# Tag Info

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}\...
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 ...
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 \...
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 ...
Accepted

### What is gamma to do with realized volatility?

I like to think about this problem graphically. The pic below shows a call option value at some point before expiry as a function of the underlying. At the expense of stating an obvious fact, we note ...
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 ...
Accepted

### What really is Gamma scalping?

Assuming all else remains equal (implied vol has not changed and very little time decay has occurred), Gamma scalping can best be explained by Gamma (or realized volatility) enhancing the value of a ...
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 ...

### 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}}\\ ...
Accepted

### 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 ...

### 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 $T$ -...

### 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, ...). ...

### What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?

I think I've found the answer to my question (I'm waiting for confirmation from you in the comments) The intuitive difference in this negative sign correlation depends on the position taken on ...