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#1
10-31-2007, 09:11 AM
 MrActuary Member Join Date: May 2006 Studying for em el see Posts: 234

If a stock pays no dividends, is the annualized forward premium = 1?

I thought I read this in the DM textbook, but Broverman problem set 16 #2 part a) has a different answer. The solution calculates it using the regular formula.
#2
10-31-2007, 09:59 AM
 jraven Member Join Date: Aug 2007 Location: New Hampshire Studying for nothing! College: Penn State Posts: 1,264

Not exactly sure what you mean, but if a stock pays no dividends then the forward price is
F = S0 exp[r T].

[However the prepaid forward price would just be the stock price, which may be what you were thinking of?]
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#3
10-31-2007, 11:09 AM
 virgirl920 Join Date: May 2007 Posts: 19

Quote:
 Originally Posted by MrActuary If a stock pays no dividends, is the annualized forward premium = 1? I thought I read this in the DM textbook, but Broverman problem set 16 #2 part a) has a different answer. The solution calculates it using the regular formula.
What does Broverman have? The risk free rate?
#4
10-31-2007, 11:42 AM
 MrActuary Member Join Date: May 2006 Studying for em el see Posts: 234

Yes, Broverman uses the standard formula for finding the annualized fwd premium, which is

(1/T) ln (Fwd price/Stock price).

So for this problem, 100 is the stock price, 108.33 is the forward price (using 8% contiuous risk-free rate), and T is 1. So you get .08 for the annualized forward premium.

However... I thought I read in DM that a stock with no dividends has an annualized fwd premium of 1.
#5
10-31-2007, 11:49 AM
 virgirl920 Join Date: May 2007 Posts: 19

I don't have the text with me, but that makes sense, since annualized forward premium = r-delta and since there are no dividends, delta=0 => annualized forward premium = r.
#6
10-31-2007, 12:41 PM
 Generalshamu Member SOA Join Date: Oct 2006 Location: LA Favorite beer: Heineken Posts: 811

Would you guys recommend using Hull for some of this stuff because he covers a lot on forwards and swaps...

He mentions how to price forward contracts given no dividends, dividends = D, investment income as a percentage, currencies, and value FRA's at any point between t = 0 and time of delivery...
#7
10-31-2007, 01:11 PM
 MrActuary Member Join Date: May 2006 Studying for em el see Posts: 234

I haven't looked at any materials from Hull. I have been using BPP (Francis and Ruckman), Broverman, and the DM text (McDonald). I like BPP the best (for the interest theory), and I prefer Broverman to McDonald for the derivatives material.

Back to my original question... it seems if you use the prepaid forward price in the calculation of forward premium, you will always get 1 if the stock pays no dividends. But by using the forward price, you will not get 1 for the forward premium on a stock that pays no dividends.

Does anyone agree with this?
#8
10-31-2007, 01:45 PM
 virgirl920 Join Date: May 2007 Posts: 19

The forward premium is by definition 1/T * ln(F0,T / S0) so I don't think putting the prepaid forward price in there would ever make sense...
#9
10-31-2007, 09:44 PM
 PinkBikini Member SOA Join Date: May 2007 Studying for FETE Posts: 47

I'm doing this question too... but I don't understand exactly what annualized forward premium IS? Does anyone have the definition (I know the formulas...)? Thanks!

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