Using the past history of short-term interest rates, you estimated by regression the model rn+dt =a +

Question:

Using the past history of short-term interest rates, you estimated by regression the model
rn+dt =a + (rt + ut+dt
Suppose that the parameter estimates generated the tree for interest rates in Table 10.16, where there is equal probability to move up or down the tree. Assume also

For simplicity that each interval of time represents 7 year, that is, A = 1. Finally, assume that the current zero coupon bond expiring at time i = 2 has a price equal to
Z0 (2) = 0.9
(a) How does the 2-year bond Z0 (2) evolve? Compute Z1.d (2) and Z1, d (2), and draw the tree for the bond that expires at time i = 2 [recall the notation: Zi. j (k) is the bond at time i in node j with maturity date k.]
(b) Use the calculation in Part (a) to compute the market price of risk A embedded in the current 2-year zero coupon bond Z0 (2).
(c) Consider an option with maturity T = 1 to buy (at T = 1) one unit of a 1 -year zero coupon bond at the price of K = 95.
i. What is the market price of risk of this option? Why?
ii. Use your calculation in part i to compute the value of the option.
iii. Confirm your calculation by using the risk neutral approach.
(d) Assume that the risk neutral probabilities computed above are constant over time. Compute the price of a 2-year European call option on a 1-year zero coupon bond, with strike price K = .96.
(e) Compute the replicating portfolio that replicates the option payoff in Part (d). Check that the portfolio indeed replicates the payoff. Discuss the intuition.

Strike Price
In finance, the strike price of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity. Coupon
A coupon or coupon payment is the annual interest rate paid on a bond, expressed as a percentage of the face value and paid from issue date until maturity. Coupons are usually referred to in terms of the coupon rate (the sum of coupons paid in a... Maturity
Maturity is the date on which the life of a transaction or financial instrument ends, after which it must either be renewed, or it will cease to exist. The term is commonly used for deposits, foreign exchange spot, and forward transactions, interest... Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...