hw10-2 - 3 Exotic Options 225 and being 1 2 n b For...

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Unformatted text preview: 3 Exotic Options 225 and η being η 1 η 2 . . . η n . b) For the European option with a payoff min( S , S 1 , ··· , S n ), its price is V min ( S 1 , S 2 , ··· , S n , t ) = S * N n ( B 10 , B 20 , ··· , B n ; ρ 120 , ρ 130 , ··· , ρ ( n- 1) n ) + S * 1 N n ( B 21 , B 31 , ··· , B 01 ; ρ 231 , ρ 241 , ··· , ρ n 01 ) . . . + S * n N n ( B n , B 1 n , ··· , B ( n- 1) n ; ρ 01 n , ρ 02 n , ··· , ρ ( n- 2)( n- 1) n ) , where B ij =- A ij . 30. Suppose that c max ( S 1 , S 2 , t ), c min ( S 1 , S 2 , t ), c ( S 1 , t ) and c ( S 2 , t ) are the prices of four call options with payoff functions max(max( S 1 , S 2 )- E, 0) , max(min( S 1 , S 2 )- E, 0) , max( S 1- E, 0) , and max( S 2- E, 0) , respectively. Show c max ( S 1 , S 2 , t ) + c min ( S 1 , S 2 , t ) = c ( S 1 , t ) + c ( S 2 , t ) . (Hint: Show that the total payoff of the two options on the left-hand side is equal to the total payoff of the two options on the right-hand side.)is equal to the total payoff of the two options on the right-hand side....
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hw10-2 - 3 Exotic Options 225 and being 1 2 n b For...

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