Pricing off of the spot rate curve

[wadswort]

Guys,

I have simulated the spot rate curve and have values for each year (1-30) with which I can price zero coupon bonds. Now, what if want to discount a coupon bond using my simulated curve. My coupon bond pays every 6 months. What discount rate would I use to discount the money i get in year 1.5? One half the two year rate?

 

[koupparis]

Stich your curve together using some interpolation scheme. The simplest is piecewise constant or piecewise linear. Of course this is not really what is used in practice, one may want to use spline interpolation instead.

 

[DStahl]

Edit: By "simulating the spot rate" do you mean the instantaneous rate or the zero rate for different maturities? If you mean the latter, ignore my post.

Original post:

If I am understanding correctly, the price of a zero bond that matures at time t is ( P\mathbb{\tilde{E}} \left[e^{-\int_0 ^ t r_s ds}\right] ) where ( r_s ) is the spot rate at time s and P is the principle. No further discounting is necessary.

Obviously this assumes no default risk, just interest rate risk.

Given a realized spot path, the current price of a zero bond is simply (Pe^{-\int_0 ^ t r_s ds}). At the current time we do not know what the realized spot rate will be, so this isn't very realistic.