L the max loss from a long position in a put on a

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l The max. loss from a long position in a put on a futures is limited by the premium and commission. l See next slide (“short forward” vs “long put”). Fin330 16
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Futures options vs futures Fin330 17 Position Payoff at Maturity Maximum Gain Long Forward S T – F 0 Unlimited F 0 – S T F 0 Long Call Max{ S T – K , 0} – FV(c) Unlimited Short Call – Max{ S T – K , 0} + FV(c) FV(c) Max{K-S T ,0} – FV( p ) K – FV( p ) Short Put -Max{ K-S T ,0 } + FV( p ) FV( p ) Recall this slide from the lecture on options:
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Selling a call option on futures l There are two types of call option selling: 1. Sell the option that you have previously bought. è Sell to Close (sell a position that you currently have). 2. Create a new option contract and sell someone the right to buy the stock from you. è Sell to Open , Writing an Option . Fin330 18
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Writing a call option on futures There are two types of option writing : 1. Naked call writing l Selling a call on a contract that you do not own. l The option writer's profit is limited to the premium received, but the loss is unlimited! l The unlimited risk is reflected in high margin requirements (see next slide). 2. Covered call writing l Selling a call on a futures contract that you own. Fin330 19
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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 20
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Possible settlement procedures Case 1. Do not exercise the option : l Option expires on a known date. Case 2. Exercise the option: a) Exerciser takes a long/short futures position at the option strike price. Usual marginal requirements for futures contracts apply. b) The exerciser may immediately liquidate the futures position by an offsetting trade. (Recall the lecture on futures/forward contracts). Case 3. Liquidate the option before maturity: l Investor may buy (sell) the option identical to the one previously sold (bought). Fin330 21
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Fin330 22 Recall that the strike price is $0.0095/Yen. Case 1: Example with the CME December 2016 Japanese Yen call
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Case 1: Example with the CME December 2016 Japanese Yen call l If the price of the underlying futures contract falls below the strike price, the investor will not exercise the option (columns “-30%”, “-20%”, “-10%” in the previous slide). l Why? l Investor’s loss is then limited to the call’s premium of -$175 (neglecting the commission). Fin330 23
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Case 2 a): Exercise the option and hold a position in the futures contract l There are both costs and significant risks involved in acquiring a position in the futures market. l The broker will require a margin deposit to provide protection against possible fluctuations in the futures price. l There is no upper limit to the extent of these margin calls. Fin330 24
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Case 2 a): Exercise the option and hold a position in the futures contract Long Position: Short Position: S T slope = +1 K S T slope = –1 K 25 π π Payoffs at maturity T from holding a futures contract:
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Fin330 Case 2 b): Exercise the option and immediately liquidate the futures contract l If the futures position is closed out immediately after the option is exercised: l
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