a2 - ActSc 446/846 Winter 2006 Assignment 2 Due Date...

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Unformatted text preview: ActSc 446/846 Winter 2006 Assignment 2 Due Date: Feb,3,2006, 5:00pm, Outside my office 1. Suppose that F 1 and F 2 are two forward prices on the same commodity with time to maturities t 1 and t 2 , where t 2 > t 1 . Prove that F 2 ≤ F 1 e r ( t 2- t 1 ) where r is the interest rate (assumed constant) and there are no storage costs. 2. Consider a forward contract written on an underlying asset with delivery price K and delivery time T . Assume that q is the annual yield of the underlying asset. Show that, the time t ( < T ) price of a long position of this forward contract is S t e- q ( T- t )- Ke- r ( T- t ) where S t is the underlying asset’s value at time t , and r is the constant risk-free interest rate. 3. The 6-month, 12-month, 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5%, with semiannual compounding. (a) What are the rates with continuous compounding? (b) What is the forward rate for the 6-month period beginning in 18 months?...
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