Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In Stein-Shakarchi's book Fourier Analysis (p. 170), the solution of the Black-Scholes equation $$\frac{\partial V}{\partial t}+rs\frac{\partial V}{\partial s}+\frac{\sigma^2s^2}{2}\frac{\partial^2 V}{\partial s^2}-rV=0$$ for $0\lt t\lt T$

with boundary condition $V(s,T)=F(s)$, is given as

$$V(s,t)=\frac{e^{-r(T-t)}}{\sqrt{2\pi\sigma^2(T-t)}}\int_0^\infty e^{-\frac{(\log(s/s^*)+(r-\sigma^2/2)(T-t))^2}{2\sigma^2(T-t)}} F(s^*)\,ds^*.$$

My own derivation shows that $ds^*$ in the formula should be replaced by $$\frac{ds^*}{s^*}.$$

Is this a typo in the book?

share|improve this question
    
That is not really the Black and Scholes equation, which is stochastic. –  AD. Nov 13 '10 at 6:11
    
That is what the book calls it. –  TCL Nov 15 '10 at 14:31

1 Answer 1

up vote 1 down vote accepted

I have checked my derivation thoroughly, and I believe now that it is a typo.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.