Approximating Delta

Quantitative Finance Level 1

Which of the following is not a good approximation for delta of a call option?

The price of the call divided by the price of the underlying Hedge ratio required to remain delta neutral The rate of change in the price of the call with respect to the underlying The negative of the rate of change in the price of the call as the strike increases The probability that the call will be ITM on expiration

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Calvin Lin by Calvin Lin

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2 solutions

Hi every one .

I got the answer after reading this .

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I'll post a complete solution later on .

A Former Brilliant Member - 6 years, 3 months ago

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I've updated your solution to link to the relevant portion in the wiki :)

Calvin Lin Staff - 6 years, 3 months ago

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Thank you very much sir :)

A Former Brilliant Member - 6 years, 3 months ago
Magyar Atlasz
Sep 27, 2015

A small change in strike price will significantly modify the value of an option with almost the same delta with limited relation to the value of the underlying.

Saying differently: you can have two options for the same underlying with different strike prices therefore having significant differences in the value of the option.

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Hm, how does that explain that "The price of the call divided by the price of the underlying" is not a good approximation of delta, while the rest of the options are reasonably valid?

Calvin Lin Staff - 5 years, 8 months ago

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Just wanted to understand what rate of change meant, I took it as dC/C and dS/S for option price and underlying price respectively?

Yang Yang - 5 years, 4 months ago

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Check out instantaneous rate of change .

The notation "dC/C" makes no sense to me, and I'm expecting another "d-something".

"The rate of change in the price of the call with respect to the underlying" refers to d C d S \frac{ dC}{dS} , where C is the price of the call, and S is the underlying.

Calvin Lin Staff - 5 years, 4 months ago

Think of the 50d px of a 1day to expiry call vs the px of a 50d 10yr to expiry call. Wildy different option value with the same underlying value (assuming constant underlying roll). Hence the call/underlying value has little relevance to delta.

Steve D - 1 year, 3 months ago

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