Derivatives. 学习 CFA 知识的个人经验三个级别的 derivatives 的框架一级 derivatives 的相关内容. Slide 1 CFA 咨询热线 : 财金学习 :cert.finance365.com

Transcription

1 Derivatives 学习 CFA 知识的个人经验三个级别的 derivatives 的框架一级 derivatives 的相关内容 Slide 1

2 学习 CFA 知识的个人经验教材和 notes 一级以 notes 为主, 辅以原版教材二级要将 notes 和教材相结合三级以教材为主, 以 notes 为辅难易程度一级较易, 二级较难, 三级考试形式特殊打实基础, 循序渐进, 水到渠成 Slide 2

3 CFA 一级的 Derivatives Derivatives 5% 12Qs Derivative Markets and Instruments Forward Markets and Contracts Futures Markets and Contracts Options Markets and Contracts Swaps Markets and Contracts Risk Management and Applications of Option Strategies Slide 3

4 CFA 二级的 Derivatives Derivatives 10% 2 cases (12Qs) Forward Markets and Contracts Futures Markets and Contracts Options Markets and Contracts Swaps Markets and Contracts Interest Rate Derivative Instruments Credit Default Swaps Slide 4

5 CFA 三级的 Derivatives Risk Management Applications of Derivatives 10% 2 cases Risk Management Applications of Forward and Futures Strategies Risk Management Applications of Options Strategies Risk Management Applications of Swaps Strategies Also applied in Currency Management, Fixed-Income Portfolio Management Slide 5

6 Comparison Level I Level II Level III Derivative Markets and Instruments Forward Markets and Contracts Futures Markets and Contracts Options Markets and Contracts Swaps Markets and Contracts Risk Management and Applications of Option Strategies Forward Markets and Contracts Risk Management Applications of Forward and Futures Futures Markets and Contracts Strategies Options Markets and Contracts Swaps Markets and Contracts Interest Rate Derivative Instruments Credit Default Swaps Risk Management Applications of Options Strategies Risk Management Applications of Swaps Strategies (Also applied in Currency Management, Fixed-Income Portfolio Management) Slide 6

7 Derivatives Level I Derivative Markets and Instruments Forward Markets and Contracts Futures Markets and Contracts Options Markets and Contracts Swaps Markets and Contracts Risk Management and Applications of Option Strategies Slide 7

8 Reading 57 Derivative Markets and Instruments Slide 8

9 Definition of Derivatives A derivative is a financial instrument that derives its value from the value of an underlying asset. The underlying asset, or the underlying Equities Fixed-income Currencies Commodities Interest rates Credit Weather, electricity, disaster claims Or even other derivatives Slide 9

10 Classification of Derivatives Forward commitment Two parties of the derivatives are obliged to transact in the future at a previously agreed-on price e.g., forward, futures, and swaps Contingent claim One party has the right but not the obligation to buy or sell the underlying at a pre-determined price, and the choice of buying or selling versus doing nothing depends on a particular random outcome. e.g., options Slide 10

11 Types of Derivatives Forward An over-the-counter derivative contract in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date at a fixed price they agree on when the contract is signed. Futures A futures contract is a standardized and exchangetraded forward contracts. Slide 11

12 Types of Derivatives Swaps An over-the-counter derivative contract in which two parties agree to exchange a series of cash flows whereby one party pays a variable series that will be determined by an underlying asset or rate and the other party pays either a variable series determined by a different underlying asset or rate or a fixed series. Interest Rate Swaps Currency Swaps Equity Swaps Slide 12

13 Types of Derivatives Options A derivative contract in which one party, the buyer, pays a sum of money (premium) to the other party, the seller or the righter, and receives the right to either buy or sell an underlying asset at a fixed price (exercise price, or strike price) either on a specific expiration date or at any time prior to the expiration date. Credit Derivatives A credit derivative is a class of derivative contracts between two parties, a credit protection buyer and a credit protection seller, in which the latter provides protection to the former against a specific credit loss. Slide 13

14 Forward Commitments vs. Contingent Claims Forward Forward Commitments Futures Derivatives Swaps Contingent Claims Options Credit Derivatives Slide 14

