第六章 AmericanOptionsandtheLongstaff-Schwartzmethodology.pptVIP

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第六章 AmericanOptionsandtheLongstaff-Schwartzmethodology.ppt

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prototype template (5428278)\print library_new_final.ppt American Options and the Longstaff-Schwartz methodology Gabor Molnar-Saska Morgan Stanley Hungary Analytics Ltd. Company profile Morgan Stanley is one of the world’s leading investment banks Managing over $600 bn of assets With 600 offices in 30 countries (2 in Hungary) Employing 54,000 people worldwide. Company profile Morgan Stanley is one of the world’s leading investment banks Managing over $600 bn of assets With 600 offices in 30 countries (2 in Hungary) Employing 54,000 people worldwide. Company profile Morgan Stanley is one of the world’s leading investment banks Managing over $600 bn of assets With 600 offices in 30 countries (2 in Hungary) Employing 54,000 people worldwide. A toy example A toy example European option American option American option American option American option American option American option American option American option American put option American put option American put option American put option American put option American put option American put option American put option American put option American put option American put option American option American option We are currently hiring Analytic Modellers 0.88 0.22 8 0.92 0.18 7 0.76 0.34 6 5 0.93 0.17 4 3 2 1.09 0.01 1 t_2 t_1 t_0 #Path Exercise 0.153 Exercise 0.117 Exercise 0.286 Exercise 0.109 Continue 0.014 Decision f1(x) 1.34 1.22 0.88 1.01 0.84 0.92 0.90 0.77 0.76 1.52 1.56 1.11 0.92 0.97 0.93 1.03 1.07 1.22 1.54 1.26 1.16 1.34 1.08 1.09 t_3 t_2 t_1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 t_3 t_2 t_1 0.22*0.94 0.18*0.94 0.34*0.94 0 0.17*0.94 0.7*0.943 0 0 t_3 t_2 t_1 Stopping rule Cashflows Stock price paths Advantages: fast computation (linear regression) price dynamics is arbitrary Problem: Option price is overestimated (foresight bias) Reason: regression coefficients are not adapted to the filtration of the price process (we use too much information from the future!) Furt