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# 075 re balance the portfolio to include 0833 stock

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Unformatted text preview: ating strategy: 75 [(0.833,−28.4); 34.075] 112.5 [62.5] 37.5 [0] 25 [(0,0); 0] 37.5 [0] 12.5 [0] 50 [(0.6815,−15.48); 18.59] Play Forward 1 2 In period 0: spend \$18.59 and borrow \$15.48 at 10% interest rate to buy 0.6815 shares of the stock. In period 1: 1 When the stock price goes up, the portfolio value becomes 34.075. Re-balance the portfolio to include 0.833 stock shares, ﬁnanced by borrowing 28.4 at 10%. One period hence, the payoﬀ of this portfolio exactly matches that of the call. 2 When the stock price goes down, the portfolio becomes worthless. Close out the position. The portfolio payoﬀ one period hence is zero. Thus No early exercise. Replicating strategy gives payoﬀs identical to those of the call. Initial cost of the replicating strategy must equal the call price. Example We want to price an exotic ﬁnancial contract that pays in period-2 the maximum the stock price has achieved between now and then: 75 112.5 112.5 37.5 75 37.5 50 12.5 50 S = 50 25 Example (continued) We can easily ﬁnd the risk-neutral probabilities for two periods: 0.6 (0.6)2 = 0.36 (0.6)(0.4)=0.24 (0.4)(0.6)=0.24 0.4 (0.4)2 = 0.16 The price of the contract is PV 0 = (0.36)(112.5)+(0.24)(75)+(0.24)(50)+(0.16)(50) (1.1)2 = 78.5/1.21 = 64.88...
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