# Introduction to call_and_put_options

Jun 28th, 2015
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A portfolio consisting of stock and a protective put on the stock establishes a minimum amount of value for the portfolio that also has an unlimited upside potential. If the stock declines below the strike of the put, the put increases in value by a dollar for every dollar decline of the stock below the strike price. If the stock climbs above the strike price, the put expires worthless, leaving only the stock. An equivalent portfolio can be established by buying a call and a risk-free T-bill that matures on the expiration day of the call. Because a portfolio that has a minimum value but unlimited upside potential can be established using either a put or a call, then they must be equivalent, because if they weren’t, then arbitrageurs could take advantage of the price discrepancy, writing one option and buying the other until equivalence was achieved.

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Put-Call ParityA portfolio consisting of stock and a protective put on the stock establishes a minimum amount of value for the portfolio that also has an unlimited upside potential. If the stock declines below the strike of the put, the put increases in value by a dollar for every dollar decline of the stock below the strike price. If the stock climbs above the strike price, the put expires worthless, leaving only the stock. An equivalent portfolio can be established by buying a call and a risk-free T-bill that matures on the expiration day of the call. Because a portfolio that has a minimum value but unlimited upside potential can be established using either a put or a call, then they must be equivalent, because if they werent, then arbitrageurs could take advantage of the price discrepancy, writing one option and buying the other until equivalence was achieved. Consider a portfolio that has 1 call with a strike price of \$100 that expires in 6 months, and a T-bill with a face value of \$10,000, bought at a discount, that matures on the call's expiration day. If the call is in the money, then the \$10,000 from the T-bill can be used to purchase the 100 shares of stock at the

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