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How do I go about proving the theorem below? Theorem 7.2. The value of a (long) forward contract at time I entered into at time
How do I go about proving the theorem below?
Theorem 7.2. The value of a (long) forward contract at time I entered into at time 0 with expiration at time T, denoted by ft(t), is given by fr(t) = (Fr(t) Fr(0)) e = (T-t), te [0,T]. (7.5) The time-t value of a short forward contract is - Fr(t). Proof. An idea of proof is to establish two portfolios at time t such that each of them produces a deterministic stream of cash flows as indicated in the table below (where ft(t) is to be determined). At time t At time T Cash flows from Ila | Fr(t) FT(t) FT(0) Cash flows from Ilp (Fr(t) FT(0)) e-r(T-t) FT (t) FT(0) With this idea, the proof is straightforward and left as an exercise to the reader. Theorem 7.2. The value of a (long) forward contract at time I entered into at time 0 with expiration at time T, denoted by ft(t), is given by fr(t) = (Fr(t) Fr(0)) e = (T-t), te [0,T]. (7.5) The time-t value of a short forward contract is - Fr(t). Proof. An idea of proof is to establish two portfolios at time t such that each of them produces a deterministic stream of cash flows as indicated in the table below (where ft(t) is to be determined). At time t At time T Cash flows from Ila | Fr(t) FT(t) FT(0) Cash flows from Ilp (Fr(t) FT(0)) e-r(T-t) FT (t) FT(0) With this idea, the proof is straightforward and left as an exercise to the readerStep by Step Solution
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