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# Delta of Short EUR Call Option

#### rahul.goyl

##### Member
Hi David,

What is the delta of a short position in 1000 European call options on silver futures? The options mature in eight months, and the futures contract underlying the option matures in nine months. The current nine-month futures price is $8 per ounce, the exercise price of the options is$8, the risk-free interest rate is 12% per annum, and the volatility of silver is 18% per annum.
a. 122.2
b. 585.5
c. 488.6
d. 765.4

I am clueless how to go about, may be d1 & d2...

Thanks
Rahul

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Rahul,

I used the BSM XLS to get the answer, please see here:
http://sheet.zoho.com/public/btzoho/sep3-shortcall

i get negative (-) 488
(it's a nit but the answers are "position deltas", where position delta = percentage delta * quantity, such that a call option has a postive percentage delta and a short call position has a negative position delta.
So here: + 0.488 percentage delta/call option * (-)1,000 quantity of short call options [i.e., long = +, short = -] = -488 position delta)

this question is totally astray from the exam, you'd never see it (nor are the two nuances even remotely testable), you need Hull Chapter 16 on Future Options (i.e., you'd have to know that the d1 is different, see calc)...

David

#### rahul.goyl

##### Member
Hi David,

Thanks a lot for the detail XLS, you are always damn quick.....
yeah this looks astray to me but better to prepare ourselves...
I have a doubt in the formula you used for d1

The book formula is d1 = ln(So/K)+(r+Variance/2)t / Vol*sqrt(t)
However you didn't use r in XLS, but you discounted the Nd1 to PV by -12%*t to arrive at d1 = Delta 0.4886
Could you please elaborate why you didn't do it according to book formula.

Thanks
Rahul

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Hi David,

for Problem 19.10, in your calculation of d1, why don't you include Rf of 12%?
I understand the calculation of d1 to be: [LN (S/K)+ {Rf+(Vol^2/2)}*T]/(vol*SQRT(T))

View attachment 2616

@elena77

Please note that I moved your question here to this thread that discusses this Hull End of Chapter question (these are not David's questions.)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @elena77 See below (Hull 18.7), d1 for options on futures is slightly different, and more advanced. Hull 18.6 actually shows the derivation. Thanks, #### elena77

##### New Member
Subscriber
Thank you David, understod.

#### San955

##### New Member
Hi David and everyone,

Delta of a long call option= N(d1) and of a short call= N(-d1)
However, in 19.10:

What is the delta of a short position in 1,000 European call options on silver futures?
The options mature in 8 months, and the futures contract underlying the option matures
in 9 months. The current 9-month futures price is $8 per ounce, the exercise price of the options is$8, the risk-free interest rate is 12% per annum, and the volatility of silver
futures prices is 18% per annum.

According to Hull solution:

e^-rt*N(d1)
N(d1) = 0.4886
A delta of a short position is -488.6.

Is delta of a call option on futures calculated wrong or not?

Thank you!

Last edited:

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Hi David and everyone,

Delta of a long call option= N(d1) and of a short call= N(-d1)
However, in 19.10:

What is the delta of a short position in 1,000 European call options on silver futures?
The options mature in 8 months, and the futures contract underlying the option matures
in 9 months. The current 9-month futures price is $8 per ounce, the exercise price of the options is$8, the risk-free interest rate is 12% per annum, and the volatility of silver
futures prices is 18% per annum.

According to Hull solution:

e^-rt*N(d1)
N(d1) = 0.4886
A delta of a short position is -488.6.

Is delta of a call option on futures calculated wrong or not?

Thank you!
Hello @San955

I moved your post to this thread, which already discusses this question. Please note the tag at the top of the page, which reflects Hull, Chapter 19, Question 10 (hull-ch19-10). You can search for tags here: https://www.bionicturtle.com/forum/tags/. If your question is not already answered in the discussion above, I'm sure someone will be able to help you, but I wanted to make sure you were aware of the tag (and search) feature to look for posts like this moving forward.