1
$\begingroup$

I want to show whether the following price at t is of a european option in Black-Scholes Framework. $$S_tlog_e (S_t^3) $$ Is it just trying to substitute the function (and partial derivates) in the Black-Scholes PDE?

$\endgroup$

2 Answers 2

7
$\begingroup$

Yes it is actually just substituting it into the Black Scholes PDE. If the PDE is satisfied, $V(t,S(t)),t\ge 0$ is a martingale and hence $V(t,S(t)) = E_t (V(T,S(T))$ so that $V(t,S(t))$ is the expected value, at time t, of an option that pays $V(T,S(T))$ at time $T$. Here I assumed $r=0$ for simplicity

$\endgroup$
1
$\begingroup$

If it was a solution to a European option PDE pricing problem, at time $T$ you have $V(T,S) = S \log{S^3}$.

Based on this terminal function, you can then solve the BS PDE using a semi-analytical approach to find $V(t,S)$. My guess is it will not be the candidate you posted (haven't checked).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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