15 Exchange-trade vs. OTC Exchange-traded OTC Contract Standardized Customized Default risk Almost none To some extent Liquidity Generally high Relatively low Transparency high Low Regulation High regulated Regulated to some extent Privacy Low High Slide 15

16 Practice Problems 1. Which of the following statements is true about contingent claims? A. Either party can default to the other. B. The payoffs are linearly related to the performance of the underlying. C. The most the long can lose is the amount paid for the contingent claim. 2. Which of the following distinguishes forwards from swaps? A. Forwards are OTC instruments, whereas swaps are exchange traded. B. Forwards are regulated as futures, whereas swaps are regulated as securities. C. Swaps have multiple payments, whereas forwards have only a single payment. Slide 16

17 Practice Problems 3. Which of the following statements most accurately describes exchange-traded derivatives relative to over-the-counter derivatives? Exchange-traded derivatives are more likely to have: A. greater credit risk. B. standardized contract terms. C. greater risk management uses. 4. Which of the following characteristics is associated with over-the-counter derivatives? A. Trading occurs in a central location. B. They are more regulated than exchange-listed derivatives. C. They are less transparent than exchange-listed derivatives. Slide 17

18 Reading 60 Option Markets and Contracts Slide 18

19 Definition of Options An option is a derivative contract in which one party, the buyer, pays a sum of money (premium) to the other party, the seller or the righter, and receives the right to either buy or sell an underlying asset at a fixed price (exercise price, or strike price) either on a specific expiration date or at any time prior to the expiration date. Option price/premium Option premium is paid when the option contract is initiated Call option have a lower premium the higher the exercise price. Put options have a lower premium the lower the exercise price. Exercise the option Exercise is the use of the right to buy or sell the underlying. Slide 19

20 Concepts about Options Long and short The long side: the buyer The short side: the seller, or the writer Unilateral credit risk Only the buyer faces credit risk because only the seller can default. i.e., default in options is only from the short to the long. Slide 20

21 Concepts about Options Call options and Put options Call: the right to buy the underlying Put: the right to sell the underlying Buying a call option is consistent with a bullish point of view while buying a put option is consistent with a bearish point of view. American options and European options American options: can be exercise at any time prior to expiration European options: can be exercised only at expiration date. Generally, value of American option value of Slide 21 European options

22 Concepts about Options Termination Actual delivery Cash settlement Moneyness of options An option s moneyness refers to the relationship between the price of the underlying, S, and the exercise price, X. Slide 22 Moneyness Call Option Put Option In the Money S > X S < X At the Money S = X S = X Out-of-the-Money S < X S > X Deep in-the-money: far in-the-money Deep out-of-the-money: far out-of-the-money

23 Payoff and Profit Payoff and Profit of options Profit = Payoff Option Premium Payoff and Profit of the call buyer Payoff: c T = Max(0, S T X) Profit: Π = Max(0, S T X) c 0 Payoff and Profit of the put buyer Payoff: p T = Max(0, X S T ) Profit: Π = Max(0, X S T ) p 0 Slide 23

24 Payoff and Profit of a Call Option Payoff & Profit of buying a call Payoff & Profit of selling a call c 0 0 -c 0 S T 0 S T Slide 24 X X

25 Payoff and Profit of a Put Option Payoff & Profit of buying a put Payoff & Profit of selling a put p 0 0 ST 0 -p 0 S T Slide 25 X X

26 Types of Options Financial options Stock options (Equity options ) Index options Bond options Interest rate options Currency options Options on futures Commodity options Options on electricity, various sources of energy, and weather Real options Slide 26

27 Index Options Example: Index Call Options Calculate the payoff at expiration for a call option on the S&P 100 stock index in which the underlying price is at expiration, the multiplier is 100, and the exercise price is: S T = Call payoff, X=450: Max(0, ) 100=$12,932 Call payoff, X=650: Max(0, ) 100=0 Slide 27

28 Index Options Example: Index Put Options Calculate the payoff at expiration for a put option on the S&P 100 in which the underlying is at at expiration, the multiplier is 100, and the exercise price is: S T = Put payoff, X=450: Max(0, ) 100=0 Put payoff, X=650: Max(0, ) 100=$7,068 Slide 28

