Advances in Risk Management

HAYETTE GATFAOUI 129

6. WhenμI(It)=λε−

(

2 −λ

)

ln(It),σI(It)=

√

ln (It), andIt>1;R(t,It)=β^2 γ^2 t^2 α+

ln(It). Then,R(t,It)=ln (It) whentis infinity, and variance follows a mean revert-

ing square-root processdR(t,It)=λ[ε−R(t,It)]dt+

√

R(t,It)dWIt. However, we avoid

logarithmic specifications, which require values of random variables to be above unity.

7. We assumed some specific constraints such that:
   ∫T

t

σV(s,Is)ρ(s,Is)dWˆIs= 0

conditional onGt. Such constraints are compatible with our following framework.

Simulations were undertaken with respect to such constraints insofar as we selected

the simulated paths satisfying this criterion while computing the firm value (that is,

call pricing).

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