Unformatted text preview: 100 120 100 90 130 70 100 (20) (0) (10) (30) (30) (0) 10 20 Using the arbitrage theorem for stock 1 and 2 we get: 20 p 110(1p 1p 2 ) = 0 30 p 130 p 2 = 0 ⇒ 30 p 1 = 30 p 2 40 p 1 = 10 ⇒ p * = (1 / 4 , 1 / 4 , 1 / 2) Since we were able to ﬁnd p * , there can’t be any arbitrage oportunity. Now using p * and the arbitrage theorem to ﬁnd the price of the options, we have S 3 = E p * ( S 1 3 ) = 10 × 1 4 = $2 . 5 , and for the spread option S 4 = E p * ( S 1 4 ) = 20 × 1 4 = $5...
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 Spring '09
 Harshad number, spread option

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