Linked Questions

8 votes
4 answers
6k views

Why do ATM call options have a delta of slightly bigger than 0.5 and not 0.5 exactly?

From the formula of the delta of a call option, i.e. $N(d1)$, where $d_1 = \frac{\mathrm{ln}\frac{S(t)}{K} + (r + 0.5\sigma^2)(T-t)}{\sigma\sqrt{T-t}}$, the delta of an ATM spot call option is ...
inquisitive's user avatar
8 votes
1 answer
8k views

Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
Victor123's user avatar
  • 1,404
7 votes
1 answer
1k views

How to explain the asymmetry of vanilla Volga?

I've plotted the charts of Volga of Vanilla Call/Put using finite difference method, and found they are the same, and an asymmetrical shape of observed for both. Any intuitive way to explain the ...
Ang Yiwei's user avatar
  • 129
5 votes
3 answers
2k views

Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...
Trajan's user avatar
  • 2,492
4 votes
5 answers
10k views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
Trajan's user avatar
  • 2,492
2 votes
1 answer
2k views

Paradox in option expiry as volatility goes to infinity

As volatility goes to infinity, the delta of a call option goes to 1. The delta approximates the probability that the option expires in the money. So it seems that the probability of expiring in the ...
user9081230912390's user avatar
2 votes
3 answers
6k views

FX Delta Conventions

I'm currently reading Iain Clark's book Foreign Exchange Option Pricing and I got stuck at one sentence in the beginning of Section 3.3 that I feel is important to understand. He writes: FX ...
DoubleTrouble's user avatar
2 votes
1 answer
1k views

Probability of exercise in the Black-Scholes Model

What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to ...
Xavi Hernandez's user avatar
1 vote
3 answers
441 views

Implied volatilities for different options that track the same stock

I have a somewhat basic question regarding option prices. Suppose we have an underlying stock and two different options (that have different strike prices, maturities, etc.) that track this stock. ...
lithium123's user avatar
1 vote
1 answer
955 views

Black-Scholes: Delta/probability of exercise increases with volatility

The delta for an ITM call option with increasing volatility initially decreases, reaches a global minimum, and then increases. If we consider delta as a representation of risk-neutral probability of ...
Trent Di's user avatar
  • 125
0 votes
1 answer
222 views

No Probability in Greeks

In an interview, I was once told that I should not consider probability when talking about option greeks since from a mathematical point of view greeks have nothing to do with probability. That is of ...
Mining's user avatar
  • 165
0 votes
0 answers
43 views

How does implied volatility affect delta and gamma for different spreads? [duplicate]

Im looking at a call butterfly spread where i am long one ITM and OTM call option, and short two ATM call options. Also i have a time spread where i am long December put and short November put. Now ...
SnG's user avatar
  • 101