September 2011, #4

Hello,

I'm a bit lost on this forward contract question. I think I've figured out some bits of it but I'm not sure. The income stream is added to the value of the share when we receive it, which means that we have to earn interest on it as well as pay costs? Also, I'm also not sure about the x% cont. compounded. Any help would be appreciated!

Thanks.

 

Think about your starting portfolios. I'd put a forward and cash equal to the discounted forward price in Portfolio A. This will end up being worth (ST-FT)+FT=ST at time T.

So we need to make sure Portfolio B gives the same payoff. Start with one unit of the asset and see what it ends up as. This won't be right because of the costs and income, so we need to adjust the starting portfolio so that we end up with exactly one unit of the asset.

 

Hi Mike,

Thanks so much for answering. I have tried my best to understand this question and this is where I'm at. I understand that when we get the income, we get it at time T-1/2. That income can now be added to the value of the asset, which means it earns the risk free rate and we also have to pay the x% storage fee on it. An income of y received at time T-0/5 will receive interest until maturity. Discount this back to time 0, I get y*exp (r-1/2). I'm ok there. My issue is the expense due. Shouldn't we pay the expense for T-1/2? The answer makes me think that at time T, the value of the storage costs is y*exp(-x/2) since this value discounted to time 0 is what is in the answer -- y*exp(x(T-1/2)). So where does y*exp(-x/2) come from?

Thanks again Mike.

 

i think ive found and an easier way to takle this

assume initially you have

-z units of asset
-short one foward contract(meaning you are to deliver at T)
-short c in cash(that you borrowed to buy your z assets)

at expiry(time T)

you have

z assets

your short on
z*s(t)expx(T-t)+c*exp r(T-t)
-yexp(r+x)(T-1\2)+p

on contract being exercised

you now have

z-1 assets

short

z*st*expx(T-t)+c*expr(T-t)-yexp(x+r)(T-1\2)-p
call this m
since no artitrage equate both to zero

i.e z=1

p=.............

at time 0 you had zero set up cost

c-z*s(t)=0

c=s(t)

where p is you foward price and you have your answer

il be happy to clarify anything