Скачать презентацию 1 Bodie Kane Marcus Essentials of
3347e1747d95a618d06b31422f281b20.ppt
- Количество слайдов: 40
Скачать презентацию 1 Bodie Kane Marcus Essentials of
Скачать презентацию 1 Bodie Kane Marcus Essentials of
1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 16 Options Markets Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
2 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Option Terminology • • • Buy - Long Sell - Short Call Put Key Elements – Exercise or Strike Price – Premium or Price – Maturity or Expiration Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
3 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Market and Exercise Price Relationships In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price>exercise price Put: exercise price>market price At the Money - exercise price and asset price are equal Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
4 Bodie • Kane • Marcus Essentials of Investments Fourth Edition American vs European Options American - the option can be exercised at any time before expiration or maturity European - the option can only be exercised on the expiration or maturity date Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
5 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Different Types of Options • • • Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
6 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Payoffs and Profits on Options at Expiration - Calls Notation Stock Price = ST Exercise Price = X Payoff to Call Holder (ST - X) if ST >X 0 if ST < X Profit to Call Holder Payoff - Purchase Price Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
7 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - (ST - X) if ST >X 0 if ST < X Profit to Call Writer Payoff + Premium Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
8 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Profit Profiles for Calls Profit Call Holder 0 Call Writer Stock Price Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
9 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Payoffs and Profits at Expiration Puts Payoffs to Put Holder 0 if ST > X (X - ST) if ST < X Profit to Put Holder Payoff - Premium Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
10 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Payoffs and Profits at Expiration Puts Payoffs to Put Writer 0 if ST > X -(X - ST) if ST < X Profits to Put Writer Payoff + Premium Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
11 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Profit Profiles for Puts Profits Put Writer 0 Put Holder Stock Price Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
12 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Equity, Options & Leveraged Equity Text Example Investment Strategy Equity only Buy stock @ 80 100 shares $8, 000 Options only Buy calls @ 10 800 options $8, 000 Leveraged equity Buy calls @ 10 100 options Buy T-bills @ 2% Yield $1, 000 $7, 000 Irwin / Mc. Graw-Hill Investment © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
13 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Equity, Options & Leveraged Equity Payoffs Microsoft Stock Price $75 $80 $100 All Stock $7, 500 $8, 000 $10, 000 All Options $0 $0 $16, 000 Lev Equity $7, 140 $9, 140 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
14 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Equity, Options & Leveraged Equity Rates of Return Microsoft Stock Price $75 $80 $100 All Stock -6. 25% 0% 25% All Options -100% Lev Equity -10. 75% 14. 25% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
15 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Put-Call Parity Relationship ST < X ST > X 0 ST - X Payoff for Call Owned Payoff for Put Written-( X -ST) Total Payoff Irwin / Mc. Graw-Hill ST - X 0 ST - X © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
16 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Payoff of Long Call & Short Put Payoff Combined = Leveraged Equity Long Call Stock Price Short Put Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
17 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Arbitrage & Put Call Parity Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S 0 - X / (1 + rf)T If the prices are not equal arbitrage will be possible Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
18 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Call Parity - Disequilibrium Example Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10. 25% Maturity =. 5 yr X = 105 C - P > S 0 - X / (1 + rf)T 17 - 5 > 110 - (105/1. 05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
19 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Put-Call Parity Arbitrage Position Immediate Cashflow Buy Stock -110 ST ST Borrow X/(1+r)T = 100 +100 -105 Sell Call +17 0 Buy Put -5 Total 2 Irwin / Mc. Graw-Hill Cashflow in Six Months ST<105 ST> 105 -ST 0 -(ST-105) 0 0 © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
20 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Option Strategies Protective Put Long Stock Long Put Covered Call Long Stock Short Call Straddle (Same Exercise Price) Long Call Long Put Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
21 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Option Strategies Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration Vertical or money spread Same maturity Different exercise price Horizontal or time spread Different maturity dates Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
