
SYLLABUS Previous: 2.1.2 Forward contract and
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A vanilla call, which carries the right to buy the underlying for a price , has a finite value only if the underlying is more expensive on the market; the riskfree profit that can be made by exercising the call option (spending to buy the underlying and immediately sell it for a higher price ) is given by the difference if this is positive and zero otherwise. Similarly, a put option has a finite value provided that its holder can sell the underlying to the writer for a price that is higher than the spot price on the market . Mathematically,

An investor who speculates on a solid rebound could buy 100 Marconi shares for GBP 1675; alternatively, he could buy 100 call (options are usually traded in units of 100) for GBP 3 each, giving him the right to buy the shares later in May for a total of GBP 2000. If the stock prices double until May (the precise expiration date is on the Saturday immediately following the third Friday of the expiration month), the net benefit from exercising the options to buy 100 shares for 20 and immediately sell them for 33 1/2 will be GBP 33502000=1350, a larger return on investment (1350/300=4.5) than the doubling that would have been achieved by using shares alone. If the price of the share remains below 20, however, the holder of calls with a strike at 20 will however never exercise his rights and will eventually loose all the investment made when buying the options, i.e. GBP 300.
This shows how speculators can use options to achieve larger gains for a higher risk, using an effect called gearing. Just the opposite can be achieved with hedging, where the negative correlation between an asset and its derivatives is exploited in the form of an insurance reducing the investment risk at the expense of for a lower expected return. To show an extreme case of hedging, imagine a portfolio that is long one asset, long one put and short one call with the same strike price and expiry time . This combination corresponds to what is called the putcall parity relation
In general, the right combination of assets (e.g. shares) and derivatives (e.g. call or put options) can be used to expose a portfolio to any level and type of risk chosen by the investor and reap the benefit from the payoff that reflects the investor's opinion. The plots in (2.1.3#fig.2) show only at the option expiry how each term (or option series, i.e. options having the same strike price and expiry date) contributes to the putcall parity relation (2.1.3#eq.2) and cancels the investment risk.
More complicated payoffs can be obtained by combining vanilla options from the same class (i.e. same type, but different strike price and expiry dates, exercise 2.052.07) or even with hybrid underlyings that have only partly correlated prices. For example, combining the right amount of put options on the NASDAQ top 100 index (a symbol called QQQ) with shares from IBM, it is in principle possible to make a profit if IBM shares fall, but less than the rest of the technology market. However, remember that individual investors who are not member of a clearing house are only permitted to write covered options, where every short position such as the call ( ) in the putcall parity relation has to appear in a combination with a long position in the underlying ( ).
Finally, note that different exercise styles do affect the price of an option before it expires : in chapter 4, we will first study the European style where the options can be exercised only on the expiry date and later in chapter 6, we will extend the models to deal with the American style where the options can be exercised anytime up to the expiry date.
SYLLABUS Previous: 2.1.2 Forward contract and Up: 2.1 The stock market Next: 2.1.4 Exotic options
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