We observe the following spot rate curve. Assume semiannual compounding and $100

Question

We observe the following spot rate curve. Assume semiannual compounding and $1000 par value. Calculate the prices of .5y and 1y Treasury bonds. period Years Annualized Spot Rate

Period - Years - Annualized Spot Rate

The binomial tree of the 6-month short-term interest rate is in the table below. Each period represents a six-month time interval. Find the risk-neutral probability (p & 1-p) under which the binomial tree model prices the 1-year zero-coupon bond correctly.

Period 0 - Period 1

Please show all work and/or steps.

Explanation / Answer

As the spot rate is given

We ould have to find the price of bond by 1000/(1+r)^t

=1000/(1+.06)^.5 =971.2859

For the one year bond

=1000/(1.061496)^1 =942.0667

Risk Neutral prbilaity should p=.5

Simply

as 6% is clealry average of 6.5 and 5.5%

so 6.5%*p +5.5%*(1-p)=6%

P= 50%=0.5

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