U6018 CLASS NOTES International Money Finance Notes Lecture Notes The FOREIGN EXCHANGE Market

Some Basic Facts 5 Trillion dollars a day - the world's largest asset market Interbank Market Transaction are Spot, Forward, and Swap Central Banks/Sovereign Wealth managers are Players

Simple Schematic Diagram of FX Market Fed ECB SAFE Citi direct DB Broker Audi Wal Mart Simple Schematic Diagram of FX Market

Foreign Exchange Market Setting Direct Dealing and Brokers Retail and Market maker Counterparties

A 5 Trillion Dollar a Day Market

USD is Leading Vehicle Currency – is on 88 percent of all FX Trades

Dollar is Still Leading Global Reserve Currency, but Share is Declining

Market Dominated by London and New York In each Triennial survey since 2001

2016 New York Fed Survey

Forwards are small part of market, Instead Foreign Exchange Swaps In recent years daily swaps volume has been more than 4 times greater than daily forward volume Swaps bundle a spot and forward transaction Spot purchase (sale) and forward sale (purchase) of equal amount of foreign exchange. The embedded rate in the transaction is the swap rate which is closely linked to the forward rate. Vehicle currencies - the emergence of the Euro Most foreign exchange transactions have the dollar on one side Even if ultimate goal is to exchange one non-dollar currency for another

Triangular Arbitrage and the Vehicle Currency The CAD/EUR exchange rate (a small illiquid market) is pinned down by the CAD/USD and USD/EUR markets which are much more liquid by TRIANGULAR ARBITRAGE. CAD/EUR = (USD/EUR)(CAD/USD) 1.5051 = 1.0835 times 1.3892 Suppose this did not hold with CAD/EUR at 1.49 USD/EURO > (CAD/EUR)/(CAD/USD) Then Take 100 USD and buy 138.92 CAD. Take these 138.92 CAD and buy 138.92/1.49 EUR. Take these Eur and sell them for (138.92/1.49)1.0835 dollars. You end up (1 second later) with $101.02. That’s $1.02 bps of profit a second with no risk. $838 of profit per minute (and 83.8 % return!) a minute. $2,221,1858 of profit a day a day. At no risk. So why stop at $100? How bout a billion? All day. Thus triangular arbitrage must hold. And it does.

Triangular Arbitrage at Work

Ask-Bid Spread: What is it? Market makers want to make money (and not to hold on to foreign currency). They charge a spread between the price they buy foreign exchange and the price they sell Spread on interbank transactions is incredibly small and much less than daily swings in the currency. A market maker who is unlucky enough to get long foreign currency at the intraday high price and unwind and the intraday low will lose a lot of money, and the ask bid spread will not be enough to make it up!

Bid – Ask Spreads are Exceedingly Narrow Relative to Daily Swings For example, on September 25th, spread on Euro at 7:01 am ranged from .0002/1.4150 to .0001/1.41525 Note that the spread is miniscule compared with the daily high - low which was 1.4154-1.4062 = .0092 Also note that at any given minute there is some variation across dealers in their quotes

Bid Ask Spreads and Volatility In periods of volatility spikes, bid ask spreads have in the past risen as dealers take on more inventory risk to make the market However, this has not happened so much in recent years

U6018 CLASS NOTES FOREIGN EXCHANGE OPTIONS AND FORWARDS

A Forward Contract If I think the USD is going to depreciate over the next 90 days against GBP relative to the forward Eet+90 > Ft,90 Then think I will earn an expected positive risk premium by being long the pound. I can enter into today a forward contract to receive GBP and deliver USD with a counterparty at a specificed date in the future. No money changes hands today. Since I am buying GBP forward, I can’t ‘pick’ the forward rate. The forward rate is what it is by CIP. A forward contract obligates me to buy a pre specified amount of GBP at a specificed price - the forward rate - agreed today for exchange at a specified date in the future. USD Cash Flow at Expiration from Long 100,000 GBP 90 day Forward [Et+90 – Ft,90]100,000 USD Cash Flow at Expiration from Short 100,000 GBP 90 day Forward [Ft,90 – Et+90]100,000

