Consider a market with two financial assets, both with a term of one year. The assets
yield a single pay-out at maturity, depending on whether the market goes up or down.
The prices and pay-outs are specified in the following table:
P0 P1(u) P1(d)
Asset (price) (pay-out if up) (pay-out if down)
A 5 6 4
B 9 12 8
(a) Find an arbitrage opportunity in this market.
(b) In which direction will the prices of A and B move as a result of this arbitrage
opportunity? Explain.
Exercise CW1.2: Platinum forwards
The current spot price of platinum is 1500 (in US dollars per troy ounce). Assume a
continuously compounded risk-free rate of interest of 5% p.a. and ignore storage costs.
(a) Find the one-year forward price of platinum, assuming that there are no arbitrage
opportunities.
(b) Suppose that someone is willing to enter into a long one-year forward contract for
platinum at $1600 per ounce. Construct a strategy from which an investor can obtain
a riskless profit.
Exercise CW1.3: Options
(a) Suppose that a share of Shell costs $21 now and that the continuously compounded risk-free rate is 1%. Compute the value of a put option to sell Shell for $22 half a year from now, under the assumption that in half a year, the share costs either $20 or $23. (This is the same situation as in the lecture, but with a put option instead of a call option.)
(b) Generalize the computation above: Suppose that a share costs S0 now and the continuously compounded risk-free rate is r. Assume that at time t (measured in years),the share costs either Sut or Sdt . Write a spreadsheet which computes the value of a put option with strike price K expiring at t. You may assume that K is between Sdt and Sut .
Hand in a print-out of the spreadsheet with the values as above (S0 = 21, r = 0:01,
t = 1/2 , Sut = 23 and Sdt = 20), a print-out of the spreadsheet displaying the formulas,
and an explanation of the formulas that appear in the spreadsheet.
Exercise CW1.4: Stock forwards
On Monday 18 November 2013, an investor takes a short position in a forward contract
on Royal Dutch Shell shares with delivery on Tuesday 18 February 2014. The price of the
shares at that time is $20.69. Shell intends to pay a dividend on Monday 16 December
2013. Assume that the dividend is $0.27 per share and that the risk-free interest rate
is 0.5% (per annum, compounded continuously). You may use any sensible day-count
convention (ignore this if you do not know what a day-count convention is).
(a) Find the forward price, assuming no arbitrage. Give your answer correct to four
decimal places (e.g., $23.4567).
(b) Suppose that on the delivery date, 18 February 2014, a share costs $22.09. Is the investor better or worse off compared to somebody who did not enter into the forward contract, but just sold the stock on 18 February 2014? By how much?
