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Lecture 5: FX Derivatives

FNCE90016 International Financial Management 1

Outline • Futures contracts • Definition • Payoffs • Margining • Options • Definition • Payoffs • Pricing • The “Greeks” • Readings: Chapter 7

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Futures Contracts: Preliminaries • A futures contract is like a forward contract – It specifies that a certain currency will be exchanged for another at a specified time in the future at prices specified today. • A futures contract is different from a forward contract in that futures are standardized contracts trading on organized exchanges with daily resettlement through a clearinghouse. • Important differences: – Credit risk of a forward contract is to the counterparty – Futures are centrally cleared so the credit risk is to the clearinghouse – Daily resettlement minimizes of futures minimizes default risk but costs money for the traders (they need to fund the margin positions)

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Futures Contracts: Preliminaries • Standardizing features: – Contract size – Trading location – Delivery month – Daily resettlement – Margin (aka initial performance bond) • Margin: – Often about 2 percent of contract value – Denominated in cash or short-dated government debt (e.g. T-bills) – Deposited into a specified collateral account held by the exchange / clearing house

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Future Contract Example: CME AUD Futures

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Future Contract Example: CME AUD Futures Each contract is for 100k AUD

Counterparties are required to exchange currencies at expiry (not just settle the net PnL)

Tick size – the minimum increment of price changes

What months are available to trade?

Maximum size of outstanding contracts allowed before additional disclosure requirements (e.g. your strategy etc.)

Source: CME FX Product Guide.pdf 6

Future Contract Example: CME AUD Futures

Source: https://www.cmegroup.com/trading/fx/g10/australian-dollar.html

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Futures Contracts: Margin • The counterparty risk in a futures contract is with the clearinghouse • If the entity on one side of a trade defaults, the clearinghouse will settle the trade in their place • By placing themselves between each trader, the clearinghouse helps reduce the informational frictions in trading – If they didn’t do this, you would want to think very carefully about who you trade with • The clearinghouse practices a number of tools to manage the risk that traders default • E.g. Due diligence on all traders who wish to trade in large size • Most importantly: Margining • Especially important for futures because they require no initial outlay but can have very large settlement cash flows 8

Futures Contracts: Margin • Margining requires traders to post a small bond when initiating a position – “The initial performance bond” – Usually this is about 2 percent of the total position – This is held in a margin account with the clearinghouse which usually earns a small amount of interest for the trader • Each day, the net profit or loss on the position vs that day’s settlement price is added or subtracted from the margin account • If sufficient losses accumulate and the account falls below a certain level, the maintenance performance bond, the trader is required to post more collateral into the account to bring it back to the level of the initial performance bond

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Futures Contracts: Margin Example • Consider a long position in the CME Euro/U.S. Dollar contract. • The contract size is €125,000 • Prices are quoted in $ per € • The contract (strike) price is $1.30 per € • Maturity is in 3 months. – In three months, if we don’t execute an offsetting trade, we must buy €125,000 at a cost of $162,500 • At initiation of the contract, the long posts an initial performance bond of $6,500. • The maintenance performance bond is $4,000.

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Futures Contracts: Margin Example • While we have this contract open (i.e. we don’t close it with an offsetting trade), we mark-to-market the position against the daily settlement price – The daily settlement price is set by the exchange according to some prespecified rules (e.g. the last traded price at a particular time of day) – If the daily settlement price increases, some collateral in the margin account is taken from the short position and deposited with the long position – Each day’s losses are subtracted from the investor’s account – Each day’s gains are added to the account • This effectively cancels the original contract and creates a new one with one fewer day to maturity

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Futures Contracts: Margin Example • In this example, at initiation of the position, the investor posts an initial performance bond of $6,500. • The maintenance level is $4,000. • If the investor losses more than $2,500, she has a decision to make: – She can maintain her long position by adding more funds – If she fails to do this, the position will be closed out by the exchange with an offsetting short position – The exchange will recoup the loss of the position from what remains in the margin account and the trader keeps whatever is left over

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Futures Contracts: Margin Example • Suppose that the strike equals the spot price at the date the contract was initiated: S($/€)=1.30 • On day 1, the euro strengthens but then soon depreciates

Settle

Gain/Loss

Account Balance

$1.31

$1,250

$7,750 = $6,500 + $1,250

$1.30

–$1,250

$6,500

$1.27

–$3,750

$2,750

+

X

= Y

• If the investor wants to keep her position open, then how much must she deposit, to get to what level of margin? 13

Futures Contracts: Margin Example • Suppose that the strike equals the spot at the date the contract was initiated: S($/€)=1.30 • On day 1, the euro strengthens but then soon depreciates

Settle

Gain/Loss

Account Balance

$1.31

$1,250

$7,750 = $6,500 + $1,250

$1.30

–$1,250

$6,500

$1.27

–$3,750

$2,750 + $3,750 = $6,500

• She must post enough money such that the account balance equals the initial performance bond ($6,500) – this costs her $3,750 14

Futures Contracts: Margin Example • Over the next two days, the euro continues to depreciate against the US dollar so she decides to close out her position

