Call Option Pricing. Using replicating portfolios. Call Options. Call Option, time T Payout Function. Call Option, Net Profit Function. Arbitrage: no riskless profits . Example: Possible stock price movements. Example: Possible call option payouts.
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Using replicating portfolios
Clearly, if the stock price goes down at t = 1, the option will be worthless (no possible payout). So let’s start at the top-right node.
Notice that probabilities do not appear in this pricing solution. Why not?
The probabilities are implicit in the current stock price (relative to probabilities and outcomes of future stock prices).
***At t = 1, borrow 22.5 more (to total 45) and buy 2/7 more shares (to total 1 share).