Linked Questions

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 ...
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 ...
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 ...
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 ...
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 ...
1 vote
3 answers
442 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. ...
0 votes
1 answer
225 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 ...
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 ...
8 votes
1 answer
8k views

Effect of volatility on the delta of a call option

In the book 'Dynamic Hedging', Nassim Taleb writes: ...
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 ...
1 vote
1 answer
956 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 ...
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 ...