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

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### Call Option Pricing

Using replicating portfolios

Example: Possible call option payouts

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.

Now, repeat the process using call option values at t = 1, to get the value as of today t = 0.

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.

Free: http://www.tradingtoday.com/black-scholes

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