Construct a three-step binomial interest rate model assuming the following:

1. The current one-period spot rate is 7%

2. The upward parameter u = 1.1

3. The downward parameter d = 1/u

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b) Value a 3-period option-free bond with the following characteristics:

1. The bond matures in 3 periods

2. The bond has no default risk

3. The bond pays an 8% coupon each period

4. The bond pays $1,000 principal at maturity

5. The probability of an up and down movement is the same (50%).

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c) Assume that the bond in part (b) is a callable bond at 1.010, starting in period 1 (The issuer cannot call the bond at time zero). Value the 3-period callable bond, showing in each period (0, 1, and 2) and for each of the interest rates, the value of the bond (non-callable), the value of the call option, and the value of the callable bond.

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d) Assume that the bond in part (b) is also convertible where the conversion value is ten times the company's stock price. Assume that the current stock price is $95, and in each period, the up movement is 1.1 (u = 1.1), and the down movement is 0.9 (d = 0.9). Estimate the value of the 3- period callable convertible bond showing in each period (0, 1, and 2) and for each of the interest rates, the conversion value, the present value the bond's value, and the final value of the bond after taking into consideration the convertible and callable options (Output similar to page 71 of the slides).