Q46_Q47 - 10 40 2.27 21.82 30 rier at every time step. Q47...

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Q46 Page 1 Stock price 1 + r = 1.1 100 120 140 160 K = 90 80 100 120 60 80 Note! Top final price must be 50 Risk-neutral p 0.750 0.800 0.850 0.700 0.750 0.533 Return from wait now, then act optimally. Return from immediate exercise 2.55 0.41 0.00 0 0 0 9.63 2.27 10 0 21.82 30 American put: P = 2.55 (as we definitely wait at the first step). In this example it's optimal to exercise at prices 80, 60 and 50. Euro put Euro put: P = 1.96 1.96 0.41 7.40 By put call parity: C = European barrier call with b = 130 V_k 5.49 3.72 0 U_o = 5.49 13.02 20.45 0 U_i = -5.49 The table for this up-and-out is a little simpler than in the notes as the price is compared with the barr To find U_i we have used the standard relation U_i + U_o = C.
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Q46 Page 2 e more than 140(1+r) to avoid arbitrage.
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Unformatted text preview: 10 40 2.27 21.82 30 rier at every time step. Q47 Page 3 S_0 = 60 r = 0.06 Sigma = 0.4 T = dt = 0.167 u = 1.177 p = 0.49 Y-values Floating strike look-back put 1.6321 1.3862 1.3862 1.1774 1.1774 1.1774 1.0000 1.0000 1.0000 1.0000 W-values Optimal returns but in units o 0.6321 0.3862 0.3862 0.2092 0.1774 0.1774 0.1580 0.1196 0.0761 0.0000 The option price is 0.158*S(0) = 9.48 We see that it is always optimal to wait so the European option has the same price as the American in Q47 Page 4 0.5 t pays S* - S(T) = S(T)(Y(T) 1). of the stock price. in this example....
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This note was uploaded on 02/04/2011 for the course MATH 3301 taught by Professor Dri.m.macphee during the Spring '10 term at Durham.

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Q46_Q47 - 10 40 2.27 21.82 30 rier at every time step. Q47...

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