# 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}\...
• 21.1k
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 ...
• 5,911
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 \...
• 21.1k
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 ...
• 6,098
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 ...
• 5,911
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 ...
• 1,068

### What really is Gamma scalping?

Gamma scalping (being long gamma and re-hedging your delta) is inherently profitable because you make 0.5 x Gamma x Move^2 across the move from your option. (You get shorter delta on downmoves, so you ...
• 271
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 ...
• 6,532

### 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}}\\ ...
• 21.1k
Accepted

### Numeric example to understand the effect of option gamma

Using our good friend Taylor, we know that \begin{align*} C(S+\Delta_S)\approx C(S)+\Delta_C\Delta_S+\frac{1}{2}\Gamma_C(\Delta_S)^2, \end{align*} where $\Delta_C$ and $\Gamma_C$ are the call's ...
• 15.9k
Accepted

• 8,059

### 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. ...
• 17.1k

### 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 $T$ -...
• 5,911

### 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, ...). ...
• 15.9k

### 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 ...
• 143
Accepted

• 9,372
Accepted

### Vega and Gamma signs

Usually vega and gamma go in the same direction, but you can have opposite exposure in a calendar spread. For an ATM option, vega decreases closer to maturity while gamma increases. If you implement ...
• 1,886