Gamma Exposure

[[email protected]]

Hi David,

I get when you calculate Delta Exposure you use = delta of the position * quantity

However, when you calculate gamma exposure why do you divide the result by 100 = (gamma of position * quantity)/100

The gamma and delta are direct output from kirk spread approximation.

 

[David Harper CFA FRM]

Hi @[email protected] I do not myself divide the result by 100. You can see my recent youtube (with XLS) that includes position gamma, in each of these I'm calculating gamma natively without /100. For example, in my latest (published yesterday), T4-19 below, For an ATM call option S(0) = K = $100, σ = 19.0%, Rf = 3%, T = 0.25 years, q = 0%, I calculate gamma = N'(d1)/[$100.00*0.18*sqrt(3/12)] = 0.04396 where the $100.00 happens to be the stock price:

• Option gamma (FRM T4-15)
• Option delta plus gamma (FRM T4-16)
• Hedging (aka, neutralizing) option delta and gamma (T4-19)

My only thought was maybe somebody does that because an contract option contract is for 100 options, not sure ...

 

[[email protected]]

Hi David,

Thank you so much for the quick reply. Please look at my delta and gamma results
Delta Gamma
0.50025 1.643934
0.50015 4.647395
0.500234 2.325189

These are all at the money options but the gamma's are unreasonably high. I am using finite difference method to estimate gamma.

As a result of large gamma my PNL attributed to gamma is huge.

 

[David Harper CFA FRM]

Hi @[email protected] But those gammas are too high! gamma is the approximate (linear) change in delta per a one unit (in this case, one unit is $1.00) change in the stock price. So, in my example above (my own calculations) where, under a low volatility of σ = 18%, the ATM gamma is 0.04396 when S(0) = K = $100.00. Here the delta, Δ = 0.55106


Now, just increase S(0) by +$1.00 to $101.00. My new delta is exactly 0.59441. The delta increased by exactly 0.59441 - 0.55106 = 0.04335. Notice that my gamma (as an instantaneous linear approximation) 0.04396 is pretty close! Strictly speaking, a gamma of 4.64 implies delta changes by 4.64 when the stock price changes by $1.00 ... doesn't make sense .... unless maybe it has been multiplied by 100 (contract instead of option? such that you are mixing %delta with position gamma, possibly? The percentage deltas look about right for ~ATM or slightly OTM call options). Thanks,

 

[ckwhan]

@david quoting from you "I calculate gamma = N'(d1)/[$100.00*0.18*sqrt(3/12)] "

i read somewhere the gamma is N'(d1) * Exp(-q*t) / (s * v *sqrt ( t ))

could you advice on the above? Thank you.

 

[David Harper CFA FRM]

HI @ckwhan Yes, your formula for gamma is correct. I was referring to the same gamma for a non-dividend-paying stock such that q = 0, where q is the dividend yield, and exp(-qt) = exp(0) = 1.0. Yours is better because it's more general. Thanks,