# Tag Info

Accepted

• 16k

### Effect of Implied volatility on option delta

In the Black-Scholes-Merton model, with model option price $V$ as a function of underlying price $S_t$, strike price $X$, continuously compounded risk-free rate $r$, continuously compounded dividend ...
• 6,822

### How is delta defined as a unit?

If you want to split hairs, as I like to do, there are 2 ways to express Delta. "Pure Delta" is a fraction, i.e. a number between 0 and 1 (for a Call). In terms of units, it is a pure number....
• 11.5k

• 5,043
Accepted

### Bartlett's delta gives wrong signs for calls and puts

Bartlett's delta as computed in your code is a simple finite difference (FD), also called bump and reprice, of the Black values. I do not think there is anything wrong here, besides the fact that you ...
• 9,024

### Delta of Black formula vs numerical

Your Delta_fd is forward delta (you're bumping the fwd). Delta is spot delta. Hence the discount factor.
• 1,426

### What is the relationship between Time-To-Expiry and Delta?

You are looking for the Greek commonly referred to as Charm. This is a quick visualization with a good chart I found on Google: https://www.optiontradingtips.com/greeks/charm.html
• 376

### Calculate strike from Black Scholes delta

Just to skip to solution from the aforementioned paper: For a volatility surface of Delta $\Delta$ vs volatility $\sigma$, we can calculate the strike $K$ with underlying $f$,$\phi$ is 1 for call, -1 ...
• 171

### Why isn't the delta of a slightly in the money American option 1?

The delta is only 1 if the option is certain to be exercised. This is not the case if it is ‘slightly in the money’. If it is deep in the money, such that immediate exercise is optimal , then the ...
• 17.2k

• 12.5k

### why Delta increases as interest rate increases

Just to strengthen the intuition in the perfect answer above: With r going very high (and hence F), all prices on cash instruments are expected to gain fast with time (to compensate for the carry) and ...
• 1,412

### Interest Rate Risk - The Greeks

Receiving fixed on an IRS is both long delta and long gamma. The delta is obvious. The gamma is because the long position in delta increases as rates go down, and decreases as rates go up. Swaps ...
• 17.2k
Accepted

### Option delta - Conditional probability definition?

IMHO the 'definition' you mention is not a mathematical definition per se, but rather an approximation used by some practitioners. Mathematically, it is $N(d_2)$ in the BS formula which figures the ...
• 14.7k
Accepted

### Why " Even if the underlying asset price remains unchanged, the option delta for an in-the-money option increases as expiration nears"

@Kiwiakos gave you the intuition. Here is the corresponding analysis that you asked for. The European plain vanilla call delta is given by \frac{\partial C_0}{\partial S_0} = \...
• 6,064
Accepted

### What is the relationship between Time-To-Expiry and Delta?

Here is a page from The Options Guide with an understandable picture. They explain, As the time remaining to expiration grows shorter, the time value of the option evaporates and correspondingly, ...
• 739

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