Derivatives_7_Option Properties.pptx - Lecture Note Seven Parity and other Option Relationships FINA0301/2322 Derivatives Faculty of Business and

Derivatives_7_Option Properties.pptx - Lecture Note Seven...

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FINA0301/2322 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Huiyan Qiu Lecture Note Seven: Parity and other Option Relationships 7-1
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Outline Put-call parity of options Generalized parity and exchange options What are calls and puts? Comparing options with respect to exercise style time to maturity strike price Reading: Chapter 9 7-2
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HSI Index Option Quotes Table Settlement price of HSI Index options, September 12, 2012. The closing price of HSI on that day was 20,075.39. Strike Expiration Calls Puts 19,000 12-Sep 1092 47 19,600 12-Sep 600 138 20,200 12-Sep 238 388 19,000 12-Oct 1209 175 19,600 12-Oct 752 324 20,200 12-Oct 414 590 19,000 12-Dec 1456 423 19,600 12-Dec 1048 593 20,200 12-Dec 684 868 7-3
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Questions Do call premiums always decrease as the strike price increases? Do put premiums always increase as the strike price increases? Do call and put premiums always change by less than the change in the strike price ? Are December options always more expensive than September and October ones? What determines the difference between put and call prices at a given strike? 7-4
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Put-Call Parity For European options with the same underlying asset, strike price, and time to expiration, the parity relationship is: One Implication: Buying a call and selling a put with the strike equal to the forward price ( F 0 ,T = K ) creates a synthetic forward contract and hence must have a zero price 7-5 ) ( ) ( ) , ( ) , ( , 0 , 0 K F e K F PV T K P T K C T rT T
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Put-Call Parity Portfolio A: Buy one put option Initial cost: P(K,T) Portfolio B: Buy one call option Buy a T-bill with face value of K Short sale of e -δT stock Initial cost: C(K,T) + e -rT K e -δT S 0 If the two portfolios have the same payoff, they should have the same initial cost. 7-6
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Payoff of The Two Portfolios S T K S T > K Portfolio A Put K – S T 0 Portfolio B Call 0 S T - K Bond K K Stock - S T - S T Total K - S T 0 7-7
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Same Payoff, Same Cost Since they have the same payoff at maturity, they should have the same initial cost (The Law of One Price) P(K,T) = C(K,T) + e -rT K e - δ T S 0 Rearrange: C(K,T) P(K,T) = e - δ T S 0 e -rT K Forward price: F 0 ,T = e (r- δ) T S 0 e - δ T S 0 = e -rT F 0 ,T C(K,T) P(K,T) = e -rT ( F 0 ,T K ) = PV ( F 0 ,T K ) 7-8
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Example: Arbitrage The price of a stock is $68 and the stock pays no dividend. Suppose a put and a call exist on the stock, both having an exercise price of $75 and the same expiration date (say, one year) The put s current price is $6.50 higher than the call s price. The continuously compounding risk-free interest rate is 3% Given these information, are there any riskless profit opportunities available? 7-9
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Example (cont’d) The stock does not pay dividend: PV(F 0,T ) = S 0 Put-call parity: C(K, T) – P(K, T) = S 0 e -rT K Using given information , LHS = C(K, T) – P(K, T) = – $6.50 RHS = S 0 e -rT K = $68 – $75e -0.03 = – $4.78 Possible problems?
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