The Mathematics of Financial Modelingand Investment Management

14-Arbitrage Page 412 Wednesday, February 4, 2004 1:08 PM

412 The Mathematics of Financial Modeling and Investment Management

1 1

SA 11 , = --------(0.5 ×0.7 × 50 + 0.5 × 075 × 100 ) = 68.75

0.8

1 1

SA 21 , = --------(0.5 ×0.75 × 70 + 0.5 ×0.8 × 110 ) = 78.05

0.9

1 1

SA 10 = ---[0.25 0.8 ( × 15 + 0.7 × 50 )+ 0.25 0.8 ( × 15 + 0.75 × 100 )

, 1

+ 0.25 0.9 ( × 20 + 0.75 × 70 )+ 0.25 0.9 ( × 20 + 0.8 × 110 ) ]

= 68.75

2

1

2

2

2

3

2

S 2 ()= S 2 ()= S 2 ()= S 2 () 4 = 0

2 1

SA 11 , = --------(0.5 ×0.7 × 30 + 0.5 ×0.75 × 120 )= 69.37

0.8

2 1

SA 21 , = --------(0.5 ×0.75 × 40 + 0.5 ×0.8 × 140 ) = 78.88

0.9

2 1

SA 10 = ---[0.25 0.8 ( × 8 + 0.7 × 30 )+ 0.25 0.8 ( × 8 + 0.75 × 120 )

, 1

+ 0.25 0.9 ( × 15 + 0.75 × 40 )+ 0.25 0.9 ( × 15 + 0.8 × 140 ) ]

= 73.2

3

1

3

2

3

3

3

S 2 ()= S 2 ()= S 2 ()= S 2 () 4 = 0

3 1

SA 11 , = --------(0.5 ×0.7 × 38 + 0.5 ×0.75 × 112 )= 69.12

0.8

3 1

SA 21 , = --------(0.5 ×0.75 × 42 + 0.5 ×0.8 × 130 ) = 75.27

0.9

3 1



SA 10 = ---[0.25 0.8 ( × 5 + 0.7 × 38 )+ 0.25 0.8 ( × 5 + 0.75 × 112 )

, 1

+ 0.25 0.9 ( × 8 + 0.75 × 42 )+ 0.25 0.9 ( × 8 + 0.8 × 130 ) ]

= 67.125