Monte Carlo Derivative Valuation by Simulating the Underlying Asset

Summary

The document addresses whether geometric Brownian motion should be applied directly to a call option or to its underlying asset when using Monte Carlo valuation. Its answer describes the usual approach: specify a stochastic process for the underlying price, simulate many possible paths of that process, and calculate the derivative’s value from the resulting outcomes. It cites a general Monte Carlo reference that describes simulation in terms of underlying prices and other relevant risk factors.

The explanation is brief and does not derive the call payoff estimator, discuss risk-neutral drift, or provide convergence and variance-reduction methods. It also does not claim that an option price can never be modeled as a stochastic process; rather, it presents underlying-path simulation as the standard valuation setup. A practical model must choose dynamics suited to the underlying and valuation purpose, since basic geometric Brownian motion may omit features such as stochastic volatility or jumps.

Key ideas

• Monte Carlo derivative valuation usually simulates paths of the underlying asset and then evaluates the derivative payoff along those paths.
• Geometric Brownian motion is one model that can be assumed for the underlying price process.
• The document presents direct GBM simulation of the call itself as distinct from the usual underlying-based valuation method.
• The brief explanation omits risk-neutral setup, payoff estimation details, and convergence analysis.
• Basic GBM may be insufficient when the underlying exhibits features such as stochastic volatility or jumps.

Tags

# Question about the process of monte carlo simulation


# Question about the process of monte carlo simulation












I have encountered an interesting question. Is it better to simulate the geometric brownian motion process for call itself or GBM for the underlying.

My question is can we actually apply GBM to call? is it possible?

## Answer by Forrest (score 2)

https://quant.stackexchange.com/a/37507

LocalVolatility's comment is correct. Just to provide a reference, the below is from Monte Carlo Methods in Financial Engineering by Paul Glasserman:

"Valuing a derivative security by Monte Carlo typically involves simulating paths of stochastic processes used to describe the evolution of underlying asset prices, interest rates, model parameters, and other factors relevant to the security in question."

The general idea is to assume the underlying price follows GBM and then simulate many price paths.

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