22 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Exotic Options • • • Asian Options Barrier Options Lookback Options Currency-Translated Options Binary Options Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
23 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 17 Option Valuation Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
24 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Option Values • Intrinsic value - profit that could be made if the option was immediately exercised – Call: stock price - exercise price – Put: exercise price - stock price • Time value - the difference between the option price and the intrinsic value Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
25 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Time Value of Options: Call Option value Value of Call Intrinsic Value Time value X Irwin / Mc. Graw-Hill Stock Price © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
26 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Factors Influencing Option Values: Calls Factor Effect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expiration increases Interest rate increases Dividend Rate decreases Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
27 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Binomial Option Pricing: Text Example 200 100 75 C 50 Stock Price Irwin / Mc. Graw-Hill 0 Call Option Value X = 125 © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
28 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Binomial Option Pricing: Text Example Alternative Portfolio Buy 1 share of stock at $100 Borrow $46. 30 (8% Rate) 53. 70 Net outlay $53. 70 Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 0 150 Irwin / Mc. Graw-Hill 150 0 Payoff Structure is exactly 2 times the Call © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
29 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Binomial Option Pricing: Text Example 150 53. 70 75 C 0 0 2 C = $53. 70 C = $26. 85 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
30 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Another View of Replication of Payoffs and Option Values Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged Stock Value 50 200 Call Obligation 0 -150 Net payoff 50 50 Hence 100 - 2 C = 46. 30 or C = 26. 85 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
31 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Black-Scholes Option Valuation Co = Soe-d. TN(d 1) - Xe-r. TN(d 2) d 1 = [ln(So/X) + (r – d + s 2/2)T] / (s T 1/2) d 2 = d 1 - (s T 1/2) where Co = Current call option value. So = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d. Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
32 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Black-Scholes Option Valuation X = Exercise price. d = Annual dividend yield of underlying stock e = 2. 71828, the base of the nat. log. r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option. T = time to maturity of the option in years. ln = Natural log function s = Standard deviation of annualized cont. compounded rate of return on the stock Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
33 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Call Option Example So = 100 X = 95 r =. 10 T =. 25 (quarter) s =. 50 d = 0 d 1 = [ln(100/95)+(. 10 -0+(. 5 2/2))]/(. 5. 251/2) =. 43 d 2 =. 43 - ((. 5)(. 251/2) =. 18 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
34 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Probabilities from Normal Dist. N (. 43) =. 6664 Table 17. 2 d N(d). 42. 6628. 43. 6664 Interpolation. 44. 6700 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
35 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Probabilities from Normal Dist. N (. 18) =. 5714 Table 17. 2 d N(d). 16. 5636. 18. 5714. 20. 5793 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
36 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Call Option Value Co = Soe-d. TN(d 1) - Xe-r. TN(d 2) Co = 100 X. 6664 - 95 e-. 10 X. 25 X. 5714 Co = 13. 70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock? Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
37 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Value: Black-Scholes P=Xe-r. T [1 -N(d 2)] - S 0 e-d. T [1 -N(d 1)] Using the sample data P = $95 e(-. 10 X. 25)(1 -. 5714) - $100 (1 -. 6664) P = $6. 35 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
38 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Valuation: Using Put-Call Parity P = C + PV (X) - So = C + Xe-r. T - So Using the example data C = 13. 70 X = 95 S = 100 r =. 10 T =. 25 P = 13. 70 + 95 e -. 10 X. 25 - 100 P = 6. 35 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
39 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Using the Black-Scholes Formula Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option Call = N (d 1) Put = N (d 1) - 1 Option Elasticity Percentage change in the option’s value given a 1% change in the value of the underlying stock Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
40 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Portfolio Insurance - Protecting Against Declines in Stock Value • Buying Puts - results in downside protection with unlimited upside potential • Limitations – Tracking errors if indexes are used for the puts – Maturity of puts may be too short – Hedge ratios or deltas change as stock values change Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
Скачать презентацию 1 Bodie Kane Marcus Essentials of
3347e1747d95a618d06b31422f281b20.ppt