medium · Quantitative Finance numerical
In numerical finance, the Feynman-Kac theorem justifies using Monte Carlo to solve the Black-Scholes PDE.
What is the main drawback of this 'expectation' approach compared to solving the PDE directly on a grid?
- Requirement that the risk-free rate stay constant across the option's life.
- Slow convergence of the error, which scales as 1/√(M) with the number of paths.
- Extra difficulty incorporating path-dependent barrier or lookback payoff structures cleanly.
- Inability to efficiently handle options written on several correlated underlying assets at once.
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