# 微积分网课代修|导数代写Derivatives theory代考|GRA6535 Long Call: Speculation

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## 微积分网课代修导数代写Derivatives theory代考|Long Call: Speculation

How might a speculator use this call option contract? As we shall see, the speculator will buy the call option if she thinks stock prices will increase (sufficiently) in the future and end up above the strike price, $K$ (on the option’s maturity date). If stock prices do increase (sufficiently) then the speculator will make a profit when she exercises the call option (on 25 October, its maturity date).

For example, if the stock price on 25 October (on the NYSE) turns out to be $S_{T}=\$ 88$, then the holder of the call option can ‘present’ (i.e. exercise) the option contract in Chicago on 25 October (the maturity date of the option), pay the strike price$K=\$80$ and receive one stock. This is exercising the option by taking delivery. She could then immediately sell the stock on the NYSE for $S_{T}=\$ 88$, making a cash profit on 25 October equal to$S_{T}-K=\$88-\$ 80=\$8$. Alternatively, the long call option can be ‘cash settled’ for $S_{T}-K=\$ 8$which is paid via the clearing house in Chicago (and no stock is delivered). In either of these scenarios (i.e. delivery or cash settlement) the option’s speculator has made$\$8$ on an initial outlay of ‘own funds’ of $C=\$ 3$, which is a percentage return of$[(8-3) / 3 \times 100 \%]=167 \%$(over a 3-month period). Had the speculator bought the stock itself (with her ‘own funds’) for$\$80$ and then sold at $S_{T}=\$ 88$, she would have made a percentage return of$10 \%$(i.e.$\$8$ on an initial outlay of $\$ 80$). The much larger percentage return when using the call option arises because you can purchase the option for the relatively small payment of$\$3$, whereas the stock costs you $\$ 80$. The higher percentage return from the option (relative to the percentage return from buying the stock with your ‘own funds’) is called leverage – here, a$10 \%$increase in the stock price gives rise to a$167 \%$return on the option strategy. If the stock price on 25 October turns out to be$S_{T}=\$75$ which is less than the strike price $K=\$ 80$then the option is not worth exercising – after all, why pay$K=\$80$ for delivery of stock-XYZ in Chicago, when XYZ is only worth $S_{T}=\$ 75$on the NYSE. In this case the option on 25 October is worth zero and the speculator ‘throws it away’ (i.e. does not present/exercise the option in Chicago). Note, however, that no matter how low the stock price turns out to be on 25 October, the maximum amount the option’s speculator can lose is known in advance and is equal to the call premium$C=\$3$.