ASM exercise 11

[rawl316]

For this problem, it's a futures. Shouldn't d1 be ln(1.6/1.5)? The answer has it as ln(1.52197/1.42684). It factors in the discount, when it is not used in the d1 equation.

[Abraham Weishaus]

You can do it either way, with or without subtracting interest.

[rawl316]

sorry, this was 8.11. It was a little late :oops:

This was a futures question. I thought the formula for d1 in regards to futures never has interest in it. Which is why I don't see why it was discounted.

[rawl316]

I'm still confused by this question. the solution lists d1 as ln(1.52197/1.42684) + .5(.2^2) /.2

Why is it that? based on the futures formula, it should be:

ln(1.6/1.5) + .5(.2^2) / .2

Please explain why the first is correct.

[Bison]

I'm still confused by this question. the solution lists d1 as ln(1.52197/1.42684) + .5(.2^2) /.2

Why is it that? based on the futures formula, it should be:

ln(1.6/1.5) + .5(.2^2) / .2

Please explain why the first is correct.

I don't have that formula right in front of me, but those two ratios inside the ln brackets work out to the same thing. For why they're both right, discounting the futures and the strike is essentially multiplying both by e^(-rt), so it really doesn't affect the ratio between the two.

When I do these problems, I use the discounted numbers just because it's easier for me to remember to discount the numbers there whether it's a forward, a stock, etc. Either way you do it, though, it's not going to affect the result.

Hope this helps.

[rawl316]

thanks for the help bison. now I think I'm confusing myself.

do you mind looking at 8.3 in ASM? I think they are bringing back the stock with r and not delta. Is that an error in the manual that Abe hasn't put in his errata?

[Bison]

It's not an error, but there's (in my opinion) a more intuitive way to get there, although it's a bit longer. Note that in this problem you're given the forward price (not the prepaid forward price.) So using the formula from Chapter 1, you get (sorry, I never figured out the tex stuff) Stock Price = 50/e^(.05-.02)=48.5223. Then take it one step further, calculating the prepaid forward price from the stock price,
48.5223*e^-.02=47.5615.

You can go straight from the forward price to the prepaid forward price as he does, but the way I tend to think about things, taking a few extra seconds to do that conversion works for me.

[rawl316]

thanks for your help bison!

[Bison]

No problem.