A put option is an option to sell a certain asset by

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A put option is an option to sell a certain asset by a certain date for a certain price (the strike price). 24
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The party adopting the short position in the contract is said to be on the short side. A short position implies the liability to sell (call option) or buy (put option). The party adopting the long position in the contract is said to be on the long side. A long position implies the right to buy (call option) or sell (put option). 25
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Options : The short party is known as the writer of the contract and sells the option. The long party is said to be the holder of the option and purchases the option. 26
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There is no price to pay in order to enter in a forward/futures contract. On the other hand, the (long) party getting the right to sell or buy must pay a premium (or price) when the option contract is written. 27
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The party adopting the long position pays a premium p when the contract is written in exchange of the right to buy or sell. Let P be the value at maturity (time τ ) of the premium: P = p (1+ r ) τ where r is again the risk free interest rate. 28
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The price (premium) of a call option is decreasing in the strike price . The premium of a put option is increasing in the strike price . The longer the maturity of an option the more expensive it usually is. 29
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An American option can be exercised at any time during its life. A European option can be exercised only at maturity. 30
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31 Strike Price Oct Call Jan Call Apr Call Oct Put Jan Put Apr Put 15.00 4.650 4.950 5.150 0.025 0.150 0.275 17.50 2.300 2.775 3.150 0.125 0.475 0.725 20.00 0.575 1.175 1.650 0.875 1.375 1.700 22.50 0.075 0.375 0.725 2.950 3.100 3.300 25.00 0.025 0.125 0.275 5.450 5.450 5.450
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Call option : long party will exercise the option if: S τ > K τ i.e. if the spot price at time τ is above the strike price. It will be profitable for the long party if: S τ > K τ + P so that the purpose is to benefit from a rise in prices. 32
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Profit from buying one European call option: option price = $5, strike price = $100, option life = 2 months Options, Futures, and Other Derivatives 7 th Edition, Copyright © John C. Hull 2008 33 30 20 10 0 -5 70 80 90 100 110 120 130 Profit ($) Terminal stock price ($)
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Profit from writing one European call option: option price = $5, strike price = $100 Options, Futures, and Other Derivatives 7 th Edition, Copyright © John C. Hull 2008 34 -30 -20 -10 0 5 70 80 90 100 110 120 130 Profit ($) Terminal stock price ($)
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Put option : long party will exercise the option if: S τ < K τ i.e. if the spot price at time τ is below the strike price.
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  • Spring '12
  • D.S.G.Pollock
  • John C. Hull