derivatives markets for soa exam fm

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(Derivatives Markets) for

Exam FM/2, 3

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Exam FM/2, 3rd Edition

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Table of Contents SOA Exam FM/ CAS Exam 2

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Table of Contents Part 1: Introduction on Derivatives and Risks .............................................................................. 4

Answer keys................................................................................................................................ 5

Solutions ..................................................................................................................................... 5

Part 2: Forward Contracts and Options ........................................................................................ 6

Answer Keys ............................................................................................................................. 13

Solutions ................................................................................................................................... 13

Part 3: Insurance and Other Option Strategies .......................................................................... 19

Answer Keys ............................................................................................................................. 33

Solutions ................................................................................................................................... 33

Part 4: Application of Derivatives- Risk Management ................................................................ 41

Answer Keys ............................................................................................................................. 55

Solutions ................................................................................................................................... 55

Part 5: Financial Forwards and Futures ...................................................................................... 63

Answer Keys ............................................................................................................................. 74

Solutions ................................................................................................................................... 74

Part 6: Swaps ................................................................................................................................ 81

Answer Keys ............................................................................................................................. 88

Solutions ................................................................................................................................... 88

Author’s Biography ...................................................................................................................... 93

Part 1: Introduction on Derivatives and Risks SOA Exam FM/ CAS Exam 2




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1. Which of the followings cannot mitigate credit risk?

(A) Collateralization (B) Bank letters (C) Haircut (D) Hedging (E) No answer is given in (A), (B), (C), and (D)

2. Which of the following is not associated with short sales?

(A) Collateral (B) Haircut (C) Credit risk (D) Lease rate (E) Investment

3. Which of the followings is not the usage of derivatives?

(A) Risk management (B) Reduce transaction cost (C) Predict future price (D) Speculation (E) Arbitrage

4. Which of the followings is false?

(A) Derivatives provide an alternative to simple sale or purchase, and thus increase the

range of possibilities for an investor or a manager seeking to accomplish some goals (B) The construction of a given financial product from other products is called financial

engineering (C) Financial market permits diversifiable risk to be widely shared (D) Catastrophe bonds are bonds that an issuer needs to repay if there is a specified

event causing large insurance claims (E) Over-the-counter market is market where buyers and sellers transact with banks and

dealers rather than on an exchange

5. Which of the following are reasons to short-sell? I. Speculation II. Arbitrage III. Financing IV. Hedging

(A) I, II, III (B) I, II, IV (C) I, III, IV (D) II, III, IV (E) No answer is given in (A), (B), (C), and (D)

Part 1: Introduction on Derivatives and Risks

Part 1: Introduction on Derivatives and Risks SOA Exam FM/ CAS Exam 2




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Answer keys 1 D

2 E

3 C

4 D

5 E

Solutions 1. Collateralization is to pledge a liability using assets. It definitely reduces the exposure of

credit risk. Bank letters is the acknowledgement letter from bank, which gives guarantee to the creditors on the payment of the debtors. Haircut is similar to collateralization, which is used in short sales.

Hedging mitigates the market risk but not credit risk. For example, a gold seller hedges the gold price by purchasing a put option. That does not protect the gold seller from the probability that the buyer is unable to pay for the gold. The answer is (D).

2. The purpose of collateral and haircut is to reduce the credit risk of counterparty. Lease rate

is the rate at which the asset borrower is charged for the borrowing. Obviously, hedging is not associated with short sales. Short selling is a speculative activity, which is not an investment. The answer is (E).

3. Derivatives are risky assets; most risky assets can be used for risk management. Derivatives

can reduce transaction costs, since replicating the derivatives might involve trading more than one asset or liability which incurs more transaction cost. When there is mispricing, there is arbitrage opportunity. Hence, the answer is (C).

4. The answer is (D). The truth is just the opposite. Catastrophe bonds are loans that need to

be repaid if the specified event does not occur. It does not repay only when the specified event happens.

5. When it is perceived that the underlying asset is falling in price in the future, the short-seller

short sells the asset. An arbitrageur may short sell to take advantage of a mispriced product. A short-sale is also a way to borrow money. Finally, market-makers and traders can undertake a short-sale to offset the risk of owning the stock or derivative on the stock. Hence, the answer is (E).

