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Q3: Binomial Option Pricing Non-dividend-paying stock is currently worth $50 per share Each month, price of stock will either rise by 1% (so u = 1.01) or drop by 1% (so d = 0.99) Risk-free rate is 0.1% per month (so R = 1.001) Put option on one share of non-dividend- paying stock has exercise price of $50 and one year to expiration Calculate risk-neutral probability of positive return for non-dividend-paying stock Use binomial option pricing model to find current price of European-style put option Use binomial option pricing model to find current price of American-style put option Stock Up Stock Down Risk-Free Rate Exercise Price Prob(Up) 1.01 0.99 1.001 $50 Time 0 1 2 3 4 5 7 9 10 11 12 $56.341 $55.783 $55.231 $55.226 $54.684 $54.679 $54.143 $54.137 $54.132 $53.607 $53.601 $53.596 $53.076 $53.071 $53.065 $53.060 $52.551 $52.545 $52.540 $52.535 $52.030 $52.025 $52.020 $52.015 $52.009 $51.515 $51.510 $51.505 $51.500 $51.494 $51.005 $51.000 $50.995 $50.990 $50.985 $50.980 $50.500 $50.495 tra $50.490 $50.485 $50.480 $50.475 $50.000 $49.995 $49.990 $49.985 $49.980 $49.975 $49.970 Stock European Put $49.500 $49.495 $49.490 $49.485 $49.480 $49.475 $49.005 $49.000 $48.995 $48.990 $48.985 $48.981 $48.515 $48.510 $48.505 $48.500 $48.496 $48.030 $48.025 $48.020 $48.015 $48.011 $47.550 $47.545 $47.540 $47.535 $47.074 $47.069 $47.065 $47.060 $46.603 $46.599 $46.594 $46.137 $46.133 $46.128 $45.676 $45.671 $45.219 $45.215 $44.767 $44.319 $56.341 $55.783 $55.231 $55.226 $54.684 $54.679 $54.143 $54.137 $54.132 $53.607 $53.601 $53.596 $53.076 $53.071 $53.065 $53.060 $52.551 $52.545 $52.540 $52.535 $52.030 $52.025 $52.020 $52.015 $52.009 $51.515 $51.510 $51.505 $51.500 $51.494 $51.005 $51.000 $50.995 $50.990 $50.985 $50.980 $50.500 $50.495 $50.490 $50.485 $50.480 $50.475 $50.000 $49.995 $49.990 $49.985 $49.980 $49.975 $49.970 Stock American Put $49.500 $49.495 $49.490 $49.485 $49.480 $49.475 $49.005 $49.000 $48.995 $48.990 $48.985 $48.981 $48.515 $48.510 $48.505 $48.500 $48.496 $48.030 $48.025 $48.020 $48.015 $48.011 $47.550 $47.545 $47.540 $47.535 $47.074 $47.069 $47.065 $47.060 $46.603 $46.599 $46.594 $46.137 $46.133 $46.128 $45.676 $45.671 $45.219 $45.215 $44.767 $44.319 Q3: Binomial Option Pricing Non-dividend-paying stock is currently worth $50 per share Each month, price of stock will either rise by 1% (so u = 1.01) or drop by 1% (so d = 0.99) Risk-free rate is 0.1% per month (so R = 1.001) Put option on one share of non-dividend- paying stock has exercise price of $50 and one year to expiration Calculate risk-neutral probability of positive return for non-dividend-paying stock Use binomial option pricing model to find current price of European-style put option Use binomial option pricing model to find current price of American-style put option Stock Up Stock Down Risk-Free Rate Exercise Price Prob(Up) 1.01 0.99 1.001 $50 Time 0 1 2 3 4 5 7 9 10 11 12 $56.341 $55.783 $55.231 $55.226 $54.684 $54.679 $54.143 $54.137 $54.132 $53.607 $53.601 $53.596 $53.076 $53.071 $53.065 $53.060 $52.551 $52.545 $52.540 $52.535 $52.030 $52.025 $52.020 $52.015 $52.009 $51.515 $51.510 $51.505 $51.500 $51.494 $51.005 $51.000 $50.995 $50.990 $50.985 $50.980 $50.500 $50.495 tra $50.490 $50.485 $50.480 $50.475 $50.000 $49.995 $49.990 $49.985 $49.980 $49.975 $49.970 Stock European Put $49.500 $49.495 $49.490 $49.485 $49.480 $49.475 $49.005 $49.000 $48.995 $48.990 $48.985 $48.981 $48.515 $48.510 $48.505 $48.500 $48.496 $48.030 $48.025 $48.020 $48.015 $48.011 $47.550 $47.545 $47.540 $47.535 $47.074 $47.069 $47.065 $47.060 $46.603 $46.599 $46.594 $46.137 $46.133 $46.128 $45.676 $45.671 $45.219 $45.215 $44.767 $44.319 $56.341 $55.783 $55.231 $55.226 $54.684 $54.679 $54.143 $54.137 $54.132 $53.607 $53.601 $53.596 $53.076 $53.071 $53.065 $53.060 $52.551 $52.545 $52.540 $52.535 $52.030 $52.025 $52.020 $52.015 $52.009 $51.515 $51.510 $51.505 $51.500 $51.494 $51.005 $51.000 $50.995 $50.990 $50.985 $50.980 $50.500 $50.495 $50.490 $50.485 $50.480 $50.475 $50.000 $49.995 $49.990 $49.985 $49.980 $49.975 $49.970 Stock American Put $49.500 $49.495 $49.490 $49.485 $49.480 $49.475 $49.005 $49.000 $48.995 $48.990 $48.985 $48.981 $48.515 $48.510 $48.505 $48.500 $48.496 $48.030 $48.025 $48.020 $48.015 $48.011 $47.550 $47.545 $47.540 $47.535 $47.074 $47.069 $47.065 $47.060 $46.603 $46.599 $46.594 $46.137 $46.133 $46.128 $45.676 $45.671 $45.219 $45.215 $44.767 $44.319