# Tag Info

1

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.

1

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 ...

2

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 ...

1

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}{\...

1

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 ...

0

The paper takes each observed smile, bumps all of the strikes by a shift term to make them positive, and the fits a SABR smile to them. When I do the same thing with the dataset you've attached above (I remove the -150 point because it's vol of 0.0 breaks things) I get the following 'smiley' fit, which looks similar to the results presented above: This was ...

4

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 ...

4

SHORT STORY: forward Libor rates need not be assumed to be log-normally distributed. For example, they can be assumed to be normally distributed (and indeed, on Bloomberg, Swaption implied vols are quoted both, in terms of normal as well as log-normal models). The only condition required is that the forward Libor rate process needs to be a martingale under ...

5

A lognormal distribution has three valuable properties (I) It ensures that the rate is only allowed to be positive; (II) the changes in the interest rate are proportional to the interest rate; and (III) the option price is analytically solvable. BTW, just to be precise, note that in Black's model, it is an assumption that the distribution of the interest ...

Top 50 recent answers are included