# Tag Info

Accepted

### Is there anywhere I can read the paper, "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves"

Partly because it's hard to get a hold of, the Arslan et. al. paper is starting to assume mythical proportions. As said by Dimitri Vulis, the general idea of the paper is set out in (one or two of) ...
• 5,087
Accepted

### Gamma Pnl vs Vega Pnl

For an option with price $C$, the P$\&$L, with respect to changes of the underlying asset price $S$ and volatility $\sigma$, is given by \begin{align*} P\&L = \delta \Delta S + \frac{1}{2}\...
• 20.5k
Accepted

### American Options relation between greeks

No, you should not expect such a relationship to hold in general. The reason is that American options have an "exercise barrier" which European options don't, and this results in different prices and ...
• 5,638

### Expectation of Gamma times S$^2$ in Black-Scholes model

What you have to do is to show that the dollar gamma satisfies the Black-Scholes PDE. Using Feynman-Kac it then follows that the dollar gamma is an expectation of a "payoff", just like the ...
• 5,087
Accepted

### Link between Vega and Gamma

Under the Black-Scholes model, \begin{align*} Gamma &= \frac{N'(d_1)}{S \sigma \sqrt{T-t}}\\ Vega &= SN'(d_1) \sqrt{T-t}. \end{align*} Then, it is easy to see that \begin{align*} Vega = S^2 \...
• 20.5k
Accepted

### Is short-gamma inherently a losing strategy?

You can't lose more than you invested by writing covered puts, because you keep enough cash to cover any potential losses from the puts. That's not to say that your losses can't be substantial, of ...
• 5,638

### Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?

the problem is that the pay-off has discontinuous first derivative. Try a contract with pay-off that is twice differentiable and it will probably work. The problem is that all the value comes from ...
• 6,763
Accepted

### How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?

Options on interest rates futures in the listed markets are always traded 1-yield (100-yield) just like the futures which are traded 1-yield. So negative rates aren't an issue and its always black ...
• 782
Accepted

### Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option

Gamma and vega have the same general shape , peaking at ATM and tapering to the tails. But gamma concentrate as the option gets closer to expiry (when vega is small). For options a long way from ...
• 1,018

### Expectation of Gamma times S$^2$ in Black-Scholes model

The conjecture is true when the interest rate is zero. Note that, from this question, under the Black-Scholes model, \begin{align*} \Gamma(t,S_t) &= \frac{N'(d_1(t))}{S_t \sigma \sqrt{T-t}}\\ ...
• 20.5k
Accepted

• 7,301

### What really is Gamma scalping?

As long as you live in a world where implied and realized vol are the same, there is no net profit (or loss) from gamma scalping. However, if they are different, then you make a gain or loss which is ...
• 794

### Gamma Pnl vs Vega Pnl

Not sure this is a valid question! Gamma p/l is by definition the p/l due to realized volatility being different from implied. Vega p/l is by definition the p/l due to moves in implied volatility. ...
• 14.3k

### How to prove Gamma is the same for a European call and European put with the same inputs?

Put-call parity says that a call and put (worth $C$ and $P$ respectively) with the same strike $K$ have the following relationship with the spot rate $S$, risk-free rate $r$, and time to maturity $T$ -...
• 5,638

### Gamma for ATM options with low spots

Gamma is the sensitivity of the delta with respect to infinitesimal changes in the price of the underlying asset (in whatever unit your underlying is nominated, typically dollar, pounds, euros, ...). ...
• 14k

### is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?

if you have a portfolio of calls and puts with the same maturity then your portfolio is gamma neutral if and only if it is vega neutral. The reasons is that the BS gamma divided by the BS vega is a ...
• 6,763
Accepted

• 20.5k

### What is the formula for beta weighted delta and gamma?

I've started thinking about this, too. My gedanken conclusion turned out to be too simple once I found what I was after: http://www.investment-and-finance.net/derivatives/o/option-beta.html, which I'...
• 346