【正文】 all option ($) Payoff to buyer of put option ($) 10 0 15 15 0 10 20 0 5 25 0 0 30 5 0 35 10 0 40 15 0 45 20 0 Options: example ? Clearly is the value of a Microsoft share exceeds the exercise prices then the holder of the call option will exercise his right to exercise and make a profit of the share price less the exercise price. If it is less then he will not, in this case the option expires worthless. ? In the case of the put option the if the Microsoft share price drops below the exercise price then she will exercise and receive the difference between these prices. If it is more then the option expires worthless. ? From this we note that options must always have positive or zero value as the least they can ever be worth is zero. Options: leverage ? Options on individual shares are actually 100 shares. ? Notice that if the value of Microsoft shares at expiry at $30 then the holder of the call option makes a profit of $500 – $220 = $280 or a return of 280/220 = 127%. If instead he would have spent this money on buying the shares then the return would have been only (30 – )/30 = %. ? This is an example of the leverage an investor can obtain from buying options rather than the underlying assets themselves. ? Notice however that is the share price is only $25, then the investor has made returns of –100% (as the option expires worthless) pared to a loss of –% from buying the shares. Payoff from a call option ? It is possible to depict the payoffs from this call option graphically: 25 Share price at expiry Call option value at expiry (PAYOFF) Payoff from a put option ? … and also the put option: 25 Share price at expiry Put option value at expiry (PAYOFF) Profit diagrams ? Notice that these graphs do not include the premium which has been paid for this option, if we include the amount paid then what we see is the following graphs: 25 25 $ $ Profit from buying the Microsoft call option for $ Profit from buying the Microsoft put option for $ Writing (or selling) options ? We have seen what happens when you buy call or put options. What about for the person who has sold (or written) these options? ? If you write a call option then it means that, first, you receive the option premium. At the expiry of the option then you are obliged to sell the underlying asset at the exercise price – if the holder wishes to buy it. In this case you lose out by the difference in the prices, if however, they don’t exercise their option then you simply keep the premium. ? Note that these transactions are zero sum games, whatever the holder gains, the writer loses. ? It is similar for a put option only you have to buy at the exercise price if the holder wants to sell. Payoff when writing options ? Returning to the Microsoft example, the payoffs are as follows: Value of Microsoft Shares on March 20 ($) Payoff to writer of call option ($) Payoff to writer of put option ($) 10 0 15 15 0 10 20 0 5 25 0 0 30 5 0 35 10 0 40 15 0 45 20 0 Payoffs from writing options ? In a similar way we can graphically depict the payoffs from writing call and put options on Microsoft. 25 25 Share price at expiry Share price at expiry Payoff at expiry from writing a call option Payoff at expiry from writing a put option Profit from writing options ? It is also to see the profit from writing the Microsoft call and put options: 25 25 Share price at expiry Profit at expiry from writing a call option Profit at expiry from writing a put option $ $ Option principles ? Clearly buying and writing (selling) options is a zero sum game. Everything made by the buyer is lost by the writer and vice versa. ? Note that both buying calls and selling puts are bets that the market will go up. Buying puts and writing calls are bets that the market will go down. ? This option was treated as if it were a European option abut in reality this option would be American thus exercisable at any time. This would make the analysis slightly different as you would have to consider if there are optimal times to exercise