Lecture 7 Options and Swaps

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

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. •

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

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,

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.

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.

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

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

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

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.

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

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

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

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

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

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

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 = $7,812.50 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

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

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

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 option @ $1.75/£ ; sells (cost) for $0.08 per £.

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

Comparison of hedging using futures and options .

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.

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.

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:

Swap example

Swap example (cont.)

Swap example (cont.) opportunity, where firms exchange interest rates. Effectively, with the currency swap: – The UK firm raises $180m @ LIBOR+25% (Saving 50bps, or $900,000 per year). – The German firm raises £100m @ 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

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