Say you have some stock of company XYZ that has appreciated remarkably during the latest tech/biotech/resource/utility/whatever stock run-up. It has made you very happy that your 1000 shares of \$20 stock you bought are today trading at \$100/share. The thing is that you now think a market drop is imminent, perhaps even a market crash.

You decide that buying a put option is the best way to preserve your exposure to a further rise in the stock price and yet limit your losses to the downside in case Black Monday (or Tuesday or Wednesday or ...) occurs next week.

Looking up the option prices for XYZ, you find that put options for a strike price of \$80/share with an expiry 3 months ahead would cost you \$5/option. While you're at this, you notice that call options for the same expiry date and strike price are selling for \$23/option (this is the only assumption in this writeup).

Being the astute trader that you are, you realize that you can attain the exact same position by either buying the put option outright or simultaneously selling your stock and buying the call option with the same strike price.

If you hold on to your stock and buy the put options, it would cost you \$5,000. On the other hand, if you sell your stock and simultaneously buy the call options, you would receive \$100,000 for your shares and pay \$23,000 for the options, meaning you receive \$77,000 in pocket. Buying the puts limits the price at which you could sell to a minimum of \$80 for the next three months, but this is the exact same position you would get by selling your shares and buying the exact same price call option.

How so? On expiry of the options, the price of XYZ could go up, down or stay the same.
If XYZ goes to \$200/share, the puts would be worthless and the shares themselves would be worth \$200,000, while the calls would be worth \$120,000 - the put buyer would be up \$195,000 while the call buyer would be worth \$197,000.
If XYZ stays still at \$100/share, the puts would still expire worthless while the calls would be worth \$20,000 - buying puts would therefore cost \$5000 while buying calls would cost \$3000.
If XYZ plummets to \$40/share, the puts would be worth \$40,000 while the calls would be worthless - the put buyer would then have a net worth of \$75,000 from XYZ while the call buyer would have \$77,000.

Buying a call option and simultaneously selling the underlying security is equivalent to buying a put option on it, assuming the strike prices and expiry dates are the same. Similarly, buying a stock and simultaneously buying a put option is equivalent to buying a call option. If you are considering buying an out of the money option (call or put), it is worth considering buying the in the money 'opposite' options and simulaneously buying or selling stock to make the position equivalent. This often works because in the money options have much lower time value attached to them as compared to out of the money options.

The effect of interest rates have been left out of this calculation.

Definitions: call option, put option, stock options, exchange traded options