2
$\begingroup$

I am trying to come up with a static hedge for a Digital Call with strike K that knocks out when price > barrier H. I know it will involve non-knockout digital calls with strike K and strike H but I am not sure in what proportion and what other digitals I will need to include in the hedge.

Appreciate any advice and suggestions. Thank you in advance

$\endgroup$
1
$\begingroup$

\begin{equation*} \begin{split} \mathbb{1}_{S_T > K, \max_{[0,T]} S_t < H} &\approx \frac{(S_T - (K-\varepsilon))^+ - (S_T - (K+\varepsilon))^+}{2 \varepsilon} \mathbb{1}_{\max_{[0,T]} S_t < H} \\ &= \frac{(S_T - (K-\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H} - (S_T - (K+\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H} }{2 \varepsilon} \end{split} \end{equation*} so you can start with the static hedge of standard knock out calls $(S_T - (K-\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H}$ and $(S_T - (K+\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H}$ if you're already familiar with that.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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