option-pricing

# option-pricing - Option Pricing STOR 890(2011 890-11 option...

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Option Pricing STOR 890 (2011) 1/13/2011 890-11 option pricing

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Option pricing Option pricing: a fundamental problem in studying derivatives Why need it? The fair price is a basis for trading, risk management (hedging), etc. Methods: (i) analytical (solving differential equations); (ii) probabilistic (computing expected values in a “ risk neutral world). Toy example: a single period binomial tree for illustration 890-11 option pricing
Basic setting Time horizon: a single period with t = 0 (now) and T = 1 (future) Risky asset: stock S = { S 0 , S 1 } with S 0 = \$ 2 ; it will go up by a factor u = 1 . 07 (up) with probability p = 0 . 6 , or go down by a factor d = 0 . 92 (down) with probability 1 - p = 0 . 4 . Risk-free asset: bank account B = { B 0 , B 1 } with B 0 = \$ 1 and a fixed interest rate r = 0 . 06 . 890-11 option pricing

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Call option on S Call option: price C = { C 0 , C 1 } Contract: signed at t = 0 , to expire at T = 1 , with strike price K = \$ 2 . 05 Pay-off: At t = 0 , you can long the contract C by paying the counter party C 0 ; at T = 1 , you would exercise the option and receive the pay-off S 1 - K if S 1 > K , or do nothing (thus
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