ExpertMultiple choice

Stepping the heat equation · Part 3 of 3

You price a European option by transforming the Black–Scholes equation into the heat equation $u_t = u_{xx}$ and stepping it on a grid with spacing $\Delta x$ and time step $\Delta t$ . Write $\lambda = \Delta t/\Delta x^2$ .

You switch to Crank–Nicolson with $\lambda = 5$ to take large steps. Prices look fine, but gamma oscillates near the strike for the first few steps. What is the standard fix?

AStart with a few fully implicit steps, then switch to Crank–Nicolson
BNothing can be wrong, because Crank–Nicolson is unconditionally stable, so the oscillations must be a coding error
CSwitch to the explicit scheme at the same step size
DHalve $\Delta x$ and keep $\Delta t$

The worked solution is in Premium

The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.

Start the 7-day free trial Practise it with Premium

Learn the method

ODE and PDE solvers: finite differences and stability

You switch to Crank–Nicolson with λ=5\lambda = 5λ=5 to take large steps. Prices look fine, but gamma oscillates near the strike for the first few steps. What is the standard fix?

More numerical methods questions

You switch to Crank–Nicolson with $\lambda = 5$ to take large steps. Prices look fine, but gamma oscillates near the strike for the first few steps. What is the standard fix?