USD Cash Flow on Long Forward Position USD CASH FLOW AT time T Expiration of a forward contract as a function of the spot rate at time T Max profit unlimited Per Unit of Notional foreign exposure Slope = 1 ET F Max loss = -F

Example If I buy 100,000 GBP forward, my cash outflow on January 2 is 0. I’m obligated on April 3rd to deliver 195,190 dollars and receive 100,000 GBP. On April 3, it turns out that the spot exchange rate is 1.9741. I can thus sell the 100,000 GBP for 197,410 dollars for a profit of 0.0222 times 100,000 at expiration. Thus in this example, speculating with a forward is ex post profitable. But this will not be the case when the dollar appreciates relative to the forward.

USD Cash Flow on Long Forward Position USD CASH FLOW AT time T Expiration of a forward contract as a function of the spot rate at time T Max profit unlimited Per Unit of Notional foreign exposure Slope = 1 Profit = 0.0222 per GBP notional ET F=1.9519 ET =1.9741 Max loss = -F

Betting on a Strong Dollar If I think the USD is going to appreciate over the next 90 days against EUR relative to the forward Eet+90 < Ft,90 Then think I will earn an expected positive risk premium by being short the Euro. I can enter into today a forward contract to deliver Eur and receive USD with a counterparty at a specificed date in the future. No money changes hands today. Since I am selling Eur forward, I can’t ‘pick’ the forward rate. The forward rate is what it is by CIP. A forward contract obligates me to sell a pre specified amount of Eur at a specificed price - the forward rate - agreed today for exchange at a specified date in the future. USD Cash Flow at Expiration from Short 100,000 Eur 90 day Forward [Ft,90 – Et+90]100,000 Note that in this case I am receiving Ft,90∙100,000 dollars from counterparty but it will cost me Et+90∙100,000 dollars to obtain the 100,000 I am obligated to deliver. In effect, I am borrowing in Euros to fund a USD investment so a forward contract is ex ante risky unless it is offset with another position.

USD Cash Flow on Short Forward Position USD CASH FLOW AT time T Expiration of a forward contract as a function of the spot rate at time T Max gain = F Slope = -1 Per Unit of Notional foreign exposure ET F Max loss = unlimited

Foreign Exchange Call Options Currency Call Option gives the buyer of the option contract the right -but not the obligation -to buy a specified quantity of foreign (home) currency at a specified price -the strike rice -at a specified date in the future - the expiration date. The price of the call option is paid up front (not on the expiration date). It is useful to think of the option buyer as borrowing funds to pay the option premium today. A Call Option has value at the expiration date T if the Spot exchange rate exceeds the strike price on that date. For example, if I hold a call option at expiration it is worth Value of Call at expiration date T = max[0, ET – Estrike]] A call option makes the buyer long the foreign currency (if exercised) and gains value if foreign currency appreciates relative to home money. Example: A call option on 100,000 GBP with strike price equal to 1.95 that expired on June 2, 2007 when spot GBP was 1.97 was worth max[0, ET – E strike]100,000 = [1.97 – 1.95]100,000 = $2000

Payoff at Expiration of a Call Option on Foreign Currency CASH FLOW AT T = Expiration A call option expires in the money whenever ET > E strike Per Unit of Notional foreign exposure Slope = 1 ET E strike E strike+ P call(1 + R) is break even level for spot at expiration -PCALL(1 + R) Note that the price of the option is paid up front not at expiration , but to compare forwards to options , it is useful to think of borrowing the money to pay for the option and paying off the loan with the proceeds for cash flow at expiration (if there are any).

