07 02:12:42
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