Hot answers tagged option-pricing
6
A simple intuitive answer why the OTM Call is more expensive than the OTM Put is because of the skewness of the log-normal distribution. Think about it, what is the probability that the stock price is above 110 at expiration and what is the probability it is below 90? This should answer your question.
Written in probability terms:
The median of the ...
4
The put call parity is given as follows:
$$c_t-p_t = S_t - \frac{X}{e^{r(T-t)}}$$
If you assume $r=0$, you get
$$c_t-p_t = S_t - X$$
So, $c_t \neq p_t$.
The rationale behind it is much more financial than mathematical. You have to look at the payoff on both side of the equation, and you see that both portfolio will give the same payoff at time $T$ (the ...
2
On a single-option basis, there is this paper comparing methods by Mark Joshi. It doesn't specifically examine portfolios, but there's a reason for that. Portfolio and scenario computations are embarrassingly parallel, so once you have achieved your most efficient available option pricer, the rest is simply about wise distribution of your computational ...
1
For part (d), instead of using Girsanov's theorem as phubaba suggested, I believe that we can state directly that the price is
$$V_t = e^{-r(T-t)} \mathbb{E}^Q \left[ u(S_T-K) \middle \vert \mathcal{F}_t \right],$$
where $u$ is the step function, $Q$ is the risk-neutral probability measure, and $\mathcal{F}_t$ is the filtration at time $t$, since the value ...
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