L an option is at the money if kf t l if an option is

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l An option is at-the-money if K=F t . l If an option is out-of-the money or at-the- money, it has no intrinsic value. Fin330 35
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Option Premium Option premium = Intrinsic Value + Time Value. l Time value – a premium over option’s current exercise value (intrinsic value), based on the probability that it will increase in value before maturity. l Option value is often higher than its intrinsic value, i.e., it has positive time value (it captures the fact that the intrinsic value may be higher in the future! ) l A positive time value explains why: l Out-of-money options are traded at positive prices. l An in-the-money American option is not always exercised immediately. Fin330 36
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Factors affecting the Time Value Fin330 37 Variable European Call European Put American Call American Put Maturity, T ? ? + + Risk-free rate, r + + + indicates that an increase in the variable causes the option price to increase . – indicates that an increase in the variable causes the option price to decrease . ? indicates that the relationship is uncertain.
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Fin330 38 Consider a December 2016 Japanese Yen ( American ) call with the strike Price $0.0095/Yen. The current price of the underlying futures contract is $0.0090165/Yen. This option is currently out-of-the-money because the strike price is above the current price of the underlying futures contract. The call premium of $100 reflects the time value only. “Moneyness” of a futures option
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“Moneyness” of a futures option Fin330 39 Consider a different example: buying one December 2016 Japanese Yen ( American ) call option with the strike price $0.009/Yen . This option is currently in-the-money because the strike price is below the current price of the underlying futures contract ($0.0090160/Yen). The call premium of $1,350 reflects now both the intrinsic and the time value.
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Overview 1. Definition 2. Settlement procedures 3. Valuation using binomial trees 4. Valuation using Black’s model 5. Futures options at the CME Fin330 40
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Fin330 Futures Price = $33 Option Price = $4 Futures Price = $28 Option Price = $0 Futures price = $30 Option Price=? Valuation of futures options using binomial trees l A 1-month call option on futures has a strike price of 29. l The annual risk-free rate (cont. compounded) is 6%. l The futures price movements are shown below: 41
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Fin330 l The portfolio at t=0: long Δ futures; short 1 call option. l Portfolio is riskless when 3 Δ – 4 = 2 Δ or Δ = 0.8 3 Δ – 4 -2 Δ Method 1: Setting up a Riskless Portfolio 42
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Fin330 l The riskless portfolio is: l long 0.8 futures; l short 1 call option. l The value of the portfolio in 1 month is 1.6. l The value of the portfolio today is 1.6e – 0.06 /12 = 1.592 l Since the value of the futures is 0 at t=0 , the value of the option must be 1.592. 43 Method 1: Setting up a Riskless Portfolio
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Fin330 l The portfolio at t=0: long x futures; short y bonds.
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