Use the following information to build the 3-year arbitrage-free binomial interest rate tree.

All bonds are issued by US Treasury and will pay coupons annually.

Assume that future interest rates can realize either one of two possible forward rates, rH and rL and will evolve based on lognormal random walk with a volatility of 10%. (rH = rL*exp(2*10%))

Bond	M	N	O
Issuer	US Treasury	US Treasury	US Treasury
Face Value	100	100	100
Coupon Rate	3.0%	3.0%	3.0%
Price	100	100.200	100.400
Maturity	1 year	2 year	3 year

1) r_1.L(lower of the two possible forward rates to be applied for a period of t=1 to t=2) is closet to:

2.257%

2.452%

2.511%

2.623%

2) r_2.LL(lowest of the three possible forward rates to be applied for a period of t=2 to t=3) is closet to:

2.257%

2.452%

2.511%

2.623%

3) Based on the 3-year arbitrage-free binomial interest rate tree, the price of a 3-year 3% callable US treasury Bond P is closet to: Consider the Bond P pays interest annually and an issuer can call the bond after paying annual coupons.

98.885

99.885

100.885

101.885

4) Based on your answer to Question 3, the value of call option embedded to the 3-year 3% callable Bond P is closet to:

1.515

0.515

-0.485

-1.485