Gamma and Delta-Hedge

CFA Level III Derivatives
#1

Hi all,

I found the following question online and it seemed wrong. I mean the gamma will be higher if the underlying is constant near the strike price.

I think it’s a Schweser, they say the correct answer is large movements upward or downward… A)

QUESTION---------------------------------------------------------------------------------------------------------------------

In delta-hedging, gamma would be important if the price of the underlying asset:

A) had a large move upward or downward. B) had a large move upward only. C) remained constant.

Your answer: C was incorrect. The correct answer was A) had a large move upward or downward.

Gamma refers to the change in value of delta given the change in value of the underlying stock. Typically, larger swings in the price of an asset will cause larger changes in delta, thus impacting the delta hedge. This means that the larger the move in the underlying asset in either direction, the more important is the second-order gamma effect.

#2

Delta hedging is a dynamic strategy: if delta changes appreciably, you need to change the number of options in your hedge.

Gamma tells us how much delta will change for a change in the price of the underlying; therefore, gamma is important if and only if there is a change in the price of the underlying. Thus, A is correct.

#3

There…that’s better. cheeky

#4

wink

#5

Well,

Considering an option that is way inside the money, the delta on the option is going to be near 1 and, I am sorry, but a large move in the underlying is not going to change the delta significantly considering the fact that our gamma is near zero.

On the other side, considering an option that is at the money, even if the underlying is almost static the gamma is going to be way bigger.

I mean:

  • I am delta-hedging my portfolio, dynamically, yeah))

  • My stock price is not moving and is ATM

=> I am watching my hedge VERY CLOSELY and my stock price is constant. In fact, my gamma is at the stars, is very important.

The question makes a direct link between dStock/** dTime **** (Volatility) to (d^2Option)/(dStock)^2 (Gamma),** two different things or dimentions… Very misleading indeed.

#6

That’s the point: gamma has one effect when it’s near zero and another when it’s large.

But the effect of those differences appear only with large changes in the price of the underlying. If the price of the underlying doesn’t change, gamma doesn’t matter.

#7

Don’t you mean gamma is important if volitility high?

#8

With all due respect,

Difference in gamma, where are you going?! You want to derivate once more?

I just took an example where a small change in your underlying is having a major impact on your delta-hedge.

But, yes, you are right, Big Volatility has more chances of changing… everything.

Just find the question wrongly simplified, thanks for your time Magician, I see your point,

#9

Nope. Think about it. The less volatile the stock is, the lower the option price, and the more delta varies with changes in price, so gamma is higher.

If the stock was volatile, and I mean _ really _ volatile, you’d have a delta close to one no matter where the stock price is at the moment, and gamma would be low due to the insensitivity of change in price to change in delta.

#10

Then the option was at the money, all else equal.

#11

Makes sense. Thanks

#12

MrSmart,

That’s the point, the strike price and not mentioning it, all the other conclusions, have no sense.

Where is the strike, where is the strike? Despair and d***ation.

But I’ll write a novel on it after the L3.

All else equal,

#13

When you say “I just took an example where a small change in your underlying is having a major impact on your delta-hedge.”, then the question, or example, must have had a strike price mentioned.

If not, then it is justifiably assumed that the option is at the money. Because this also has to do with more than gamma.