case04sol - the underlying asset and the cost of...

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Introduction to derivatives, Fall 2011 BUSI 588, Case 4 solutions Solutions to Bachelier: forward contracts and foreign bonds 1. (*) The basic point of this question was to make you scratch your head and realize the forward prices are determined solely by the current spot prices and riskfree rates (in the case of currency forwards). In particular, forward prices at date t should be given by F t = S t (1 + r $ ) T - t (1 + r e ) T - t where r $ denotes the US riskfree rate, r e the euro-zone riskfree rate and S t is the spot exchange rate. If one is bullish on euros one may want to take a long position in euro’s, but what should be clear is that the forward prices are independent of future expectations about the spot price. By the arbitrage argument discussed in class, the forward price gets determined by the value of the “synthetic forward” portfolio that goes long the underlying asset financed completely by borrowing. The only determinants of the cost of this strategy are indeed the current value of
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Unformatted text preview: the underlying asset and the cost of borrowing (with foreign exchange as the underlying asset you should note that the underlying asset actually “pays a dividend,” namely the interest rate on foreign bonds). Expectations are irrelevant for forward pricing . 2. (**) This question and the next simply ask you to back out the euro-rates from F t = S t (1 + r $ ) T-t (1 + r e ) T-t ; where T-t = 4 / 12, r $ = 1 . 5%, S t = 1 . 40 and F t = 1 . 395. The implied rate was 2.60%. 3. (***) Carrying out the same calculation for the other maturities one can back out the term-structure of interest rates in the euro-zone. Time Spot rate 0.33 2.60% 0.58 2.63% 0.83 2.82% 1.08 2.99% 1.33 2.88% Note how our implied term structure is slightly upward-sloping in the euro-zone. c ± Diego Garc´ ıa, Kenan-Flagler Business School Page 1 of 1...
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.

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