1. Lecture 7 Options and Swaps

2. Learning Objectives terminology. • Learn how options can be useful.
• Understand the types of currency options and option
terminology.
• Learn how options can be useful.
• Understand the operation of currency and interest rate swaps
Reading: Ch 5 and Ch 11

3. Currency Options An option gives the option contract holder
the right, but not the obligation,
to buy or sell a given quantity of an underlying asset,
commodity or financial security,
at a pre determined price at (European option) or prior (American option)
to a specified time in the future.
An option contract involves two parties,
the writer who sells the option and
the holder who purchases the option. •

4. A currency option is an option where the underlying asset is a currency.
• Options are traded on
both organised exchanges
and over-the-counter (OTC).
• OTC volumes are much larger than those of exchange traded.
Just as with forward and futures contracts

5. Calls and Puts Call options give the holder the right,
but not obligation,
to buy a given quantity of an asset,
which is a currency for currency options,
at a future time, at the price agreed upon today.
Put options give the holder the right,
to sell a given quantity of an asset, which is a currency for currency options,

6. European vs. American Options
European options
–They can only be exercised on the expiration date.
• American options
–They can be exercised at any time up to and including the
expiration date.
• Since the option to exercise early has value (generally),
American options are usually worth more than, or at least equal to, that of European options, ceteris paribus.

7. Option Terminology Strike price / exercise price (X)
• The pre determined price at which the underlying asset may be
sold or bought.
• Depending on the actual exchange rate (spot, S) at the time of
expiration and the exercise rate of the option a profit/loss can
be made.
• Premium (c)
•The price that the buyer of an option pays (the seller of an
option receives) for the rights conveyed by an option.
Expiry date
- a certain date in the future"(T): date on which the
option can be exercised.

8. Option Terminology When is option worth exercising:
An option will be exercised only when it is in the money.
For call options
-- In the money (ITM): S > X
-- At the money (ATM): S = X
-- Out of the money (OTM): S < X
For put options
-- In the money (ITM): S < X
-- Out of the money (OTM): S > X

9. Option Positions Long call Long put Short call Short put
The investor has taken the long (buy) position, i.e., has bought the option.
Long call
Long put
Short call
Short put
The writer has taken the short(sell) position, i.e., has sold/written the option

10. Option Positions Writer Holder Writer Holder long call short call
Long put
short put

11. Option Profit/Payoff
Being in the money does not mean profit, it just means the option is worth exercising.
This is because the option costs (premium) money to buy.

12. Option Profit/Payoff: Long Call
Profit from buying one European call option:
option price c , strike price X, Terminal price ST
The net profit of a “long call” is: Max: (ST - X – c, c)
The maximum loss is c X
Profit ($)
Terminal
price ST ($) c

13. Option Profit/Payoff: Short Call
Profit from writing one European call option
The payoff of a “short call” is just the opposite to that of a long call
The Maximum net profit is c, the loss can be infinite X
Profit ($)
Terminal
price ($) c

14. Option Profit/Payoff: Long Put
Profit from buying a European put option:
option price p, strike price X, Terminal price ST
The net profit of a “long put” is: Max: (X - ST – p, p)
The maximum loss is p X
Profit ($)
Terminal
price ST ($) p

15. Option Profit/Payoff: Short Put
Profit from writing a European put option
The payoff of a “short put” is just the opposite to that of a long put
The Maximum net profit is p, the loss can be infinite X
Profit ($)
Terminal
stock price ($) p

16. Payoffs from Options X ST
X = Strike price, ST = Price of asset at maturity
Long Call Payoff
Short Call Payoff ST X
Long Put Payoff
Short Put Payoff

17. Option Profit/Payoff - Examples: A Currency Call
Consider long a call option on £31,250
The option premium/price is $0.25 per pound
What is the total cost of the call option?
The exercise price is $1.50 per pound
What have you committed yourself to? How much could you gain or lose?
c=$0.25
Profit ($)
ST ($)
X=$1.50
$1.75

