Options trading

Mathematical finance   http://en.wikipedia.org/wiki/Financial_mathematics
Options exercise     http://en.wikipedia.org/wiki/Exercise_%28options%29

Example of a put option on a stock

• I purchase a put contract to sell 100 shares of XYZ Corp. for $50. The current price is $55, and I pay a premium of $5. If the price of XYZ stock falls to $40 per share right before expiration, then I can exercise my put by buying 100 shares for $4,000, then selling it to a put writer for $5,000. My total profit would equal $500 ($5,000 from put writer - $4,000 for buying the stock - $500 for buying the put contract of 100 shares at $5 per share, excluding commissions).    At first, you buy the underlying stock shares in margin then exercise instruction
  
• If, however, the share price never drops below the strike price (in this case, $50), then I would not exercise the option. (Why sell a stock to someone at $50, the strike price, if it would cost me more than that to buy it?) My option would be worthless and I would have lost my whole investment, the fee (premium) for the option contract, $500 ($5 per share, 100 shares per contract). My total loss is limited to the cost of the put premium plus the sales commission to buy it.