673_06 - 1 SIMPLE ARBITRAGE RELATIONSHIPS FOR FORWARD AND...

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Unformatted text preview: 1 SIMPLE ARBITRAGE RELATIONSHIPS FOR FORWARD AND FUTURES CONTRACTS (2) NBA 673 February 9, 2006 2 Value of a Forward Contract That Began Earlier At start, value of a forward, V (0) = 0 At maturity, value of a forward to Long is V ( T ) = S ( T ) F (0 ,T ) (and opposite to Short). Long gains, Short loses if spot soars. At intermediate date t , value of a forward to Long is V ( t ) = PV[ S ( T ) F (0 ,T )] = PV[S(T)]-PV[F(0,T)] = S ( t ) B ( t,T )F(0 ,T ). Why must the present value of S(T) equal S(t)? (if there are no dividend payments from 0 to T) 3 PV[S(T)] = S(t)? Time t (start) Time T (end) Portfolio Net Cash Net Cash Buy share-S(t) S(T) Borrow S(t)-S(t)/B(t,T) Total 0 S(T)-S(t)/B(t,T) No arbitrage: S(T)-S(t)/B(t,T) = 0. So S(t) = S(T)*B(t, T) = PV[S(T)]. Is this proof correct? Why? 4 Result & Example: Value of a Forward That Began Earlier Result 2 Value of a forward that began earlier is V ( t ) = S ( t ) B ( t,T )F(0 ,T ) [or, V = S BF (0)]. Example: F (0,6) is $25.89. Delivery in 6 months. After 3 months, stock is $23, i S = 8.08%. Current value of the original forward is V (3) = 23 25.89/[1 + 0.0808 (1/4)] = $2.38. Long must pay Short $2.38 to close this. 5 Value of a Forward Contract That Began Earlier Time 0 (start) Time T (end) Portfolio Net Cash Net Cash Buy share-S(t) S(T) Borrow +S(t)-S(t)/B(0,T) Sell forward V(t)-[S(T) - F(0,T)] Total V(t) F(0,T)-S(t)/B(t,T) No arbitrage: V(t) = -PV[F(0,T)-S(t)/B(t,T)]. Finally: V(t) = S(t)-F(0,T)*B(t,T). Set price to that of the pre-existing forward. 6 Cash-and-Carry with Known Cash Flows to Underlying Asset Result 3 At time t, cash-and-carry gives a) B ( t,T ) F ( t,T ) = S ( t )- PV t [of all cash flows over the remaining life of the forward] [Or, BF = S [PV of future cash flows] ]....
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This note was uploaded on 09/28/2008 for the course NBA 6730 taught by Professor Janosi,tibor during the Spring '06 term at Cornell University (Engineering School).

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673_06 - 1 SIMPLE ARBITRAGE RELATIONSHIPS FOR FORWARD AND...

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