# Problem 5 (20 points) ABC stock has a share price of \$150 today. All rates of interest are 3% per annum on a continuously compounded basis. A one-year European call option on one share of stock struck at \$147 is worth \$15. Finally, ABC is scheduled to

Problem 5 (20 points)

ABC stock has a share price of \$150 today.   All rates of interest are 3% per annum on a continuously compounded basis.  A one-year European call option on one share of stock struck at \$147 is worth \$15.  Finally, ABC is scheduled to pay the following dividends per share over the next year: a dividend of \$3.0 per share in three months and a dividend of \$3.0 per share in nine months.

1. a) Derive the forward price of the stock for delivery in one year.
2. b) What is the value of an otherwise identical European put option?

Problem 3 (20 points)

All index options are European and have a one year maturity.  The annual continuously compounded financing rate is 5%, the spot price of the underlying index is \$100, and the continuously compounded annual dividend yield on the index is 2%.  Finally, you know that a call option with a strike of \$100 is worth \$12.00 and a call option with a strike of \$120 is worth \$5.00.

1. a) Derive the value of a put with a strike of \$100.
2. b) Derive the value of a put with a strike of \$120.
3. c) Derive an upper bound on the value of a put option with a strike of \$110.

Problem Set 2

Problem 1 (20 points)

 Mat. Date Rate(%) 1/15/2017 0.5 4/15/2017 0.6 7/15/2017 0.75 10/15/2017 1.0 1/15/2018 1.25 4/15/2018 1.5 7/15/2018 1.75 10/15/2018 2.0 1/15/2019 2.1 4/15/2019 2.2 7/15/2019 2.3 10/15/2019 2.4

Table 1: Continuously compounded zero rate

As of 10/15/2016, Table 1 gives continuously compounded zero rates for the corresponding quarterly maturity dates.  Using this data:

1. a) Derive the present value factors as of 10/15/2016 for these dates.
2. b) As of 10/15/2016 (trade date), derive the corresponding fixed rate on a 3-year interest rate swap where fixed is exchanged for floating.  Assume that both the fixed and floating payments are made twice a year. Assume that there is no difference between trade date and effective date, and that the payments fall on the corresponding semi-annual maturity dates with no adjustment for holidays.  Finally, assume that the rates are paid on a 30/360 basis.
3. c) Using the same information as in b), show all the payments on the three-year interest rate swap where you pay the annual three-year fixed swap rate and receive the 6-month floating rate.  List expected payments at the forward rates when the floating payments are not known on the trade date.  Assume a notional of \$50 Million on the swap.
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