Cash Flow on Call Option Struck ATMF versus Forward CASH FLOW AT T = Expiration Per Unit of Notional foreign exposure Slopes = 1 ET F E strike = F -PCALL(1 + R) -F

Speculating with a Call Option If I think the USD is going to depreciate against GBP, I can buy a call option on GBP. Since I am buying the call (I am ‘long’ the call) I can pick my strike price. The further away is the strike from the current spot, the cheaper is the call option, but the less likely it is that the call expires in the money. For ease of comparison, I price a GBP 90 day call with a strike equal to the forward exchange rate. This is said to be ATMF (at the money forward) and is the most liquid strike in the OTC options market. Cash Flow at Expiration from Long GBP Call Max [ET – Estrike, 0]100,000 – Pcall(1 + Rt,90)100,000

Example As on January 2, 2007 the strike price on a 90 day ATMF GBP call was 1.9519. The $ price of the 90 day ATMF call on January 2 was 0.0272. If I bought 100,000 GBP calls, my cash outflow on January 2 was $2,717.06. It is useful to think of financing this cash outflow on January 2 with a loan financed at LIBOR. On April 3, the spot exchange rate was GBP = 1.9741. My option was worth 1.9741- 1.9519 = 0.0222 at expiration. But the price of the option was 0.0272 and I accrued interest liability of this amount. Thus even though the option was ‘in the money’ it did not cover the cost of the option.

Betting on a Weaker USD – ATMF Long GBP Calls versus Forwards CASH FLOW AT T = Expiration, April 3,2007, per pound E F ET -PCALL(1 + R) 1.9741 -0.0272(1.0134) 1.9519

Foreign Exchange Put Options European Currency Put Option gives the buyer of the option contract the right - but not the obligation – to sell a specified quantity of foreign currency at a specified price - the strike rice - at a specified date in tile future - the expiration date. The price of the put option is paid up front (not on the expiration date). It is useful to think of the option buyer as borrowing funds to pay the option premium today. A Put Option has value at the expiration date T if the Spot exchange rate falls short of the strike price on that date. For example, if I hold a put option at expiration it is worth Value of Put at expiration date T = max[0, Estrike] - ET] A Put option makes the buyer short the foreign currency (if exercised) and gains value if foreign currency depreciates relative to home money. Example: A put option on 100,000 EUR with strike price equal to 1.30 that expired on June 2, 2007 when spot EUR was 1.35 was worthless max[0, Estrike - ET]100,000 = max[0,1.30 – 1.35]100,000 = $0

Cash Flow at Expiration of a Put Option per unit of Notional CASH FLOW AT T ET strike -Pput(1 + R)

Speculating with a Put Option If I think the USD is going to appreciate against EUR, I can buy a put option on EUR. Since I am buying the put (I am ‘long’ the put) I can pick my strike price. The further away is the strike from the current spot, the cheaper is the put option, but the less likely it is that the put expires in the money. For ease of comparison, I price a EUR 90 day put with a strike equal to the forward exchange rate. This is said to be ATMF (at the money forward) and is the most liquid strike in the OTC options market. Cash Flow at Expiration from Long EUR Put Max [Estrike - ET, 0]100,000 – Pput(1 + Rt,90)100,000

Example As on January 9, 2012 the strike price on a 90 day ATMF EUR put was 1.2774. The price of the 90 day ATMF put on January 9 was 0.03357 . If I bought 100,000 EUR puts, my cash outflow on January 9 was 3357 dollars. It is useful to think of financing this cash outflow on January 9 with a loan financed at LIBOR. On April 9, the spot exchange rate was EUR = 1.3206 . My option was worthless at expiration. I also pay off my loan at expiration.

Speculating with a Forward Contract If I think the USD is going to appreciate against EUR relative to forwards Eet+1 < Ft,1 I expect to earn a risk premium by being short the GBP and borrowing in pounds to invest is US bonds. Note that even though I am investing in US bonds, this is risky because a forward contract is equivalent to borrowing in foreign currency I can sell EUR forward. Since I am selling EUR forward, I can’t ‘pick’ the forward rate. The forward rate is what it is by CIP. Unlike an option, a forward contract obligates me to sell EUR at the forward rate agreed today for execution in 90 days. If I sold 100,000 EUR forward, my cash flow on January 9 was 0. On April 9, the spot exchange rate was EUR = 1.3206. My position was underwater by an amount equal to [1.2774 – 1.3206]100,000 Cash Flow at Expiration from short EUR Forward [Ft,90 – ET]100,000

Betting on a Weaker EUR – ATMF Long EUR Puts vs. Forwards CASH FLOW AT April 09, 2012 per Euro 1.3206 F ET -Pput(1 + R) 1.2774 -0.0336(1.0014)