Derivatives Mid PDF

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Derivatives mid semester exam...

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Derivatives Mid-semester Examination Question 1 (1 mark) The S&P/ASX 200 Index (ie the physical market) is trading at 4915.36. What is the price of the June 2021 SPI200 futures contract, which has 98 days to expiry, when the continuously compounded risk free rate of return is 0.85332% and the dividend yield on the S&P/ASX 200 Index is 3.25%pa? a) 4884 b) 4883.83 c) 4861.50 d) 4862 A: applying : 𝐾𝐾 = 𝐾0 × 𝐾 ^(𝐾𝐾𝐾−𝐾𝐾𝐾𝐾 +𝐾𝐾𝐾𝐾𝐾𝐾 )×𝐾 we get K=4883.83, but the futures contract is traded in whole numbers, thus the correct answer is rounded to the nearest whole number 4884

Question 2 (2 marks) How much profit or loss would a trader make if they shorted 15 bank bill futures contracts at 98.87 and purchased them back two days later at 98.16? a) Loss of $1,133.25 b) Gain of $16,998.77 c) Gain of $26,069.10 d) Loss of $6,692.58 C: applying : 𝐾 = $1,000,000 (1+ 𝐾𝐾𝐾𝐾𝐾 /100 × 90/ 365) for both the shorting yield (1.13%) and the purchase yield (1.84%) we get a value of 997,221.44 and 995,483.50 respectively for a difference of $1,737.94. As the first transaction was the sale transaction and it occurred at a higher price (lower yield) the transaction results in a profit. Multiplying that gain by 15 gives $26,069.10

Queston 3 (4 marks) How much profit or loss would you a trader make if they went long 5 3-year bond futures contracts at 99.16 and closed them out 2 days later at 99.12? a) Loss of $3,611.45 b) Gain of $643.85 c) Gain of $3,611.45 d) Loss of $643.85 D: Applying 𝐾 = 1000 × [ 𝐾×(1−𝐾 6)/ 𝐾 + 100 × 𝐾 6 ] for both the purchase price 99.16 (yield 0.84%) and sale price 99.12 (yield 0.88%) we get $115,254.96 and $115,126.19 for a difference of $128.77. Note: v is calculated to 8 decimal places. This trade results in a loss and 5 contracts results in a total loss of $643.85

Questions 4 and 5: Consider the following table of trades in the SPI200 futures contract.

Number of contracts traded

Price

Open Position

Profit in $

Profit (points)

25 (ie long 25 contracts)

6402

25

0

0

-20 (ie short 20 contracts)

6398

5

(63986402)*(25)*25 =-2,500

-100

30

6371

35

-3,375

-135

35

6386

70

13.125

525

15

6392

85

10.500

420

Close

6408

85

34,000

1360

$51,750

2,070

Total

Question 4 (1 mark) What is the open position at the close of trading? a) Long 25 b) Long 85 c) Short 15 d) Long 45 B The open position at the close from the above table is long 85 contracts

Question 5 (3 marks) In points, what was the total profit or loss from the day’s trading? a) Gain of 2070 points b) Gain of $51,750 c) Loss of 325 points d) Gain of 175 points . A In points is the key term. If it were dollars, then B would be the correct answer

Questions 6 and 7: Consider the following table of trades in the 6375 call option on the SPI200 futures contract.

Number of contracts traded

Premium (points)

Open Position

Total Premium Received / (Paid)

100 (ie long 100 contracts) -150 (ie short 150 contracts) -100

16.2

100

-1620

19.3

-50

2895

23.7

-150

2370

100

4.2

50

-840

-150

12.2

0 breakeven

610

Total

3,415

Question 6 (1 mark) What is the open position at the close of trading? a) Long 250 b) Square (ie no open contracts) c) Short 250 d) Long 200

Question 7 (2 marks) In dollars, what was the total premium received / paid from the day’s trading? a) Received $85,375 b) Paid $85,375 c) Received $3,415 d) Paid $3,415 A: the amounts of points received was 3415, but in dollars we need to multiply this figure by 25 and hence we receive $85,375

Questions 8 through 13 Consider the information provided below and answer the following questions Questions 8 through 13 Consider the information provided below and answer the following questions. A stock is trading at $63.15 and you wish to purchase an AMERICAN put on this stock with a strike price of $60 and 2 years to expiry. At the end of the first year, the stock is expected to pay a dividend of $4.75 per share. At the end of the second year, the stock is expected to pay a dividend of $4.25. The continusously compounded risk free rate is 0.75% and the volatility of the stock is 45%.

