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March 25th, 2013, 09:00 AM  #1 
Newbie Joined: Mar 2013 Posts: 5 Thanks: 0  Formula for bond price at time t
Hi everybody, I am reading a book called "Mathematical Methods for Foreign Exchange" and I am not quite sure I understand the very first (quite unexplained) equation there. It's supposed to express a price of a zero coupon bond at time t as: where the refers to the price at time t = 0 f the obligation to pay $1 dollar at time T in the future. In my opinion, the (constant) could be something like $0.613913 for a 10years bond at yield of 5%. I am not sure what would be the graph of . I tend to think that it models prices for ever more distant maturity dates, so if the t is in the (0, 10) years interval, the value at t = 0 should be $1 and the value at t = 10 should be those $0.613913, i.e. equal to . For those two values, the should be 0.613913 (for t = 0) and 1 (for t = 10) respectively. That makes sense. But I have a problem with the values in between. I am trying to picture the graph of the intermediate values of like this (modeling using t in (0, 1) interval): (see http://forums.babypips.com/attachment.p ... 1364195247) If the graph of above is correct, then the graph of looks like this: (see http://forums.babypips.com/attachment.p ... 1364196164) ...which seems weird, because I believe it shouldn't be convex just like the graph of wasn't convex. The reasoning I have for that is that I believe the first derivative (slope) of the function as it approaches the value 1 (or $1; from right in the first graph and from left in the second graph) should be the same, because that simply expresses that the outlook an investor has  say  over the next year is a lot more "certain" that the outlook she has over a longer period of time. Can anyone shed some light on this for me please? 
March 26th, 2013, 07:30 PM  #2 
Newbie Joined: Mar 2013 Posts: 5 Thanks: 0  Re: Formula for bond price at time t
To partially answer my own question, the book further models the bond prices as: , which makes the formula above look like this: So the fraction holds. But still, the restriction on the the bond price given by the first formula seems a little far fetched, considering how many different ways there are for bond pricing... I guess it is based off of the "continuous compound interest formula" as in here: http://cs.selu.edu/~rbyrd/math/continuous/ 

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