29 Bond Options Example: Bond Call Options Calculate the payoff at expiration for a call option on a bond in which the underlying is at $0.95 per $1 par at expiration, the contract is on $100,000 face value bonds, and the exercise price is: $0.85. $1.15. S T = $0.95 Call payoff, X=$0.85: Max(0, ) 100,000=$10,000 Call payoff, X=$1.15: Max(0, ) 100,000=$0 Slide 29

30 Bond Options Example: Bond Put Options Calculate the payoff at expiration for a put option on a bond in which the underlying is at $0.95 per $1 par at expiration, the contract is on $100,000 face value bonds, and the exercise price is: $0.85. $1.15. S T = $0.95 Put payoff, X=$0.85: Max(0, ) 100,000=$0 Put payoff, X=$1.15: Max(0, ) 100,000=$20,000 Slide 30

31 Currency Options Example: Currency Call Options Calculate the payoff at expiration for a call option on the British pound in which the underlying is at $1.438 at expiration, the options are on 125,000 British pounds, and the exercise price is: $1.35. $1.55. S T = $1.438 Call payoff, X=$1.35: Max(0, ) 125,000=$11,000 Call payoff, X=$1.55: Max(0, ) 125,000=$0 Slide 31

32 Currency Options Example: Currency Put Options Calculate the payoff at expiration for a put option on the British pound where the underlying is at $1.438 at expiration, the options are on 125,000 British pounds, and the exercise price is: $1.35. $1.55. S T = $1.438 Put payoff, X=$1.35: Max(0, ) 125,000=$0 Put payoff, X=$1.55: Max(0, ) 125,000=$14,000 Slide 32

33 Interest Rate Call Options Payoff of an interest rate call: Days in underlying rate NP Max(0, Underlying rate at expiration Exercise rate)( ) 360 Payoff of an interest rate put: Days in underlying rate NP Max(0, Exercise rate Underlying rate at expiration)( ) 360 NP: Notional Principal Interest rate options are settled in cash. The payoff is paid at the end of the period implied by the underlying rate, instead of at expiration of the option. Therefore, no discount is needed. Slide 33

34 Interest Rate Call Options Borrowers use interest rate call options to hedge the risk of rising rates on floating-rate loans. Lenders use interest rate put options to hedge the risk of falling rates on floating-rate loans. Slide 34

35 Interest Rate Options Example: Interest Rate Call Options Calculate the payoff at an interest rate call option under the condition given. The underlying is a 90-day interest rate and is at 9 percent when the options expire. The notional principal is $50 million. The exercise rate is: 8 percent percent. S T = 9% Call payoff, X=8%: Max(0, 9% 8%) (90/360) 50,000,000=$125,000 Call payoff, X=10.5%: Max(0, 9% 10.5%) (90/360) 50,000,000=$0 Slide 35

36 Interest Rate Options Example: Interest Rate Put Options Calculate the payoff at an interest rate put option under the condition given. The underlying is a 90-day interest rate and is at 9 percent when the options expire. The notional principal is $50 million. The exercise rate is: 8 percent percent. S T = 9% Put payoff, X=8%: Max(0, 8% 9%) (90/360) 50,000,000=$0 Put payoff, X=10.5%: Max(0, 10.5% 9%) (90/360) 50,000,000=$187,500 Slide 36

37 Cap and Floor Interest rate cap A series of call options on an interest rate, with each option expiring at the date on which the floating loan rate will be reset, and with each option having the same exercise rate (cap rate). Each component call option is called a caplet. Each caplet is independent of the others and exercise of one caplet does not affect the right to exercise any of the others. The price of an interest rate cap is the sum of the price of the caplets that make up the cap. Slide 37

38 Cap and Floor Interest rate floor A series of put options on an interest rate, with each option expiring at the date on which the floating loan rate will be reset, and with each option having the same exercise rate (floor rate). Each component put option is called a f1oorlet. Each floorlet is independent of the others and exercise of one floorlet does not affect the right to exercise any of the others. The price of an interest rate floor is the sum of the price of the floorlets that make up the floor. Slide 38

39 Cap and Floor An interest rate collar A combination of a long cap and a short floor or a short cap and a long floor. The proceeds from shorting can reduce or even eliminating the cost of longing. Zero-cost collar Set the exercise rates such that the price received for the sale of the floor precisely offsets the price paid for the cap, thereby completely eliminating the upfront cost. Slide 39

