PS1 Forward Contract Pricing 2011

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FIN 5207, Advanced Derivative Securities Fall 2011 Professor FengHW1, Forwards and SwapsPost Date: 9/17/11Due Date: 9/26/11 at 9AM EST

Please send your homework to our course GA Dan Martin at [email protected] .

Formalities

Every spreadsheet or word or pdf must have the first tab showing the students submitting and their e-mailaddresses:

The name of the submission should be of the form: Medvedev_kapoor_koopman_assignment1.xls



1. Assume the appropriate discount rates for 3, 6, 9 and 12 months are the same as the LIBOR

rates given. A hypothetical stock, XYZ , has a price of $125 on 09/10/11 and will paydividends as shown below:

Date Dividend Amount

11/11/11 $1.5002/11/12 $2.0005/11/12 $2.0008/11/12 $2.00

LIBOR Interest Rates1 3mo 0.35 %6mo 0.50 %9mo 0.69 %12mo 0.82 %

a) Determine the price to enter a long one-year forward position in XYZ .

b) Calculate the one-year forward price for delivery of XYZ , as of 9/10/11

c) Assume the traded forward price is different from the value you calculated in part b. Forconcreteness, let’s assume the forward price is lower by $2. How would you construct anarbitrage trade around this discrepancy? Be precise about long or short position in thestock, money borrowed and/or deposited at risk-free rate, and the timing of all cashflows. You can ignore transaction costs, stock borrowing/lending fee and all other marketfrictions.

d) Plot the payoff pattern of a long position in a one-year forward contract at maturity.

e) How would the 1-year forward price of XYZ on 9/11/12 have changed if the 3 month, 6month, 9 month and 12 month LIBOR rates all suddenly increased by 1% (increased by100 bps) while the stock price remained unchanged at $125?

f) Another hypothetical stock, PQR, had a price of $100 on 9/11/12 and pays no dividends.What is the price to enter into a 1-year asset swap that receives the total return on XYZ and pays the total return on PQR?

2. Go to the website http://finance.yahoo.com, enter Ebay symbol (EBAY) to get the close priceon Friday, 9/16/11. Assume Ebay will never pay dividends. Use this spot stock priceinformation to calculate the forward price on 09/16/11 of a one-year forward contract for

Ebay, assuming the interest rates in Question 1.

3. Suppose that a stock currently selling at S0 is just about to go ex-dividend. The immediate

dividend will be D0 dollars. Show that the parity value for the futures price on the stock can

be written F0 = S0 (1 + r) (1 – d), where d = D0 /S0 and r is the risk-free interest rate for a

period corresponding to the term of the futures contract. Construct an arbitrage table

1 LIBOR is based on ‘actual/360’ day-count convention and simple compounding



demonstrating the riskless strategy assuming that the dividend is reinvested in the stock. Isyour result consistent with the claim in class that the parity value is F0 = S0 (1 + r) – FV(D)?

[ Hint : how many shares will you hold after reinvesting the dividend? How will this affectyour hedging strategy? Also, notice that I’ve defined d here slightly differently than I did inclass. Here it is D0 /S0; in class it was D1 /S0.]

4. Prove using a no-arbitrage argument that the parity relationship for time spreads is

F0(T2) = F0(T1) (1 + r) – FV(D)

where F0(T) is today's futures price for delivery at time T, T2 > T1, and FV(D) is the future

value to which any dividends paid between T1 and T2 will grow if invested risklessly until

time T2. r is the risk-free interest rate for the period from T1 to T2. [ Hint : You need to

maintain a continually-hedged position. Start with offsetting long and short positions in thetwo futures contracts. When the shorter-maturity futures expires, maintain your hedgedposition by replacing the contract with a position in the stock.]

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PS1 Forward Contract Pricing 2011