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