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5

[Short answer] IMHO there is a fundamental problem with wanting to extract a sound implied volatility figure out of a deep ITM option's price. You should use out-of-the-money forward options (OTMF) instead: put options for strikes smaller than the forward price (left wing of the volatility surface) and call options otherwise (right wing of the volatility ...


4

Typically when running a Monte Carlo simulation we might simulate an SDE similar to $$ \dfrac{dS}{S} = \mu\:dt + \sigma \: dW(t) $$ by some appropriate method (e.g. Euler-Maruyama, Milstein, etc). We notice by dimensional analysis that if $t$ is in units of $\textrm{years}$ then $\mu \sim \textrm{years}^{-1}$ and $\sigma \sim \textrm{years}^{-1/2}$. ...


2

I would definitely recommend Volopta as a reliable source of self-contained and commented financial engineering source codes (useful for prototyping/understanding but clearly not production code). I have for instance copy-pasted, the explicit PDE solver you are looking for (centred in space, backward in time) below (+ edited for clarity + improved ...


1

Assuming deterministic interest rates, the price of an American call option struck at $K$ and expiring at $T$ is given by $$ V_0 = \text{sup}_{\tau \in \mathcal{T}[0,T]} \mathbb{E}_0^\mathbb{Q}\left[ e^{-r\tau} \max(S_{\tau}-K, 0) \right] $$ where $\mathcal{T}[0,T]$ denotes a family of stopping times with values in $[0,T]$ and where, under the risk-neutral ...



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