40 Payoff Values Intrinsic value (exercise value) is what the option is worth to exercise it based on current conditions, which is Max(0, S T X) for calls or Max(0, X S T ) for puts. c T = Max(0, S T X) C T = Max(0, S T X) p T = Max(0, X S T ) P T = Max(0, X S T ) At expiration, a European option and an American option have the same payoff. An option s payoff is its value at expiration. Slide 40

41 Payoff Values Time value / speculation value the difference between the market price of an option and its intrinsic value. It reflect the potential for the option s intrinsic value at expiration to be greater than its current intrinsic value. At expiration, the time value is zero. Option Price = Intrinsic Value + Time Value Prior to expiration, option price > intrinsic value. At expiration, option price = intrinsic value Slide 41

42 Option Price = Intrinsic Value + Time Value Slide 42

43 Put-Call Parity Fiduciary call = A European call + a risk-free bond Protective put = A European put + the underlying asset Fiduciary Call Transaction Current Value (t=0) Value at Expiration (t=t) S T X S T > X Buy a call c 0 0 S T X Buy a bond X/(1+r) T X X Protective Put Total c 0 + X/(1+r) T X S T Buy a put p 0 X S T 0 Buy the underlying asset S 0 S T S T Total p 0 + S 0 X S T Slide 43

44 Put-Call Parity Put-call parity fiduciary call = protective put call + risk-free bond = put + underlying asset c + X (1 + R f ) T = p + S 0 Note: For European options only The risk-free bond matures on the option expiration day and has a face value equal to the exercise price of the call. The call and the put have the same underlying asset, strike price, and term. Slide 44

45 Synthetics Synthetic call = long put + long underlying + short bond c 0 = p 0 + S 0 X/(1+r) T Synthetic put = long call + short underlying + long bond p 0 = c 0 S 0 + X/(1+r) T Synthetic underlying = long call + long bond + short put S 0 = c 0 + X/(1+r) T p 0 Synthetic bond = long put + long underlying + short call X/(1+r) T = p 0 + S 0 c 0 If put-call parity does not hold, arbitrage can be carried out by buying the lower and selling the higher. Slide 45

46 Practice Problems 1. Which of the following statements about call options at expiration is true? A. The profit potential for the buyer of the option is unlimited. B. The long s largest loss is the option premium. C. Both are correct. 2. Which of the below positions is most risky, in the sense of having largest potential loss? A. A long position in call options. B. A short position in put options. C. A short (written) position in call options. Slide 46

47 Practice Problems 3. Consider a put option on Deter. Inc. with an exercise price of $45. The current stock price of Deter is $52. What is the intrinsic value of the put option? How about the moneyness? A. $7 At-the-money B. $0 Out-of-the-money C. $0 At-the-money 4. Which statement about option valuation is FALSE? A. Prior to maturity, out-of-the-money options have no value. B. The value of an option is its time value plus its intrinsic value. C. The buyer of a call option contract can never lose more than the initial premium. Slide 47

48 Practice Problems 5. Based on put call parity for European options, a synthetic put is most likely equivalent to a: A. Short call, long underlying asset, short bond. B. Long call, short underlying asset, long bond. C. Long call, long underlying asset, short bond. Slide 48

49 Practice Problems 6. European put and call options with an exercise price of 45 expire in 115 days. The underlying is priced at 48 and makes no cash payments during the life of the options. The risk-free rate is 4.5%. The put is selling for 3.75, and the call is selling for a) Is the call option correctly priced? b) How could we execute the arbitrage opportunity? Solution to A: C 0 = P 0 + S 0 X/ (1 + r) T T = 115/365 = C 0 = /(1.045) = 7.37 Hence, the actual call is overpriced. Slide 49

50 Practice Problems 6. European put and call options with an exercise price of 45 expire in 115 days. The underlying is priced at 48 and makes no cash payments during the life of the options. The risk-free rate is 4.5%. The put is selling for 3.75, and the call is selling for a) Is the call option correctly priced? b) How could we execute the arbitrage opportunity? Solution to B: Sell the call for 8.00 and buy the synthetic call for To buy the synthetic call, buy the put for 3.75, buy the underlying for 48.00, and issue a zerocoupon bond paying at expiration. This transaction will bring in = Slide 50

51