European Options in BS Markets - Computational Methods for Quantitative Finance - page 56

Fig. 4.1 Option price of
European call ( top )and
digital ( bottom ) option

We set strike K = 100, volatility σ = 0 . 3, interest rate r = 0 . 01, maturity T = 1.

3 and apply the L 2 -projection

For the discretization we use N = 300, θ = 1 / 2, R =

for u 0 . As in Remark 4.1.6 ,weuse K = 1 in the calculations, for which R = 3is

a sufficiently large localization parameter. Using time steps M = O (N) , we obtain

the option prices shown in Fig. 4.1 .
For G 0 =

(K/ 2 , 3 / 2 K) we measure the discrete L 2 (J L 2 (G 0 )) -error defined by ;

M N

2

ε m

2 2 ,

ε m

k m h

2 ,

with

2 :=

1 |

u(t m ,x i ) − u N (t m ,x i ) |

m = 1 i =