Settle

Gain/Loss

Account Balance

$1.31

$1,250

$7,750 = $6,500 + $1,250

$1.30

–$1,250

$6,500

$1.27

–$3,750

$2,750 + $3,750 = $6,500

$1.26

–$1,250

$5,250

$1.24

–$2,500

$2,750

= $6,500 – $1,250

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Futures Contract: Margin Example At the end of her trading, our investor has three ways of computing her total gains and losses: 1. Sum of daily gains and losses. – -$7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500 2. Contract size times the difference between initial contract price and last settlement price. – -$7,500 = ($1.24/€ – $1.30/€) × €125,000 3. Ending balance on the account minus beginning balance on the account, adjusted for deposits or withdrawals. – -$7,500 = $2,750 – ($6,500 + $3,750) • All of these are equivalent – and the investor can simply withdraw her remaining $2,750 in her account

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Futures Contracts: Margin • By using daily margin resettlements the clearinghouse never takes more than one day’s risk against a trader for a given position • Otherwise the risk would increase with the length of the contract – The EUR can plausibly move 30 – 40% or more against the USD in a year – Over a day, a move of 3-5% would be considered very large

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EUR / USD Currency Futures OPEN

HIGH

LOW

SETTLE

OPEN CHG INTEREST

Euro/US Dollar (CME)—€125,000; $ per € Jun Sep

1.3084 1.3089

1.3118 1.3126

1.3054 1.3062

1.3087 1.3094

.0005 .0005

223,380 16,814

• Open interest refers to the number of contracts outstanding for a particular delivery month – Notice that open interest is greatest in the nearby contract. – In general, open interest typically decreases with term to maturity of most futures contracts. – This information is from June 6, 2013 Wall Street Journal

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Observations • The holder of a long position is committed to pay $1.3084 per euro for €125,000—a $163,550 position. – As there are 223,380 such contracts outstanding, this represents a notational principal of over $36.5 billion – But this amount is smaller than what will be dealt in the FX spot and swaps dealer markets – The majority of institutional and corporate FX flow occurs in the OTC dealer market, not in the futures contracts • Question: Whose interest rates are higher according to these quotes (assuming CIRP holds)?

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Observations • The holder of a long position is committed to pay $1.3084 per euro for €125,000—a $163,550 position. – As there are 223,380 such contracts outstanding, this represents a notational principal of over $36.5 billion – But this amount is smaller than what will be dealt in the FX spot and swaps dealer markets – The majority of institutional and corporate FX flow occurs in the OTC dealer market, not in the futures contracts • Question: Whose interest rates are higher between June and September according to these quotes (assuming CIRP holds)? – We should expect to see higher interest rates in dollar denominated accounts – If not, there may be an arbitrage with spot and money markets 20

Payoffs of a Futures Contract Position: Long Euro futures at strike of The payoff and the profit of a futures are the same since there is no initial cost. The payoff diagram is nearly identical to that of a forward

Payoff

0

ST($/€) F($/€)

• Funding costs of margin will lead to some small deviations 21

Options Contracts: Preliminaries An option gives the holder the right but not the obligation to buy or sell a given quantity of an asset in the future at a price agreed upon today. An important classification of options: Calls vs. Puts – Call options give the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future at prices agreed upon today. – Put options give the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future at prices agreed upon today. • E.g. a call on a stock gives you the right to buy that stock • But we’re getting used to the fact that currencies are more complicated: – A call on the AUD vs. the USD is a put on the USD vs. the AUD 22

Options Contracts: Preliminaries • A second important classification of options: European vs. American Options – European options can only be exercised on the expiration date – American options can be exercised at any time up to and including the expiration date. – American options are usually worth more than European options, all else being equal. – But options have time value and exercising the option discards this time value so usually it is not worth exercising early – Very large differences in interest rates can induce early exercise of American options

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Basic Option Payoff Profiles: Call Payoff at maturity

is the price of the call option (the “premium”) 

is the contract (strike) price

c0 –c0

ST E + c0 E

is the spot price at expiry 

Out-of-the-money In-the-money 24

Basic Option Payoff Profiles: Call Payoff at maturity

Payoff of a long call position can be written as: 

c0 –c0

ST E + c0 E Out-of-the-money In-the-money



At any time we say the call is “in-themoney” if  The call is “out-of-themoney “ if 

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Basic Option Payoff Profiles: Put Payoff at maturity

E – p0 is the price of the put option (the “premium”) 

Short 1 put ST

– p0 E – p0

Long 1 put

is the contract (strike) price is the spot price at expiry 

E In-the-money

Out-of-the-money 26

Basic Option Payoff Profiles: Put Payoff at maturity

E – p0

Payoff of a long put position can be written as:

Short 1 put ST

– p0 E – p0

Long 1 put



At any time we say the put is “in-themoney” if  The put is “out-of-themoney “ if 

E In-the-money



Out-of-the-money 27

Call Option Example • Consider a call option on €10,000 vs. the US$. • The exercise price is $1.50 per € • The option premium is $0.25 per € – If I buy this option, I have the right to buy 10,000 euros and sell 15,000 US dollars at the expiry date – The option costs $2,500 today – It will break-even if the spot price is 0.25 higher at expiry than today (i.e. ), ignoring the opportunity cost of the premium  – Actually, it needs to go up by a little bit more than that to make sure we also earn back the foregone interest on the $2,500 which we could have earned.

