Formula for bond price at time t

Trading Discussion News and Economy
1

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 of 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 10-years 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):


If the graph of
above is correct, then the graph of
looks like this (continued in the next post…)

2

(…continued from the first post)… graph looks like this:


…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 they simply express how an investor would evaluate a price of a - say - 1 year bond).

Can anyone shed some light on this for me please?

3

Math isn’t everything. Finance is also a behavioral science.

There are a few different theories regarding Bond Yield Curves:
Liquidity Preference Theory
Market Segmentation Theory
Preferred Habitat Theory
Expectations Theory

If you’re serious about studying bond yields you should probably factor these into your analysis too.

I don’t know if I’ve been of help because I haven’t gone that deep into the math behind bonds. I’m more focused on intermarket analysis (john murphy) Bonds vs. Stocks vs. Commodities vs. Currencies.

Let me know how it goes. =)

4

I am in fact not interested that much in bonds. It’s the Forex that I am interested in and I believe the book I’ve mentioned tries to build the theory on top of some fundamental concepts like bonds. It would be enough for me to understand the formulas and what they express. I am not exactly looking for any deeper knowledge about bonds themselves. The reason I believe this book mentions the bonds, is that their yield is sometimes used as a benchmark for a risk-free yield.

But to continue with my problem, the book further models the bond prices as:


, which makes the formula above look like this:


So the fraction holds. But still, the bond price given by the first formula seems a little wild…