Chapter 12: Characteristics of Derivatives securities Flashcards
What is a derivative?
> A derivative is a security or contract that promises to make a payment at a specified time in the future.
the amount of which depends on the upon the behaviour of some underlying security
up to and including the time of the payment
What is an option?
An option gives the investor a right, but not an obligation, to buy or sell a specified asset on a specified future date.
Define:
1. Call option
2. Put option
- A call option gives the right, but not an obligation, to buy a specified asset on a set date in the future for a specified price
- A put option - gives the right, but not an obligation, to sell a specified asset on a set date in the future for a specified price.
What is the difference between a long forward position and a short forward
position?
A long forward position is where an individual undertakes to buy the underlying asset at the agreed price and the specified time in the future. XX
A short forward position is where the individual undertakes to sell the underlying asset at the agreed price and the specified time in the future. XX
What is the difference between entering into a long forward contract when the forward price is R50 and taking long position in a call option with a
strike of R50?
> The difference is between right and obligation. X
When entering into a long forward contract, you are obligated to purchase the asset at the agreed price on the specified date. X
However, with a long call option, the holder has
right to purchase the asset in the future and does not have to exercise this right. X
Therefore, the holder of the long call option is not obligated to purchase the asset in the future, and for this right a premium will be paid whereas in a forward no premium is paid. X
A speculator is bullish of BHP Billiton. Would he/she be prepared to (2)
(a) Buy a call option on BHP Billiton?
(b) Write a call option of BHP Billiton?
(c) Buy a put option of BHP Billiton?
(d) Write a put option on BHP Billiton?
If a speculator is bullish on BHP Billiton, it means they believe the stock price will increase in the future
(a) Yes
(b) No - they would be obligated to sell the stock at the strike price if the buyer exercises the option.
Bullish - they would have to sell the stock at a lower price than the current market value, resulting in a loss.
(c) No
(d) Yes - might be willing to write (sell) a put option, as this would allow them to collect the premium from the buyer. If the stock price increases as expected, the buyer is unlikely to exercise the option, and the speculator would profit from the premium received
A trader enters into a short forward contract on ¥100 million. The 3 month forward exchange rate is R18.77 per ¥. How much does the trader gain or
lose if the exchange rate at the end of the contract is
(a) R19.02 per ¥
(b) R17.76 per ¥
The trader agreed to sell ¥100 million at R18.77 per ¥, which is equal to R18.77 * ¥100 million = R1,877,000,000.
(a) Loses (19.02 - 18.77)R100 million = R25 million XX
(b) Gains (18.77 - 17.76)R100 million = R101 million X X
(v) The current gold price is $540 per ounce. The forward price in one year is $700. Assuming that an arbitrageur can borrow funds at 10% (simple
interest), is it possible for him to make a riskless profit by taking offsetting positions in the spot and forwards markets? How? (3)
Yes it is possible for him to make an arbitrage profit. X
An individual can borrow $540 to buy 1 once of gold for $540 today in the spot market. X
Then the individual can enter into a short forward position to sell the once of gold in 1 year’s time for $700. X
In 1 year’s time, the individual will have to pay back the loan of $540(1.1) = $594. X
Making a riskless profit of $106. X X
Q3) A company knows that it will need to buy equipment valued at £1 million in 6 months time. It can hedge the foreign exchange risk by using a forward contract or a call option on the pound.
Explain how, and compare the advantages/disadvantages of each method [4]
The company can hedge the foreign exchange risk using a forward contract by locking into an exchange rate today. X
The forward contract will obligate both
parties to exchange in 6 months and thus enable the company to fix the cost of the
machine today. X
- However, the company will have both upside and downside risk. X
+ The company also has no initial outflow i.e. does not need to pay a premium to enter into contract. X
By hedging the foreign exchange risk using a call option on the pound, the company has the right to buy pounds at a fixed rate in the future. X
If the exchange rate increases, then the holder can exercise the option and purchase pounds at
a cheaper rate. X
+ If however, the exchange rate decreases, the holder does not have to exercise the option and can purchase pounds in the open market. Therefore, company only has upside risk. X
- The disadvantage is that for this right the
company has to pay a premium upfront. X
- Consider a forward on a dividend-paying asset S. The contract is entered into at time t and initially has a value of zero. At time T (maturity) the holder must buy the asset for an amount F (the forward price). Suppose that it is known at time t that a dividend of D will be paid at time td, where t < td < T (i.e. D is a known amount to be paid at a known time td). Determine the forward price
by means of a no-arbitrage argument. You may assume that the continuously compound risk free interest rate is constant r.
Total [5]
At time t
* Short forward contract X
* Buy asset St and invest dividends received at time td into the bank. X
* Borrow St from the bank X
* Initial position has zero value. X
At time T
* receive F and sell assetX
* Payback loan of Stexp(r(T −t)) − Dexp(r(T −td)) X
Since initial position has zero-value, the final position must have zero value as wellX
otherwise arbitrage will be available.X
Therefore,
F = Stexp(r(T −t)) − Dexp(r(T −td)) = (St − Dexp(−r(td−t)))exp(r(T −t))
- A stock is currently priced at R47.50. The price of a six month European call option with an exercise price of R50 is R1.20.
