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4

You are trying to price an option through Monte Carlo simulations. Here is how it should work, assuming the Black-Scholes diffusion framework. Under the Black-Scholes model's assumptions, the value of a risky asset $S$ at the time $t=T$ is a random variable which reads $$ S_T = S_0 e^{\left(\mu-\frac{\sigma^2}{2}\right)T + \sigma \sqrt{T} Z}\tag{1}$$ with ...


2

First of all, it is not conceivable to do all that work by hand! You are crazy to have just thought it! Second, if you want to repeat your work with different datasets, I suggest you to use R, since, once you have written a script, you can use it all the times you want. But, there's a 'but': you cannot think we are going to write some code for you (you ...


2

It is true that FF always use December for their fundamental metrics as this is the end of the fiscal year for most companies. However, the annual reports of the companies are not directly available and so are fundamental data. Thus, the main reason for using June it to avoid look ahead bias.


1

The most common approach is to calculate returns as $r_t=\frac{p_t-p_{t-1}}{p_{t-1}}$ or $r_t=ln\left (\frac{p_t}{p_{t-1}}\right)$ using close prices at the end of the month.


1

APT assumes that idiosyncratic risk is zero on average: $E[e_i]=0$. The law of large numbers. From 1 and 2 it follows that as N increases, the weighted sum of idiosyncratic risks will converge to zero: $\lim\limits_{N\to\infty}\sum\limits_{i=1}^N e_p=\lim\limits_{N\to\infty}\sum\limits_{i=1}^N w_ie_i=0$ Strictly speaking some restrictions on the weights ...



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