, . . : (forward contracts) (futures) (options) (swaps)

1. (forward contracts)

. , , , . , . , . . : 10. $0,98/1 3 . , 3 . $1/1, (10,98)x10=$0,2., . , . . . , S (spot) , F (forward price) , R , , , K=F.

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, , F , , , S. , F S, arbitrage.

2. (futures) ( - futures) .

. . : ) , , , ) . , (mark to market) . : . F. F>, () () F-. , , . , , F-K . futures forwards. futures , . . , F . , F . F-K , 2

. , Barrings Nikkei, futures. , .

2.1 15 1 . 3 . , , . , : , , , . , . , . . . $19 3 $18,75 . , . (1000 ) . $18,75 . $19,50. $19,50 . , $0,75 . , $18,75 $19,50 F=$19,50. 15 future spot, , $19,50. 19,50-18,75=$0,75. , $19,50-$0,75=$18,75 .

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, 15 $17,50 $17,50 (18,7517,50=$1,25) . , 17,50+1,25=$18,75. , , , $18,75.

2.2 futures. 1979-80. spot. , . cornering .

2.3 Short selling ( ) (margin account) . . ,

. . , . short selling, . .. , . . short selling, , , . , , . . , 4

. , . . 10% short selling .

2.4 forwards futures , R, . arbitrage . , .., , : F=SeRT. , . , arbitrage, : F> SeRT, arbitrage S, S ( ). , , F SeRT, , . : F- SeRT>0. F< SeRT, arbitrage

short sell, , , S . , . , F : : SeRT-F>0. , , .

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arbitrage, . F= SeRT. : S . S , , F . F , R. , arbitrage. , S=Fe-RT. R . , , (cost of carry) . . : , .., , I, . , Q, , . R-I+Q : F=Se(R-I+Q)T. : 10%. 3% $100. , F, ; F=Se(R-I)T=100e(0.10-0.03)(6/12)=$103,56. , $90. ; F=Se(R-I)T=90e(0.10-0.03)(4/12)=$92,12. , ; , $103,56, ( ). , . , . futures, , . ;

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, . , $103,56 , $92,12. : 92,12-103,56=-$11,44 -11,44e-(0,10)(4/12)=-$11,06. , , $11,06. .

2.5 , . , R r, S. , R-r. ( ), , . , r , , : F=Se(Rr)T

: 7% 5% . $0,98, ; F=Se(R-r)T=0,98e(0.07-0.05)(3/12)=$0,9849.

2.5 future-forward Forward . - . 90% . , . . . . : bid-ask spread. . . 7

Futures . . . 1% . . . . . . . .

3. (call options) , , (, , , ) , , . , call option , , . (put options) . . : (long position, ) (short position, ) (long position, ) (short position, )

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. , , . , , . : ) ) , . , . , (option price, option premium). . , max((X-S), 0) S . : ) S, ) , ) ) , ) R, ) D . , , c, c=c(S, X, , T, R, D) . , , S, c.

3.1 . , , , , , , . . 9

, , . : ) S, S. ) S. ) : call put , .

3.2 . c , p , : c + Xe-RT= p + S. call . put . , : ST>X. Xe-RT . call ST. ST put . ST