Part 3: Insurance and Other Option Strategies SOA Exam FM/ CAS Exam 2




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Part 3: Insurance and Other Option Strategies 1. Which of the followings is false? (A) Floor involves the purchasing of put options (B) Floor is to guarantee a minimum sale price of the underlying asset (C) Floor is a strategy for long position in underlying asset and short position in put option (D) Floor incurs a huge sum of money at t=0 and 0 cost at expiration date (E) The profit diagram of a floor is similar to the profit diagram of a purchased call 2. Which of the followings is true? (A) A zero-cost collar must be a written forward (B) A zero-cost collar must consist of 2 options with the same strike price (C) A zero-cost collar must have zero collar-width (D) A zero-cost collar is a strategy used only by long position on the underlying asset (E) A zero-cost collar serves as a cheaper put option 3. Which of the followings is false? (A) An option spread is a position consisting of only calls or only puts (B) A bull call spread can be constructed to replicate a bear call spread (C) A bear call spread can be constructed to replicate a bear put spread (D) The maximum profit of a bull spread is always bounded (E) The answer is not given in (A), (B), (C), and (D) 4. You are given the following 6-month option premiums: Which of the followings makes the greatest profit when the spot price at expiration is $33.50,

if the risk free rate is 2%? (A) Purchased 30-call (B) Synthetic forward at forward price $32.50 (C) 30.00-32.50 bull call spread (D) 30.00-32.50 bull put spread (E) 30-32.50-35 butterfly spread

Strike Price, K K-strike Call Option Premium

K-strike Put Option Premium

$30.00 $0.6984 $0.9577

$32.50 $0.1066 $2.8042

$35.00 $0.0080 $5.1438

Part 3: Insurance and Other Option Strategies SOA Exam FM/ CAS Exam 2




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Answer Keys

1 C 11 E 21 D 31 E 41 B

2 E 12 D 22 E 32 E 42 E

3 E 13 C 23 B 33 A 43 E

4 B 14 E 24 E 34 C 44 C

5 D 15 B 25 D 35 B 45 B

6 D 16 C 26 C 36 A 46 C

7 E 17 E 27 C 37 B 47 D

8 E 18 C 28 E 38 B 48 A

9 D 19 C 29 E 39 C 49 A

10 A 20 D 30 E 40 E

Solutions

1. (C) is incorrect. A floor is a strategy applied by sellers who want to hedge their downward risk using put option. It is short position in underlying asset and long position in put option.

2. (A) is incorrect, because a zero-cost collar may also consist of a call option and a put

option with different strike prices yet the same premium. (B) is false because the 2 options may have different strike prices. (C) is incorrect also, since zero collar-width implies having 2 options with the same strike prices. (D) is incorrect, since a zero-cost collar can be applied for both long and short position on underlying asset, depending on the intention of the use of the collar. (E) is correct, because a collar consists of buying a put option and selling a call option. When a call option is sold, this reduces the cost of the put option, hence, a cheaper put option.

3. (E) is the answer. Essentially, a bull call spread and a bull put spread can have exactly

the same payoff. Besides, an opposite position of a bull call spread can replicate a bear call spread. For example, shorting a bull call spread can be used to replicate a long bear spread position. Try and see!

4. For (A), the profit is ($33.50- $30)- $0.6984e0.02(0.5)= $2.79458.

For (B), the profit is ($33.50- $32.50)- ($0.1066-$2.8042)e0.01= $3.7247. For (C), the profit is ($33.50- $30)- ($33.50- $32.50)- ($0.6984- $0.1066)e0.01= $1.90225. For (D), the profit is (-$0.9577+ $2.8042)e0.01= $1.865. $0.9451. For (E), the profit is -$0.9577e0.01 + $2.8042e0.01 – ($33.50– $32.50) + $0.1066e0.01 – $0.080e0.01 = $0.8919 The answer is (B).

5. A 30-35 written strangle consists of selling a 30-strike put option and a 35-strike call

option. Since the price at expiration is $32, both the options are out-of-the money. The profit of the profit is the future value of the premium: ($0.9577+ $0.0080)e0.02(0.5)= $0.9754. The answer is (D).

Biography SOA Exam FM/ CAS Exam 2



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Author’s Biography

Alvin Soh was born in Penang, Malaysia. He has been keen in sharing and helping his peers in

actuarial exams. His strong passion in mathematics and actuarial career is reflected in his fast

progress in actuarial exams. He has passed all the preliminary exams in the mere 1.5 years and

he is more than willing to share his study methods and experience to every actuarial student

striving to progress in exams. He has also passed an advanced level exam and is pursuing his

CERA and FSA in Finance and Enterprise Risk Management. He is now working as an actuarial

analyst in Prudential Financial Inc.

The following is the progress of his exams:

Exam Passed Sitting

P/1- Probability Spring 2007

FM/2- Financial Mathematics Fall 2007

MLC- Models for Life Contingencies Spring 2008

MFE/3F- Models for Financial Economics Fall 2008

C/4- Construction and Evaluation of Actuarial Models Fall 2008

AFE- Advanced Finance and Enterprise Risk Management Spring 2009

derivatives markets for soa exam fm

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