28.Suppose that LIBOR rates for maturities of 1,2,3,4,5, and 6 months are 2.6%,

Question

28.Suppose that LIBOR rates for maturities of 1,2,3,4,5, and 6 months are 2.6%, 2.9%, 3.1%, 3.2%, 3.25% and 3.3% with continuous compounding. what are the forward rates for future 1-month periods?

29. A bank can borrow or lend at LIBOR. The 2-month LIBOR rate is 0.28% per annum with continuous compounding. Assuming that interest rates cannot be negative, what is the arbitrage opportunity if the 3-month LIBOR rate is 0.1% per year with continuous compounding? How low can the 3-month LIBOR rate became without an arbitrage opportunity being created?

30. Consider an 8-month European put option on a Treasury bond that currently has 14.25 years to maturity. The current cash bond price is $910, the exercise price is $900, and the volatility for the bond price is 10% per annum. A coupon of $35 will be paid by the bond in 3 months. The risk-free interest rate is 8% for all maturities up to 1 year. Use Black’s model to determine the price of the option. Consider both the case where the strike price corresponds to the cash price of the bond and the case where it corresponds to the quoted price.

Explanation / Answer

30.

Solution:

Strike price corresponds to cash price

Using Black Scholes model,

d1 = [ln (S/X) + (r + ?/2) t] / ? ? t

    = [ln (910/900) + (0.08 + (0.10)/2) (8/12)] / 0.10 ?8/12

    = 0.067717/0.08165

   = 0.829

Using excel,

=NORMSDIST (0.829)

N (-d1) = 0.2036

d2 = d1 - ? ? t

     = 0.829 0.10?8/12

     = 0.7474

Using excel,

=NORMSDIST (0.7474)

N (-d2) = 0.2274

Value of put, P = N (-d2) Xe-rt - N (-d1) S

                       = 0.2274 (900 e-0.08*8/12) 0.2036 (910)

                      = 194.03 185.28

                         = $8.75     

Strike price corresponds to quoted price

Quoted price = $910 + $35 = $945

Using Black Scholes model,

d1 = [ln (S/X) + (r + ?/2) t] / ? ? t

    = [ln (945/900) + (0.08 + (0.10)/2) (8/12)] / 0.10 ?8/12

    = 0.1055/0.08165

   = 1.29

Using excel,

=NORMSDIST (-1.29)

N (-d1) = 0.0985

d2 = d1 - ? ? t

   = 1.29 0.10?8/12

     = 1.21

Using excel,

=NORMSDIST (0.7474)

N (-d2) = 0.1131

Value of put, P = N (-d2) Xe-rt - N (-d1) S

                     = 0.0985 (900 e-0.08*8/12) 0.1131 (945)

                        = 84.05 106.88

                        = -$22.83   

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