Hull, Ch 15 - question

[carzymathematician]

I am somewhat confused and I hope someone can help clarify this issue. If a portfolio can be made delta-neutral with a long position in 14,900 AUD but you wish to use a fwd contract instead and the delta for the fwd contract on 1 AUD is 0.9068, does this not mean that for every 1 AUD, you would need 0.9068 fwd contracts? And, as such, you would need 14900*0.9068 to make your pos'n delta neutral? (refer to pg 352)

[marlie]

This is what I was confused too. I don't have book with me now. But I think I get it now. delta1=call/stock, delta2=forward/stock, now you want delta3=call/farward, so your delta3=delta1/delta2, in your problem, this means you use 14900/0.9068. I don't know how to type in the formula, those ratios should have partial derivative in front.

[onceandforall]

I am somewhat confused and I hope someone can help clarify this issue. If a portfolio can be made delta-neutral with a long position in 14,900 AUD but you wish to use a fwd contract instead and the delta for the fwd contract on 1 AUD is 0.9068, does this not mean that for every 1 AUD, you would need 0.9068 fwd contracts? And, as such, you would need 14900*0.9068 to make your pos'n delta neutral? (refer to pg 352)

for every AUD, you would need 1/.9068 forward contract to be delta neutral. 1 AUD has delta of 1. 1/.9068 forward contract has delta of 1 too.

[bagheera]

I am somewhat confused and I hope someone can help clarify this issue. If a portfolio can be made delta-neutral with a long position in 14,900 AUD but you wish to use a fwd contract instead and the delta for the fwd contract on 1 AUD is 0.9068, does this not mean that for every 1 AUD, you would need 0.9068 fwd contracts? And, as such, you would need 14900*0.9068 to make your pos'n delta neutral? (refer to pg 352)

It would perhaps be easier to think of it this way. Since delta of forward is less than delta of AUD, the "sensitivity" of forward price to change in the value of the underlying asset is *lesser* than that of AUD. Therefore you would need *more* forwards than AUD to hedge because each forward takes you slightly "lesser" toward a delta neutral position than an AUD. So the answer is 14900/0.9068 and not 14900*0.9068.

[carzymathematician]

It would perhaps be easier to think of it this way. Since delta of forward is less than delta of AUD, the "sensitivity" of forward price to change in the value of the underlying asset is *lesser* than that of AUD. Therefore you would need *more* forwards than AUD to hedge because each forward takes you slightly "lesser" toward a delta neutral position than an AUD. So the answer is 14900/0.9068 and not 14900*0.9068.

Aaaaahh, I do see what u're saying. Thanks!