(i) State the put-call parity relationship, defining all terms used. (1)
(ii) Hence, and assuming no arbitrage in the market, calculate the price of a six month European put option with the same exercise price, if the risk free interest rate (continuously compounded) is 10% p.a. and no dividends are
to be paid during the term of the option. (2)
Total [3]
(i) The put-call parity relationship is given by:
ct + Ke−r(T −t) = pt + St X
where:
ct is the price of the call option at time t,
K is the strike price of the put and call options,
r is the risk-free rate of interest (continuously
compounded),
T −t is the time to maturity,
pt is the price of the put option and
St is the price of the underlying asset. X
(ii) pt = 1.20 + 50exp(-0.1*0.5) - 47.5 = R1.26
- State upper and lower bounds for the prices of European call and put options on a non-dividend-paying stock, justifying each by reference to the trading strategy that could be adopted to yield a riskless profit if the inequality did not hold.
Total: [6]
European call:
* ct ≤ St as the option cannot be worth more than the stock, otherwise a riskless profit could be made by buying the stock and writing the option. X
X
*ct ≥ max(0, St − Ke−r(T −t)), as otherwise a riskless profit could be made by buying the option, short-selling the stock and investing the net proceeds at
the risk-free rate. X X X X
European put:
* pt ≤ Ke−r(T −t), as otherwise a riskless profit could be made by writing the option and investing the premium at the risk-free rate. X X
- pt ≥ max(Ke−r(T −t) − St, 0), as otherwise a riskless profit could be made by borrwing at the risk-free rate to buy the option and the share. X X X X
- On the 1st June 2011, Jolly Rodger shares, which are non-dividend paying shares, were trading at R15.75. Kathryn would like to short a 9 month forward contract on Jolly Rodger shares.
The current risk-free rate of interest is 8.64% per annum effective.
(i) Define what is meant by a forward contract and explain the difference between a long forward position and a short forward position, in the context of derivatives. (2)
(ii) Determine the no-arbitrage forward price on the short forward contract that Kathryn would agree to. (2)
(iii) On the 1st October 2011, Jolly Rodger shares are priced at R14.23 per share.
Determine the no-arbitrage forward price on a 5 month forward contract on Jolly Rodger Shares. (1)
(iv) Determine the value of the short forward contract, that Kathryn entered
into on the 1st June 2011, on the 1st October 2011. (2)
Total: [7]
(i) A forward contract is an agreement between two parties to buy (or sell) an asset in the future on a set date at a specified price. X X
A long forward position is when an individual agrees to buy the asset,X
whereas a short forward position is when an individual agrees to sell the asset. X
(ii) No-arbitrage forward price F0 = 15.75(1.0864)9/12XX = 16.75995606 ≈R16.76 X X
(iii) No-arbitrage forward price F1 = 14.23(1.0864)5/12 = 14.72992828 ≈ R14.73
X X
(iv) Value of the short forward is (F0−F1)(1+i)
−(T −t)X = (16.76−14.73)(1.0864)−5/12X =
1.961129403 ≈ R1.96XX
- (i) Define what a European put option is and state the payoff function. (2)
(ii) Explain the difference between a European put, a Bermuda put and an American put option. (2)
(iii) Describe the difference between a long European put option and a short forward. (2)
Total: [6]
(i) A European put option gives the holder the right, but not the obligation,
to sell an underlying asset at maturity for a specified price.
The payoff at maturity is given by max(0, K − ST ) X
(ii) A European option can only be exercised at maturity, X
a Bermuda option can only be exercised on specific dates during the term of the contract X and on maturity and
an American option can be exercised any time up to and including maturity. X (If all correct - X)
(iii)
The difference is between right and obligation. X
When entering into a short forward contract, you are obligated to sell the asset at the agreed price on the specified date. X
However, with a long put option, the holder has right to sell the asset in the future and does not have to exercise this right. X
Therefore, the holder of the long put option is not obligated to sell the asset in the future, and for this right a premium will be paid whereas in a forward
no premium is paid. X
- (i) Explain what is meant by an arbitrage-free market (2)
(ii) Give four reasons why price anomalies might exist in a real market. (4)
(iii) Describe briefly the role of speculators, hedgers and arbitrageurs in the
derivatives market and how these groups may use derivatives (6)
Total: [12]
(i) A market is said to be arbitrage-free if there are no opportunities to make a risk-free profit by taking advantage of inconsistencies in the prices of different assets. XX XX
(ii) Price anomalies might exist in a real market for various reasons, including:
* The expenses associated with buying and selling the assets involved might be so high that they would “cancel out” and profit XX
* There might be delays involved in buying and selling the assets and/or in obtaining up-to-date prices. XX
* Different traders might have access to different information about the securities involved XX
* Different traders might use different models to determine the theoretical price or may use different economic assumptions XX
(iii)
* Role of speculators
> Speculators aim to make a profit by taking a view on the direction in which and/or the extent to which they anticipate the market will move,
e.g. they might buy oil futures if they think that oil prices will go up in the future. XX
> They adopt a risky position that will be profitable if the prices move in the direction and/or to the extent expected, but are exposed to losses if the opposite happens. XX
- Role of hedgers
> Hedgers aim to protect an existing position by acquiring an offsetting position involving other securities, e.g. gold producers might sell gold
futures to protect themselves against a fall in the gold price. XX
> They aim to adopt a risk-free position, i.e. one that is not affected by market price movements. XX
- Role of Arbitrageurs
Arbitrageurs aim to make a risk-free profit by exploiting price anomalies in the markets, e.g. it might be possible (taking into account the current exchange rates) to buy a 10-year dollar-denominated zero-coupon bond more cheaply in New York than in London. By exploiting such
anomalies, arbitrageurs keep the price in the cash and derivative markets in line. XX
If an arbitrage opportunity arises, they simultaneous buy the cheaper asset and short sell the more expensive equivalent. When they subsequently unwind this position, after the market prices have moved back into line, this should generate a profit. X
They need to pay special attention to transaction and delivery costs, since these could easily turn a profit into a loss. X
