John Hull Ito's Lemma

[matiz]

Hi,

On page 227 of this book, the derivative of the equation F = Se^r(T-t) with respect to t is given by

del(F)
----- = -rSe^r(T-t)
del(t)

I do not really understand how this has been worked out. This might be a Math question but any help would be greatly appreciated

Thanks,

 

[Lyosha]

It's worked out by chain rule. First lets rewrite F as F=Se^(rT-rt). T is a constant, r is a constant, S is a constant, t is a variable that we are taking a derivative with respect to.

by chain rule, derivative of F with respect to t = S * derivative of e^f * derivative of (rT-rt) where f is a placeholder for derivation (I don't remember how to best write chain rule out)

derivative of e^t is e^t, since r and T are constants, the derivative of rT is 0, the derivative of -rt is -r.

Multiply across and we get S*e^f*-r = -rSe^(rT-rt)=-rSe^r(T-t)

 

[matiz]

Understood..

Thanks, Alexei