A Short Primer of Options

Options Options give the holders a right to buy or sell the underlying asset by a certain date for a certain price. Four key components of an option contract: –Underlying asset –Exercise price/strike price –Expiration date/maturity –Long position and short position

Call and Put Options There are two basic types of option: –A call option gives the option holder the right to buy an asset by a certain date for a certain price. –A put option gives the option holder the right to sell an asset by a certain date for a certain price.

European and American Options European-style options ( 歐式期權 ) can be exercised only on the date of the maturity of the contract. American-style options ( 美式期權 ) can be exercised at any time up to the maturity of the contract.

An Example of a Call Option Consider a 3-month European call option on Intel’s stock. Suppose that the strike price is $20 per share and the maturity is Jan 2, The long position is entitled a right to buy Intel shares at the price of $20 per share on Jan 2, –Options are rights. The holders are not required to exercise them if they do not want to. In this case, the contract will be left to mature without exercising.

Payoffs of Long Position in Call Options Suppose that Intel stock price turns out to be $25 per share on Jan 2, The long position buys shares at the price of $20 per share by exercising the option. He/she buys shares at lower price than the spot price. The gain he/she realizes is = $5 per share.

Payoffs of Long Position in Call Options Suppose that Intel stock price turns out to be $15 per share on Jan 2, The contract charges a higher price than the spot market. Of course, the holder will choose not to exercise it. The contract does not generate any economic outcomes to the holder.

Payoffs of Long Position in Call Options In general, suppose that the strike price is, and the underlying asset price at the maturity is. Then, the payoff of the long position of the option should be

Diagram of Payoffs for Longing a Call Payoff Call Options K Stock Price

Payoffs for Shorting a Call The writer of a call option has liability to satisfy the requirement of the long position if he/she asks to exercise options. In the previous example, –If = $25 per share, the option is exercised. The writer loses $5 per share. –If = $15 per share, the option is not exercised.

Diagram of Payoffs for Short Positions Payoff Call Options K Stock Price

Options Premium (Option Price) The long position of an option always receive non- negative payoffs in the future while the writer always has non-positive payoffs. The long position must give a compensation to the writer of an options. The compensation is known as the options premiums or options prices.