f0=1, alpha=1.23%, nu=27.48%, rho=11.48%, beta=0%, tau=10 y

FIGURE 6.6: Exact conditional probability for the normal SABR model versus numerical PDE.

Performing the integration according to a leads to an exact solution for a European call option for the normal SABR model

C(T,K|f0) = √

ν √

dt e−

b(amax − amin)e− b 2

4t√ cosh b− cosh lmin

db

+ max(f0 −K, 0) with amin, amax and lmin defined by (6.57,6.58,6.59).