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# Call Option Pricing - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Call Option Pricing' - maili

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### Call Option Pricing

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.

Calculating today’s value of the call option C to get the value as of today t = 0.0

Arbitrage Pricing to get the value as of today t = 0.

Call Value Payouts to get the value as of today t = 0.

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).

*** Notice this portfolio costs: – (5/7)(50) + 22.5 = -13.21, the same as the option price.

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***At t = 1, borrow 22.5 more (to total 45) and buy 2/7 more shares (to total 1 share).

How the model stops working -13.21, the same as the option price.

Black-Scholes Calculator (online) -13.21, the same as the option price.