Chapter 16 - The 5-step method in continuous time

Question 1

Martingale approach vs PDE approach

Answer 1

1. In the PDE approach we have to “guess” the solution, whereas with the martingale approach we do not.
2. The martingale approach provides an expectation that can be evaluated explicitly in some cases and in a straightforward numerical way in other cases.
3. The martingale approach also gives the replicating strategy for the derivative.
4. The martingale approach can be applied to any FT- measurable derivative payment, whereas the PDE approach cannot always.
5. However, the PDE approach is much quicker and easier to construct, and more easily understood because it doesn’t require understanding of stochastic calculus.