429week12f07 - Week 12: Nov 12 Options General Pricing...

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Week 12: Nov 12 Options General Pricing Hedging
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Options General Written on a particular underlying asset (usually stock). Right to buy or sell at a particular price, K, the strike price at or before some future time T. Call = right to buy, Put = right to sell European = buy or sell at T, American = before Are exchange traded and cash settled. Contract size is 100 shares, but K and T are available for each option listed.
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Options Payout Graphs K Call S K Put S
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Options Netting out the cost just shifts the curves down We can combine options to get any payout we want. Adding a call, increases the slope, adding puts decreases the slope. Pricing Put-Call Parity C = Sd^-t - Kr^-t + P At T, C = (0, S-K), Sd^-t = S, Kr^-t = K, P = (K-S, 0) So, (0, S-K) = S-K + (K-S,0) so Put-Call Parity holds by no arbitrage
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Options Binomial Pricing Imagine only two things have happen tomorrow Stock goes up by U or down by D Conjecture that C= S+B S US DS B Br Br C Cu Cd
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Options Hence we find that a call is just a position in stock
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429week12f07 - Week 12: Nov 12 Options General Pricing...

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