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mst13k
04-24-2007, 09:36 PM
So this has been messing me up for some time now when it comes to helping me memorize formulas...

Let F symbolize the forward price, F_0,t

In Mahler's study notes, on page 4 in section 1 we've got
PV(F) = F*e^(-rT)
which makes sense, you're discounting back the forward price to now.
Now at the bottom of the page we are told that F*e^(-rT) = S + PV(Div).
That means PV(F) = S + PV(Div)
For continuous dividends, that means PV(F) = S*e^(delta *T)

However, in later formulas for options where we are commonly taking the difference between PV(F) - PV(K), these formulas all seem to be subtracting the dividends.
Turn to page 26 in section 3 on the put-call parity, and right there under "Stocks with Discrete Dividends" it states
PV(F) = S - PV(Div)

What am I missing here? How is the present value of the forward price both the initial stock plus and minus the PV of the dividends?

pug
04-25-2007, 12:47 AM
PV(F)=S-PV(DIV)

mingchenckm
04-25-2007, 11:22 AM
Think about the meaning of forward.
A forward let you buy an asset at time T by paying price F at time T (note that "at time T" appears two times). If you are obligated to pay price F' now (let this be time 0) and receive the asset at time T, then F' is what we called the "prepaid forward price".

Remember that, since you are receiving the stock at time T, you cannot receive ANY dividends between time 0 and time T! Therefore, to compensate your loss, you need not to pay for the dividend portion of the stock price. We should then subtract the PV of dividend from the prepaid forward price!
F' = PV(F) = S - PV(Div)

Skowron
04-25-2007, 02:48 PM
mst13k,

I've consistently had problems applying the (seemingly simple) concepts of futures and forward prices to the pricing models. This is a shame, for I expect there to be oodles of questions on the exam on this topic.

I think what you've run into concerns the Prepaid Forward method of a binomial pricing model (the end of the Binomial Pricing II chapter in the text). During part of the construction of the tree, you take the dividends out, and at another part you put the dividends back in. Figure 11.11 shows a tree like this, and one thing I notice is that the stock price and the prepaid forward price are equal in the node following the dividend, but are different before the dividend.

I would go further in explaining where these parts are, and why they're there, but I suspect I'd make a mistake and mislead you.

Skowron
04-26-2007, 07:21 PM
You need to add the (interest adjusted) dividends back into the prepaid forward prices, in the nodes in which there is a dividend and before, in order to arrive at the true forward price to check for early exercise in an American option. That is when you see the dividend added back into the prepaid forward price.