Finance School of management Chapter 15: Options Contingent claims Objective .To show how the law of one price may be used to derive prices of options To show how to infer implied volatility from option Prices uesTc
1 Finance School of Management Chapter 15: Options & Contingent Claims Objective •To show how the law of one price may be used to derive prices of options •To show how to infer implied volatility from option prices
Finance School of management Chapter 15 Contents How Options Work Investing with Options e The Put-Call Parity relationship Volatility option Prices Two-State Option Pricing . Dynamic replication the binomial model The black-Scholes model Implied volatility uesTc
2 Finance School of Management Chapter 15 Contents ❖ How Options Work ❖ Investing with Options ❖ The Put-Call Parity Relationship ❖ Volatility & Option Prices ❖ Two-State Option Pricing ❖ Dynamic Replication & the Binomial Model ❖ The Black-Scholes Model ❖ Implied Volatility
Finance School of management Objectives To show how the law of one price can be used to derive prices of options To show how to infer implied volatility from option prices uesTc
3 Finance School of Management Objectives ❖ To show how the Law of One Price can be used to derive prices of options ❖ To show how to infer implied volatility from option prices
Finance School of management Terms Underlying Asset, Call, Put, Strike(Exercise) Price, Expiration(Maturity)Date, American European Option Tangible(Intrinsic)value, Time Value ey Out-of-the-money, in-the-money, at-the-mor uesTc
4 Finance School of Management Terms – Underlying Asset, Call, Put, Strike (Exercise) Price, Expiration (Maturity) Date, American / European Option – Out-of-the-money, in-the-money, at-the-money – Tangible (Intrinsic) value, Time Value
Finance School of management Table 15.1 List of IBM Option prices (Source: Wall Street Journal Interactive Edition, May 29, 1998) IBM(IBM) Underlying stock price 120 1/16 Call Put Strike Expiration Volume Last Open Volume Last Open Interest Interest 115Jun13727448375613/169692 115O 2584 10 5 967 115 Jan 155363440 120 Jun 2377 312 8049 873 2718 9849 120 Oct 12195/162561457181993 120 Jan 911212 8842? 5259 125 Jun 1564 112 9764 17 53/4 5900 125 Oct 9171/22360? 731 125 Jan 87101/2124 70 uesTc
5 Finance School of Management Table 15.1 List of IBM Option Prices (Source: Wall Street Journal Interactive Edition, May 29, 1998) IBM (IBM) Underlying stock price 120 1/16 Call . Put . Strike Expiration Volume Last Open Volume Last Open Interest Interest 115 Jun 1372 7 4483 756 1 3/16 9692 115 Oct ? ? 2584 10 5 967 115 Jan ? ? 15 53 6 3/4 40 120 Jun 2377 3 1/2 8049 873 2 7/8 9849 120 Oct 121 9 5/16 2561 45 7 1/8 1993 120 Jan 91 12 1/2 8842 ? ? 5259 125 Jun 1564 1 1/2 9764 17 5 3/4 5900 125 Oct 91 7 1/2 2360 ? ? 731 125 Jan 87 10 1/2 124 ? ? 70
Finance School of management Table 15.2 List of Index Option Prices Source:Wall Street Journal Interactive Edition, June 6, 1998) S&P500 INDEX-AM Chicago exchange Underlying High Low Close Net % Change 31-Dec Change S8P500111388108428111386190314343148 (SPX Net open Strike Volume Las hange Interest ch Jun 1110 call 2081171481215754 1110 put 1.077 10 -11 17,104 Jul 1110 call 12783312912 3,712 Jul 1110 put 1522338-121/8 1.040 In 1120 call 80 12716585 Jun 1120 put 21117-119947 1120 call 67271481/45.546 Ju1120 102712-114,033 uesTc
6 Finance School of Management Table 15.2 List of Index Option Prices (Source: Wall Street Journal Interactive Edition, June 6, 1998) S & P 500 INDEX -AM Chicago Exchange Underlying High Low Close Net From % Change 31-Dec Change S&P500 1113.88 1084.28 1113.86 19.03 143.43 14.8 (SPX) Net Open Strike Volume Last Change Interest Jun 1110 call 2,081 17 1/4 8 1/2 15,754 Jun 1110 put 1,077 10 -11 17,104 Jul 1110 call 1,278 33 1/2 9 1/2 3,712 Jul 1110 put 152 23 3/8 -12 1/8 1,040 Jun 1120 call 80 12 7 16,585 Jun 1120 put 211 17 -11 9,947 Jul 1120 call 67 27 1/4 8 1/4 5,546 Jul 1120 put 10 27 1/2 -11 4,033
Finance School of management Terminal or Boundary Conditions for Call and Put Options 120 Call- Put 0= 0 Underlying Price uesTc
7 Finance School of Management Terminal or Boundary Conditions for Call and Put Options -20 0 20 40 60 80 100 120 0 20 40 60 80 100 120 140 160 180 200 Underlying Price Dollars Call Put
Finance School of management The Put-Call Parity relation Two ways of creating a stock investment that is insured against downside price risk buying a share of stock and a put option (a protective- put strategy) Buying a pure discount bond with a face value equal to the options exercise price and simultaneously buying a call option uesTc
8 Finance School of Management The Put-Call Parity Relation ❖ Two ways of creating a stock investment that is insured against downside price risk – Buying a share of stock and a put option (a protectiveput strategy) – Buying a pure discount bond with a face value equal to the option’s exercise price and simultaneously buying a call option
Finance School of management Terminal Conditions of a Call and a Put Option with Strike =100 Share Put share put bond call Bond 0 100 100 100 100 10 90 100 100 100 80 100 100 100 70 100 100 100 40 00000000000 60 100 100 100 100 100 100 40 100 100 100 70 30 100 100 100 100 100 100 90 10 100 100 100 100 100 100 100 110 10 110 100 110 120 20 120 100 120 130 30 130 100 130 140 40 00000000000 140 100 140 150 150 100 150 160 60 160 100 160 170 170 100 170 180 100 180 190 190 100 190 200 100 200 100 200 uesTc
9 Finance School of Management Terminal Conditions of a Call and a Put Option with Strike = 100 Share Call Put Share_Put Bond Call_Bond 0 0 100 100 100 100 10 0 90 100 100 100 20 0 80 100 100 100 30 0 70 100 100 100 40 0 60 100 100 100 50 0 50 100 100 100 60 0 40 100 100 100 70 0 30 100 100 100 80 0 20 100 100 100 90 0 10 100 100 100 100 0 0 100 100 100 110 10 0 110 100 110 120 20 0 120 100 120 130 30 0 130 100 130 140 40 0 140 100 140 150 50 0 150 100 150 160 60 0 160 100 160 170 70 0 170 100 170 180 80 0 180 100 180 190 90 0 190 100 190 200 100 0 200 100 200
Finance School of management Stock, call, Put Bond 200 Call 180 话 9160 Share Put 当140 *- Bond 2A… Call bond E20 Share 680 60 话40 20 020406080100120140160180200 Stock Price uesTc 10
10 Finance School of Management Stock, Call, Put, Bond 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Stock Price Stock, Call, Put, Bond, Put+Stock, Call+Bond Call Put Share_Put Bond Call_Bond Share