Nonlinear Option Pricing

Fully nonlinear PDEs 419

Table 13.13: Monte Carlo price quoted in percent as a function of the number

of Monte Carlo paths 2

N

. T = 1 year. Exact price −

σ

2

2

ln



1 −

2

3

T



= 2.20.

β = 1, σ = 0.2, g(x) = x

2

/3. Blow up for T ≥ 1.5 as expected.

N Fair Stdev

12 2.01 0.09

14 2.40 0.08

16 2.14 0.09

18 2.19 0.03

20 2.20 0.02

diffusion algorithm described in Section 13.5. From a numerical point of view,

our algorithm can deal without any modification with this infinite-dimensional

system. Up to the maturity T , we generate species.

This approach can be generalized for a fully nonlinear PDE

∂

t

u + Lu + f(t, x, u, Du, D

2

u) = 0

where f is a polynomial in u, Du and D

2

u.

We have numerically ...