0
$\begingroup$

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ?

Any help would be appreciated.

$\endgroup$
2
$\begingroup$

One does not estimate the local volatility at a given $T$ and $K$. Instead, Dupire's formula actually gives $\sigma(T,K)$ for all $T$ and $K$. $$ \sigma^2(t_0,S_0;T,K)= \frac{\frac{\partial C}{\partial T} + (r - q)K \frac{\partial C}{\partial K} + qC}{\frac{1}{2} K^2 \frac{\partial^2C}{\partial K^2}} $$ where $C(t_0,S_0;T,K)$ are the call prices for maturity $T$ and strike $K$. You can also express this directly in terms of the whole implied volatility surface $\Sigma : (T,K) \mapsto \Sigma(T,K)$.

Once you computed the function, you can evaluate at $T = t$ and $K = S$ or any other value you want.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

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