hw7-1 - 126 3 Exotic Options Consequently, noticing ˜ C o...

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Unformatted text preview: 126 3 Exotic Options Consequently, noticing ˜ C o ( S, t K ; B * l ) = ˜ C o ( S, t K ; B ** l ) = G c ( S ), we obtain ˜ C o ( S, t k ; B * l ) = max ˆ e- rΔt Z ∞ B * l ˜ C o ( S , t k +1 ; B * l ) G 1 ( S , t k +1 ; S, t k , B * l ) dS , G c ( S ) ! ≥ max ˆ e- rΔt Z ∞ B ** l ˜ C o ( S , t k +1 ; B ** l ) G 1 ( S , t k +1 ; S, t k , B ** l ) dS , G c ( S ) ! = ˜ C o ( S, t k ; B ** l ) , k = K- 1 , K- 2 , ··· , . Letting K → ∞ and noticing that ˜ C o ( S, t ; B l ) generates C o ( S, t ; B l ) as K → ∞ , we arrive at the conclusion C o ( S, t ; B * l ) ≥ C o ( S, t ; B ** l ) if B * l ≤ B ** l . 3. Show that a European up-and-out put option with B u > E plus a Euro- pean up-and-in put option with the same parameters is equal to a vanilla European put option. Solution : For S ≤ B u , the value of the European up-and-out put option satisfies ∂p o ∂t + 1 2 σ 2 S 2 ∂ 2 p o ∂S 2 + ( r- D ) S ∂p o ∂S-...
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This note was uploaded on 02/11/2010 for the course MATH 6203 taught by Professor Zhu during the Spring '10 term at University of North Carolina Wilmington.

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hw7-1 - 126 3 Exotic Options Consequently, noticing ˜ C o...

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