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#1




Reconciling two "prepaid forward" formulas; understanding "cost of carry"
Hi everyone  I have two questions from Chapter 5 of McDonald, which seems like a prerequisite for the MFE material. I've searched the forums and not quite found these addressed.
The two "prepaid forward" formulas Here are the two formulas for pricing prepaid forwards with dividends (McDonald, pp. 13132): With discrete dividends:I understand each of these formulas on its own, but I am having a hard time reconciling them. I did find a forum discussion about why the riskfree rate is omitted from the continuousdividend formula, but that's not the reconciliation I'm looking for. Here's as far as I got: I did some figuring using the approximation (this seems to be the gist of the "daily dividend" formula on Page 132), which led me toand ultimately (after substituting and simplifying) to. Is this accurate/meaningful? Is there some other way of understanding the two prepaidforward price formulas simultaneously? Am I barking up the wrong tree? Understanding "cost of carry" I don't understand McDonald's discussion of this concept on Page 141: Quote:
Forward price = Spot price + Interest to carry the asset  Asset lease rate,where the last two terms on the righthand side are grouped together as "cost of carry." This formula seems to apply directly to the discretedividends case, but I don't see how to apply it directly to the continuousdividends case. Is there a clearer interpretation? I will munch on popcorn while you discuss TIA 
#2




Chapter 5 of McDonald is on the FM syllabus. You didn't study this material for that exam?
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"One must do no violence to nature, nor model it in conformity to any blindly formed chimera." Janos Bolyai "Theoria cum praxis." Gottfried von Leibniz 
#4




Keep reading, I think it would help for you to compare the prepaid forwards to the forwards  see page 134 of McDonald.
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"One must do no violence to nature, nor model it in conformity to any blindly formed chimera." Janos Bolyai "Theoria cum praxis." Gottfried von Leibniz 
#5




Quote:
You might get more responses if you post this question in the FM forum.
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"One must do no violence to nature, nor model it in conformity to any blindly formed chimera." Janos Bolyai "Theoria cum praxis." Gottfried von Leibniz 
#6




OK, I'll try the FM forum, thanks. As for comparing the prepaid forwards to the forwards: There is a very straightforward connection between discrete prepaid forward and discrete forward. Likewise for continuous prepaid forward and continuous forward. I am asking about discrete prepaid forward and continuous prepaid forward.

#7




Concerning your first question, have you considered that the two formulas are based on 2 different assumptions?
The continuous dividend formula assumes that the dividends are continuously reinvested in the stock The discrete dividend formula does not assume reinvestment in the stock. The discrete dividends may be invested in a riskfree investment; their value is discounted at the riskfree rate. 
#8




Intuitively I like to think of S0  PV(dividends) is the discrete case, and S0e^(st) is the same thing in the continuous case, and it works out because at time 0, you lose out the dividends because you don't get the stock until time t. If s=.05 and t=1, then S0e^(st) is S0e^(.05), and it's nearly equal to .95S0....but the discrete case would be S0  .05S0 if the present value of the dividend was equal to .05*S0, and you would have exactly .95S0. Mathematically I'm not sure of a quick way to put them together, but I can't think of a reason to either answering or understanding an exam question.

#9




Quote:

#10




Addendum: in the first free online lecture at The Infinite Actuary  the one where they review topics such as this one that have already been gone over  the guy says that you can "calculate the present value by solving a stochastic differential equation" to get
.Maybe someday sooner or later I'll learn how those stochastic differential equations work...for now I'll accept that it's out of scope. Last edited by Marid Audran; 01122009 at 04:49 PM.. Reason: Correcting formula and formatting 
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