Question 8 (1 mark) Is the proportional move up and down for this stock… a) 56.83% up and 36.24% down b) 1.57% up and 0.64% down c) 35% up and 35% down d) 15% up and 15% down A: u-1= proportional move up and 1-d= proportional move down. Applying 𝐾 = 𝐾 𝐾√𝐾 we get u=1.568312, which means u-1=0.568312, which in percentage terms is 56.83%. As 𝐾 = 1/ 𝐾 we get d=0.63762823, which means 1-d=0.362372, which in percentage terms is 36.24%

Question 9 (1 mark) Is the probability that the stock decreases in price… a) 39.74% ie (0.3974) b) 60.26% (ie 0.6026) c) 35% (ie 0.3500) d) 15% (ie 0.1500) B The probability of a decrease in the price of the stock is 1-p. Applying 𝐾 = 𝐾 𝐾×𝐾−𝐾 𝐾−𝐾 =0.3974, thus 1-p=0.6026 or 60.26%

Question 10 (2 marks) Are Su’, Sd’, Suu’, Sud’, Sdu’, Sdd’… a) $99.04, $40.27, $155.32, $63.15, $63.15, $25.67 respectively

b) $99.04, $40.27, $151.07, $58.90, $58.90, $21.42 respectively c) $94.29, $35.52, $143.62, $55.87, $51.45, $18.40 respectively d) $94.29, $35.52, $147.87, $60.12, $55.70, $22.65 respectively C applying 𝐾𝐾𝐾 = 𝐾𝐾−1 × 𝐾 we get S0u=99.04, but as this stock pays a dividend, we must subtract that dividend from the stock price BEFORE we go any further, thus S0u’=$94.29. Similarly. applying 𝐾𝐾𝐾 = 𝐾𝐾−1 × 𝐾 we get S0d=$40.27, which after subtracting the dividend becomes $35.52. Repeating this process and subracting the second dividend we get S0uu=$147.87, S0uu’=$143.62, S0ud=$60.12, S0ud’=$55.87, S0du=$55.70, S0du’=$51.45, S0dd=$22.65, S0dd’=18.40

Question 11 (1 mark) Are fuu, fud, fdu, fdd…. a) $83.62, $0, $0, $0 respectively b) $4.13, $2.13, $0, $0 respectively c) $39.64, $0, $0, $0 respectively d) $0, $4.13, $8.55, $41.60 respectively D Its at this point that students who got the last question wrong will realise their error. it is hoped that students will go back and find their error and correct it. How much is the option in the money based upon the ex-dividend price of the stock at the second stage of the tree?

Question 12 (1 mark) Are fu’, and fd’… a) $0 and $19.74 respectively b) $0 and $28.26 respectively c) $2.47 and $0 respectively d) $2.47 and $28.26 respectively D applying 𝐾𝐾 −1 = (𝐾 × 𝐾𝐾𝐾 + (1 − 𝐾). 𝐾𝐾𝐾)𝐾 −𝐾.𝐾 to the answers in question 11 we get fu=$2.47 and fd=28.26, but as this is an American option we need to test for the potential for early exercise: fu (exercise)=$0 as the price of the stock is above the strike price of the put option and fd (exercise)=$24.48. The early exercise price is below the price of the option, thus the option would not be exercised early. We therefore get fu’=fu=$2.47, and fd=fd’=$28.26

Question 13 (1 mark) The price of the call option is… a) $17.02 b) $22.65 c) $17.87 d) $8.47

C applying 𝐾𝐾−1 = (𝐾 × 𝐾𝐾𝐾 + (1 − 𝐾). 𝐾𝐾𝐾)𝐾 −𝐾.𝐾 to the answers in question 12 we get f=$17.87

Question 14 (2 marks) A stock that is trading at $95.52 has the $95 call option that expires in 297 days trading at a premium of $7.23 and the put option of the same series is trading at $6.34. These prices seem odd to you and you suspect that an arbitrage opportunity exists. You note the continuously compounded risk free rate is 1.25%. What trade do you place and what is your expected profit from this trade? a) Buy the put and sell the synthetic call for a profit of $3.53 b) Buy the call and sell the synthetic put for a profit of $3.53 c) Buy the call and sell the synthetic call for a profit of $0.60 d) Buy the put and sell the synthetic put for a profit of $0.60

C applying put / call parity 𝐾 = 𝐾 + 𝐾 − 𝐾 × 𝐾 −(𝐾×𝐾) we get the theoretical price of the call at $7.82, and the theoretical price of the put at $5.75, thus the call price is cheap and the put price is expensive. Answer c suggests buy the call and sell the synthetic call. The profit from this trade is determined by 𝐾′ = (ℎ ℎ − 𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾) × 𝐾 𝐾𝐾 which gives $0.60

Question 15 (4 marks) A stock is trading at $130. This stock has a volatility of 35%. What is the price of the 9 month put and call options over this stock that have a strike price of $125, when the risk free rate is 1.25%? a) Put price is $11.95 and the call price is $18.25 b) Put price is $9.13 and the call price is $4.85 c) Put price is $18.57 and the call price is $4.85 d) Put price is $12.40 and the call price is $18.57