18. Option Profit/Payoff - Examples: A Currency Call
Answer:
If the exchange rate at maturity is ST < $1.50/£,
-- The maximum loss of the option holder is $0.25 per pound
-- The maximum loss of the option holder is
$0.25/£ * £31,250 = $7, for the whole contract.
• If ST = $1.75/£, the option holder breaks even.
( ie, ST - X – c = 1.75 – 1.50 – 0.25 = 0)
• If ST > $1.75/£, the option holder makes a profit of $(ST -1.75）per pound
• The investor makes a profit of $(ST – 1.75)/£* £31,250 for the whole contract

19. Option Profit/Payoff - Examples: A Currency Put
Consider long a put option on £31,250
The option premium/price is $0.15 per pound
The exercise price is $1.50 per pound
What have you committed yourself to? How much could you gain or lose?
p=$0.15
Profit ($)
ST ($)
X=$1.50
$1.35

20. Exercise: A Currency Put
The maximum loss of the option holder is ？ ？
• The maximum loss of the option holder is ？ ？ for the whole contract
• If the exchange rate at maturity is ST = $1.35/£, the option holder ？ ？
• If the exchange rate at maturity is ST < $1.35/£, the option holder makes
a profit of ？ ？
• The investor makes a profit of ？ ？ for the whole contract

21. Currency Options v. Currency Futures (cont.)
Example: In January a US firm orders £1m worth of goods from a UK firm deliverable in 6 months. The £ against the $ has depreciated last year from $2.00/£ to $1.80/£ though the US firm feels that the £ will bounce back. US firm is going to buy £1m to pay UK firm in 6 month Can they hedge their position? S0 = $1.80/£. Choice 1: enter forward contract Forward/Futures = $1.75/£. Choice 2: long call option A 6-month call $1.75/£ ; sells (cost) for $0.08 per £.

22. Currency Options v. Currency Futures (cont.)
Answer:
Cost with the forward contract
$1.75/£ * £1m = $1.75m
Cost with the call option contract (X = $1.75/£, c = $0.08 per £)
- If ST > $1.75/£ Exercise the option contract
$1.75/£ * £1m + $0.08 * £1m= $1.83m
- If ST < $1.75/£ Do not exercise the option contract
But the firm will go to the spot market to buy £, as £ is cheaper.
eg, if ST = $1.74/£,
$1.74/£ * £1m + $0.08 * £1m= $1.82m

23. Comparison of hedging using futures and options.

24. Epilogue • Forwards & Futures are obligations to buy or sell;
Preceding sessions discussed possible means of hedging exchange rate risk
• Forwards & Futures are obligations to buy or sell;
Currency options are not obligations. The holder of the option can
choose to let the option expire and not exercise it.
• Owners of expired call options can lose their premium which is
the maximum they can lose.
Losses for futures contracts purchases are virtually unlimited – though losses
can be halted by closing out.

25. Swaps
A currency swap is an agreement between two parties to exchange two
different currencies.
• Swaps are used to manage risk exposure.
• The swap market is an integral part of the international bond markets; it
involves financial institutions, governments and major corporations.
• The swap market is organised by the International Swap Dealers Association
(ISDA), which is responsible for standardising documentation and dealing terms.
One of the main reasons of swaps’ popularity is that they enable parties to raise
funds more cheaply.

26. Swaps
Example: A UK firm wants to raise $180m for 10 years at a floating interest rate for investing in the US and a German firm wants to raise £100m for 10 years at a fixed interest rate for investing the UK. The spot rate is $1.80/£. The borrowing opportunities for the UK and German firms are shown below:

27. Swap example

28. Swap example (cont.)

29. Swap example (cont.) opportunity, where firms exchange interest rates.
Effectively, with the currency swap:
– The UK firm raises LIBOR+25% (Saving 50bps, or $900,000
per year).
– The German firm raises 8% (Saving 0.5% or £500,000 per
year).
• In sum, the swap agreement exploits an arbitrage
opportunity, where firms exchange interest rates.
• Before, swaps firms could use currency forward contracts
but up to two years

30. Options differ from forwards / futures
Conclusions
Options differ from forwards / futures
Not obliged to exercise
Consequently the ‘writing’ counterparty bears some risk
So an option must be paid for
Have seen the different types of option and how they work
Also discussed swaps
and how they might serve to manage risk