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Call Option Pricing

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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Call Option Pricing

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  1. Call Option Pricing Using replicating portfolios

  2. Call Options

  3. Call Option, time T Payout Function

  4. Call Option, Net Profit Function

  5. Arbitrage: no riskless profits

  6. Example: Possible stock price movements

  7. 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.

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

  9. Calculating today’s value of the call option C0

  10. Arbitrage Pricing

  11. Call Value Payouts 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).

  12. *** Notice this portfolio costs: – (5/7)(50) + 22.5 = -13.21, the same as the option price. *** *** ***At t = 1, borrow 22.5 more (to total 45) and buy 2/7 more shares (to total 1 share).

  13. How the model stops working

  14. Black-Scholes Calculator (online) Free: http://www.tradingtoday.com/black-scholes

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