=0 −× 1−

−× 2

= −− − × − − 2 − 0 × −−𝐾1 𝐾1 = 𝐾𝐾[(𝐾0−𝐾0 )/𝐾]+(𝐾+ 𝐾 2 2 ).𝐾 𝐾.√𝐾 = 0.3119 and 𝐾2 = 𝐾1 − 𝐾. √𝐾= 0.0088. Although the normal distribution table only goes to 2 decimal places we can determine the fractional difference to find N(d1)=0.62244174, N(d2)=0.50351065, N(-d1)=1-N(d1)=0.37755826, and N(-d2)=1N(d2)=0.49648935. Applying Black Scholes for the call we get 𝐾0 = (𝐾0 − 𝐾0 ). 𝐾[𝐾1 ] − 𝐾.𝐾 −𝐾𝐾 . 𝐾[𝐾2 ]=$18.57, and for the put 𝐾0 = 𝐾𝐾 −𝐾𝐾 × 𝐾(−𝐾2 ) − (𝐾0 − 𝐾0) × 𝐾(−𝐾1 )=$12.40

If BHP is trading at $72.56, price the $72.50 European put and call options over this stock which have 289 days to expiry, the risk free rate is 0.25%, the volatility of BHP is 48.5%, and BHP is expected to pay a dividend of $2.51 in 34 days and $2.68 in 216 days. a) call price is $9.61 and the put price is $14.59 b) call price is $14.59 and the put price is $9.61 c) call price is $9.65 and the put price is $14.63 d) call price is $14.63 and the put price is $9.65 Answer: a) Call price is $9.61 and the put price is $14.59

Week 1 Derivatives are a risk management tool • They can be used for speculation and profit, BUT…. • They are best used for risk management

Q: How do you make a small fortune trading derivatives? A: Start with a large one

Derivatives in our daily lives • Just about everyone participates in derivatives in their daily lives without knowing it; purchasing over the counter derivative contracts. These are complex contracts. What are they?

Derivatives are derived from something For a derivative to exist there must be an underlying physical Security

There are offshore derivatives too… • Precious metals Gold, silver, platinum • Industrial metals

Copper, palladium, aluminium • Energy commodities Crude, gasoline, heating oil, coal… • Agriculture commodities Pigs, cattle, wheat, soybeans, orange juice, …. • Building products Lumber • Financial products Equity & debt markets, volatility measures, currencies…

Market • Australian Equity • Australian short-term money market • Australian debt market

Physical • S&P/ASX 200 Index • Bank bills • Bonds – Commonwealth government securities, corporate bonds Derivative • SPI 200 futures contract • 30-day bank bill futures contract • 90-day bank Bill futures contract • 3-year bond futures contract • 5-year bond futures contract • 10-year bond futures contract • 20-year bond futures contract

Clearing House • An entity that stands between participants in a trade that guarantees performance of the trade • Gives confidence to participants of performance

• Eg ASX Clearing House

Novation • The act of swapping one party in a contract for another • For the clearing house to stand between participants to guarantee trades, all contracts must be novated in favour of the clearing house

Physical Delivery • Upon expiry the holder of the short futures position must deliver the appropriate quantity of the underlying physical commodity in the appropriate quality to the clearing house • Upon expiry the holder of the long futures position must take delivery of the physical commodity

Cash Settlement • Upon expiry the party that made a loss pays the amount of that loss to the clearing house • Upon expiry the party that made a gain receives the amount of that gain from the clearing house

Derivatives employ leverage • Because there is no physical asset transaction only a small margin is required to trade • The margin may be only 5% of the principal value of the contract • It therefore is possible to make huge gains and losses

Common derivative types • We will cover these in this course • Futures • Forwards • Options • Swaps More exotic derivative types • Not covered in this course • Binary options

• Collateralised debt obligations • Collateralised loan obligations • Credit default swaps • Swaptions

Homework 1 1. Name four offshore futures exchanges and one Australian futures exchange 1. Chicago Board of Trade 

Agricultural • Wheat • Sea corn • Black Sea Sunflower Oil • Soya beans

2. New York Mercantile Exchange    

Fuel oil Alberta Power Propane Brent Crude

3. London Metals Exchange • • • • •

Gold Silver Steel scrap Lead

4. Tokyo Commodities Exchange 

Barge Gasoline • Barge Kerosene • Dubai Crude oil

•

East Area Peakload Electricity

Australian Securities Exchange • • • •

Feed Barley Sorghum East Australian Wheat WA Wheat

3. What is the point value of the 90-day Bank Bill Futures contract traded on the Australian Securities Exchange? (ASX.com.au) Approximately $24

4. What is the expiry date of the June 10-year government bond futures contract traded on the Australian securities exchange? Expiry of current 10 year Bond contract is: 12pm on Tuesday, 15 June 2021

5. Explain the concept of “novation” Novation is the legal concept whereby one party assigns their obligations under the contract to another party

6. Explain the role of the clearing house The role of the clearing house is to stand between participants and act as the counterparty to all trades and thereby clear all trades each day. Thus, the clearing house provides protection to all participants against default.