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Put Option Example • Consider a put on €10,000 vs. US$ with exercise price of K = $1.50 per € • The option premium is $0.15 per € – If I buy this option, I have the right to sell 10,000 euros and buy 15,000 US dollars at the expiry date – It costs me $1,500 to buy this option • What is the maximum gain on this put option? – €10,000×($1.50 – 0) - $1,500 =$13,500 – The logic: If the price goes to 0 when you exercise, you sell €10,000 for 1.50. You can buy them back at 0 so your revenue is $15,000 – But you paid $1500 for the right to do this so your net profit is $13,500 • At what exchange rate do you break even (ignoring funding costs of the option premium)? 29

Put Option Example • At what exchange rate do you break even (ignoring funding costs of the option premium)? – Now we the need spot price to move such that we make exactly $1,500 at exercise    

– So we need the spot to fall $0.15 to S($/€ ) = 1.35 to get back the initial premium paid to buy the put

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Option values prior to maturity • The greater the range of possible values that the underlying asset price can take, the more likely you will earn a large and positive profit • So the more volatility in the underlying asset price, the greater the value of the asset, all else being equal • Since volatility rises with time to maturity (volatility of returns scales up with the time over which we calculate the return), options with more time to maturity are worth more than options with less time to maturity, all else being equal

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Option values prior to maturity • You would never exercise an option at maturity that was out-of-the-money – You would be choosing to guarantee a loss vs. the current spot price – Even if you want the underlying asset, you could obtain it a better price in the spot market • Once we have paid our premium (i.e. it is a sunk cost), all options are worth something (if only a very small amount) • You would never prefer not to own an option if it costs you nothing, regardless of the spot price • There is some chance it will expire in the money and no chance you will exercise it out-of-the-money – There is no downside and possibly some upside – this is valuable

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Option values prior to maturity • So we are always willing to pay something to hold an option • The difference between the payoff line if exercised today (the intrinsic value) and the market value is referred to as the time value of an option

Option value

Long 1 call

The red line is the payoff at maturity, excl. premium. The green line is the market value of the option

Intrinsic value

Even an out-of-the-money option has value—time value. It is worth something to have the possibility of upside at expiry

Time value Out-of-the-money

St

In-the-money 33

E

European Option Pricing • How is the green line in the previous line determined? – In other words, how do we price an option that expires in the future? • Remember we found that the FX forward price for exchange one currency for another should be close to the price implied by covered interest rate parity – If not, we could make a riskless profit by arbitraging the FX forward with the price of the offsetting contract in the spot and money market • Option pricing works off a similar principle – If we can find an investment strategy that has the same payoff as an option, and we can work out the cost of that strategy, then we can use that to price the option – We can call the investment strategy a “replicating portfolio”

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European Option Pricing • A related idea: – If we can find an investment strategy that always has a payoff that is always at least as high as our option, the option cannot be worth more than this strategy – If we can find an investment strategy that always has a payoff lower than the option, the option must be worth more than this strategy. – E.g. we know the option is worth more than zero since it has a positive payoff in some states of the world and never has a negative payoff – We can get limits (bounds) on the price of the option in this way

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European Option Pricing • Consider a one-year European Call option for GBP vs. USD • The strike price is 1.5 USD/GBP. • The option is in-the-money if in one year time, the spot rate is at least .  • Today, the spot rate is

.



• The interest rates at US and UK are:

𝑈𝑆

and

𝑈𝐾

• We want to get a lower bound of the option price, C, today – This investment has a payoff of in USD at expiry  – But we don’t know  so we can’t discount that payoff to today – As prior slide, this payoff is weakly better than doing nothing (which costs us zero) 36

European Option Pricing • Consider trying to replicate just



• We can break this into two parts – in the first part we get – This is tricky because we don’t know 



• But in the second part we owe 1.5 USD • So let’s just borrow an amount of USD such that we owe 1.5 USD at expiration – this replicates -1.5USD at expiry • How much USD to borrow? – We need to borrow

. 

. .

.

• If we borrow 1.4851 USD today then with 1% interest rate, in one year’s time we need to pay back the bank . – We’ve replicated one part of the payoff 37

European Option Pricing • What about 𝑇 ? – 𝑇 is the spot rate of one GBP is one year time. – So if we own exactly one GBP in one year’s time, we could sell that one GBP in the market at the rate  – This gives exactly 𝑇 USD in one year’s time • To earn 1 GBP in one year, we need to deposit some amount of GBP in a bank account today. • How much to deposit? – We need to deposit .  – If we deposit this amount, we earn 2% interest on it and in one year’s time we will get 0.9804 X 1.02= 1 GBP.

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European Option Pricing • What is the cost of depositing 0.9804 GBP in a bank account? – The spot rate now is  – So obtaining 0.9804 GBP costs us • But we borrow 1.4851 USD today too (a cash inflow today) • Net cost of this strategy today is: – This is the cost of replicating a portfolio that pays



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