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I'm no special expert on options and their Greeks. However, I have had a decade plus experience of almost-daily discussions with a bank derivatives desk, on pin risk and the behaviour of autocallable, cliquet etc. structures.
You are correct that a gamma hedge would require an options as opposed to underlying hedge. However, the traders' obsession with gamma ...
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The collar strategy combines one unit of stock with a (long) put option with strike $K_1$ and a (short) call option with strike $K_2$. The payoff of this strategy is exactly $K_1$ if $S_T\leq K_1$, $S_T$ if $K_1<S_T\leq K_2$ and $K_2$ if $S_T>K_2$. The easiest way to see that the statement is false is by comparing the payoff profiles of the collar and ...
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You can take a derivative $\frac{\partial}{\partial m}\frac{\ln m}{m-1}$ at point $m=1$, so you will get $-\frac{1}{2}$.
Yes, Black-Scholes volatility is log-normal volatility.
In other terms it's comparison of Black-Scholes IV and Bachelier IV.
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Try the code below. It consumes less memory and takes about 6 minutes to run.
Please note that when simulating the stock price for purposes of pricing derivatives, we use the risk-neutral stock price process. The drift of the risk-neutral process becomes the risk free rate minus half the square of annualized volatility as indicated in the code.
import numpy ...
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This discussion has also confused me slightly, so I will add something that is possibly clarifying, although most likely will not be. It is also a reminder that I need to stop programming and brush up on options pricing theory.
The Black Scholes hedge portfolio is given by:
$$
\Pi_t = \frac{\partial V}{\partial S}(t,S_t)S_t + \left[1 - \frac{\partial V}{\...
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I have not read the paper except for the Abstract and the Introduction but I completely agree with the OP: The statements by the authors are confusing.
The convergence rate of crude Monte-Carlo is $\mathscr{O}(\frac{1}{\sqrt{n}})$ which is independent of the dimension of the problem. This is arguably THE greatest strength of Monte-Carlo: It avoids the curse ...
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