7. Explain the difference between a derivative contract that is exchange traded and over the counter

Exchange traded contracts are traded on an exchange, are standardised and all elements of the contract are published, including price and volume traded. Whereas OTC contracts are privately traded between individuals, hence are customised and are opaque.

8. Explain the difference between cash and physical settlement

Cash settlement is as it sounds, only cash, in fact net cash, is used to settle positions. Whereas, physical settlement means delivery and receipt of the physical commodity

9. What benefits does having a clearing house bring to the efficiency of the market? The prime benefit of the clearing house is that counterparties do not need to perform a credit check on each other, thus every participant in the market is assured of trade performance and therefore is willing to trade without knowing the identity of the counterparty to the trade. Thus, trading is executed with astonishing speed.

Week 2 A futures contract is a legal agreement to buy or sell a particular commodity or asset at a predetermined price at a specified time in the future

Futures contracts • • • • • • • • • • •

Legal agreement Legally binding obligation You must perform Buy or sell You can sell something you don’t own Commodity or asset Common everyday items Predetermined price Price agreed today At a specified future time On a future date agreed today

futures contract

Contract

SPI 200 Index

Bank Bills

3-year Bond

5-year Bond

10-year Bond

20-year Bond

Physical

S&P/ASX 200 Price Index

$1m 90 day bank bill

CGS basket 3years to maturity

CGS backet 5years to maturity

CGS basket 10years to maturity

CGS basket 20years to maturity

Face value

Index x $25

$1m

$100,000

$100,000

$100,000

$65,000

Quoted price

Points (ie $25)

100-yield in points

100-yield in ½ points

100-yield in ½ points

100-yield in ½ points

100-yield in ½ points

Contract months

March, June, Sept, Dec

March, June, Sept, Dec

March, June, Sept, Dec

March, June, Sept, Dec

March, June, Sept, Dec

March, June, Sept, Dec

Expiration

12pm on the 3rd Thursday of the month

12pm on the 15th of the month

12pm on the 15th of the month

12pm on the 15th of the month

12pm on the 15th of the month

Settlement

Cash

12pm on the Thursday before the second Friday of the month Deliverable

Cash

Cash

Cash

Cash

6%

2%

6%

4%

3 years

5 years

10 years

20 years

Coupon Term

90 days

The price of a futures contract is the price of the underlying security TODAY, PLUS The time value of money, MINUS Any missed cashflows associated with the underlying security

Futures payoff • Before expiry is the difference between the purchase price and the sale price • If held to expiry is the difference between the purchase/sale price and the settlement price • Settlement price is the price of the physical at expiry

A forward rate agreement is a transaction in the physical market where the buyer agrees to purchase the physical security from the seller on a future date for a price agreed today

FRAs are very similar to a futures transaction except… • The buyer pays the full market value of the security • The transaction occurs in the physical market • The transaction occurs OTC

Homework 2 1. On what date do the following June futures contracts expire: a. SPI 200: 12pm on third Thursday in contract month which is Thursday, 17 June 2021 b. Bank Bills: 12pm on Thursday before 2nd Friday of the month which is Thursday 10 March 2021 c. 3-Year Bond: 12pm on the 15th day of the month which is Tuesday, 15 March 2021 d. 10-Year Bond: 12pm on the 15th day of the month which is Tuesday, 15 March 2021 e. 20-Year Bond: 12pm on the 15th day of the month which is Tuesday, 15 March 2021

2. A trader shorts 20 SPI 200 contracts at 6745 but the market rallies to 6755 before she sells an additional 20 contracts. The market subsequently falls to 6732 at which point she buys back 35 contracts. How many contracts does she have? How much is her total profit?

At close: Short 5 contracts, for a profit of 720 points = $18,000 6745 *25= 168,625 6755*25=168,875 First loss = 168,825-168,875*20=-5,000 Second trade 6755*25=168,875

6732*25=168,300 (168875-168300) *40=23,000-5,000 At close: Short 5 contracts, for a profit of 720 points = $18,000 3. Draw the payoff diagram for a long SPI200 futures position at 6732. 50 40 30 20 10 0 -10 -20 -30 -40 -50 6710

Profit/ loss points

6720

6730

6740

6750

6760

6770

4. On the same chart, draw the payoff diagram for a short SPI 200 futures position at 6...