Choosing Monte Carlo or PDE Methods for Exotic Option Pricing

Summary

The document compares finite-difference PDE methods with Monte Carlo simulation for pricing options under complex models. In a relatively simple setting such as Black–Scholes with a payoff that does not require modeling volatility convexity, a PDE can be practical. More exotic models may require integro-differential equations, while stochastic volatility, stochastic interest rates, or multi-asset payoffs increase the problem’s dimensionality and computational burden.

The response presents Monte Carlo as a common choice when those added dimensions make PDE approaches difficult. Its rationale is that Monte Carlo scales more favorably with dimension than grid-based methods. The document offers no benchmarks, accuracy comparisons, or discussion of variance reduction, boundary conditions, or cases where specialized PDE solvers remain competitive. Method selection therefore depends on model and payoff structure, and the stated guidance is a broad rule of thumb rather than a universal ranking.

Key ideas

• Finite-difference PDE methods can be suitable for simpler models and payoffs.
• More complex dynamics may require solving an integro-differential equation.
• Stochastic volatility, stochastic rates, and multiple underlyings increase PDE dimensionality.
• Monte Carlo is commonly used for high-dimensional pricing problems.
• The comparison is qualitative and gives no runtime or accuracy evidence.

Tags

# Which method is used to price highly exotic options in exotic models?


# Which method is used to price highly exotic options in exotic models?












What is the go-to method to price exotic options in exotic models?

If we are in Black Scholes, then this is hard to answer, since we can both do various sorts of Monte Carlo or solve various sorts of simple PDEs.

However, in more exotic models, the PDE approach becomes harder since we typically require solving a PIDE.

So my question is, if both the model and the option is exotic, is Monte Carlo then the go-to method? Or do solving these PIDE's still remain competitive enough compared to MC?

## Answer by siou0107 (score 1)

https://quant.stackexchange.com/a/51286

Most of the time the answer will depend on the dimensionality of your problem. If the payoff is simple enough, for example, to have no volatility convexity so that the Black-Scholes model is sufficient, the PDE approach will be enough: you solve by finite differences.

However, if you introduce Stochastic volatility, interest rates or for a multi-asset option, the PDE will become too complex and you will have to use Monte Carlo methods. Those do not suffer from the curse of dimensionality.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.