2
$\begingroup$

I'm looking to price a call option with an exotic feature. The price I'm trying to calculate at time $t=0$ is
\begin{equation} C = E^\mathbb{Q}[(S_T-K_T)^+] \end{equation}

where $S_t$ is the stock price with dynamics \begin{equation} dS_t =\sigma S_t dW_t \end{equation}

The strike price $K_T$ is a stochastic variable given by \begin{equation} K_T = \min\{K_{max}, \max\{K_{min}, \lambda A\}\}, \quad \lambda < 1 \end{equation}

i.e., $K_T\in[K_{min},K_{max}]$, where $A$ is the average price during some future interval $[t_1,t_2]$ \begin{equation} A = \frac{1}{t_2-t_1}\int_{t_1}^{t_2} S_t dt \end{equation}

What is a good and fast way to calculate this and also solve for the implied volatility from market prices?

$\endgroup$

0

Your Answer

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

Browse other questions tagged or ask your own question.