Payoff from call f t k l payoff from put k f t where

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Payoff from call = F t K ; l Payoff from put = K F t ; where F t is futures price at time t T, when the option is exercised. 26
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Fin330 27 Recall that the strike price is $0.0095/Yen. Case 2 b): Example with the CME December 2016 Japanese Yen call
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Case 2 b): Example with the CME December 2016 Japanese Yen call l Suppose the price of the underlying futures contract rises to $0.0109710/Yen (column “+20%” in the previous slide). l Suppose the investor closes out the position immediately after the option is exercised. l Then investor’s profit is (neglecting the time value of money and the commission): (0.0109710 – 0.0095) x 12,500,000 = $18,212.5 Fin330 28
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Numerical example for case 2 b) l On April 1st, investor buys a July call option on gold futures with a strike of K=$1,800 per ounce. l The option premium is $20 per ounce. l One contract is on 100 ounces. l Investor exercises the option on May 1st, when the futures price is F=$1,840 per ounce. l The investor immediately closes out the long position. l The annual (cont. comp.) interest rate is 0.5%. l How large is investor’s profit as of May1st? Fin330 29
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l The buyer of the option: l pays the premium $20*100 = $2,000 in April; l receives a payment in May: ( F K)*100=(1,840 – 1,800)*100=$4,000 l As of May 1st, investor’s profit is: 4,000 – 2,000e 0.005 x(1/12) = $1,999.17 Fin330 30 Numerical example for case 2 b)
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Case 3: Liquidating the option before maturity l When an option is liquidated , no position is acquired in the underlying futures contract. l Liquidating an option prior to its expiration in the same marketplace, where it was bought, is the most frequent method of realizing option profits. l Note that there is no guarantee that there will be an active market for the option at time t ! Fin330 31
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Example for case 3 l On April 1 st , an investor buys a call option on a sugar futures contract. The premium cost is $950. l On May 1 st , the option has a premium of $1,250. The investor liquidates his position in the option on May 1 st . l The annual (cont. comp.) interest rate is 0.5%. l How large is investor’s profit as of May1st? l Answer: 1,250 – 950 e 0.005 x(1/12) = $299.6 Fin330 32
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Overview 1. Basics 2. Settlement procedures 3. Option premium 4. Valuation using binomial trees 5. Valuation using Black’s model Fin330 33
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“Moneyness” of a futures option l An option is in-the-money if it is profitable to exercise: l A call option is in-the-money at time t T if the option exercise price is below the underlying futures price: F t > K . l A put option is in-the-money if the option exercise price is above the underlying futures price: F t <K . l Option’s intrinsic value at time t = the maximum of zero and the value the option would have if it were exercised immediately. Fin330 34
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“Moneyness” of a futures option l An option is out-of-the-money if it is not profitable to exercise: l For a call option: K>F t . l For a put option: K<F t .
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