Topic 1: Introduction to Foreign Exchange markets and Risks Flashcards
Types of contracts
Immediate: Spot
Future: Forwards/FX Swaps
Futures
Options
Quoting foreign exchange rates
GBP100 = USD1 (same as..)
¥100 = $1 (…)
¥100/$
JPY100/USD
USDJPY=100
(^Whatever you are converting into, you put as the denominator)
Direct Quotes
e.g., in U.S., every good is denoted as the domestic currency ($) price of
the good (e.g., $2 per an apple)
In the US, what is a direct quote for the British pound?
the number of dollars that it takes to purchase one pound
Indirect quotes
In principle, we could also use the quote “0.5 apple per $1”
– the number of apples that it takes to purchase one dollar. This is
called as indirect quote
In the US, what is the indirect quote for the British pound?
the number of pounds that it takes to purchase one dollar
Reciprocals in quoting FX rates
Q: In the US, what is the indirect quote for the British pound?
A: the number of pounds that it takes to purchase one dollar
We need to compute ‘X’ in ‘USDGBP = X’
Note: GBPUSD =1.3545 → exchange GBP1 for USD1.3545
GBP 1/1.3545 for USD1
Then USDGBP = 1/1.3545 = 0.7382
(USDGBP = 𝟏/GBPUSD)
Market conventions
For GBP and EUR, we frequently use the Dollar price of these currencies
(e.g. $1.3/£ and $1.2/€ - GBPUSD=1.3, EURUSD=1.2)
For other currencies, we use the foreign currency price of one dollar
(e.g. ¥107.10/$ - USDJPY = 107.10)
Cross rates
Exchange rates between two currencies that do not involve USD (often not posted in FX markets)
Computing cross rates
Formula: EURCAD = EURUSD × USDCAD
Triangular transactions
GBPEUR = USDEUR × GBPUSD
How to interpret the above equality?
A trader can
i) buy GBP by selling EUR directly (GBPEUR) in the market or
ii) buy USD by selling EUR (USDEUR) and simultaneously selling USD to buy GBP (GBPUSD). In other words, buy GBP by trading three currencies.
Triangular arbitrage
GBPEUR ≠ (USDEUR) × (GBPUSD)
Then a trader can conduct a triangular arbitrage. Triangular arbitrage is
a process that keeps cross-rates in line with exchange rates quoted
relative to the US dollar until we recover the equality.
Note: arbitrage profits are earned when someone can buy something at a
low price and sell it at a higher price, without risk.
No arbitrage equilbrium
Follows the same process as Arbitrage strategy, however when you buy a certain currency it drives up its value, and when you sell its decreases its value.
Bid Price
The Bid price of GBPUSD is the dollar price at which the FX dealer buyers pounds from customer.
Ask price
The Ask price of GBPUSD is the same, but for selling to the customer
Bid-Ask spread
FX dealers buy at low price and sell at high price (Bid-ask spread)
The Bid price of USDGBP = ( 𝟏/
the Ask price of GBPUSD)
The Ask price of USDGBP = ( 𝟏/
the Bid price of GBPUSD)
Changes in Exchange rates
Currencies ‘Appreciate’ and ‘Depreciate’, instead of increase and decrease.
When we compute, we always put the currency we are computing in the denominator.
(e.g. if computing JPY, we use JPYUSD)
Calculating Ap/Dep
The percentage rate of change of the exchange rate:
100 ×
(𝑁𝑒𝑤 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 −𝑜𝑙𝑑 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒)/
(𝑜𝑙𝑑 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒)
Foreign Exchange Risk
The possibility of taking a loss in the foreign exchange transactions because future spot exchange rates are not known today with certainty.
Quantifying FX Risk
Can calculate using Historical data:
(New ex. rate - old ex. rate)/ (old ex. rate)
Foreign exchange risk/Forecasting
What if you believe the future is not going to be similar to the past? (unprecedented event like Brexit)
Then you want to forecast the future distribution of GBPUSD (say, next month) using all information available today (conditional distribution).
For simplicity, we are going to assume the conditional distribution of exchange rate follows normal distribution.
Mean + volatility forecasts
Suppose the conditional volatility (i.e., STD) of the change in GBPUSD ($/£) over 90 days is 4%. What is the conditional volatility of the
distribution of future spot exchange rate at t+90?
STDt[S(t+90, $/£)] = 1.50 × 0.04 = 0.06
Forward contract
A (outright) forward contract between a bank and a customer calls for a delivery at a fixed future date (maturity), of a specific amount of one currency with payment of another using the price (known as the forward rate) today.
Attributes of a forward contract
Highly customisable
Most active maturities are 30,60,90,180 days
No money changes hands till the maturity date
Forward bid-ask spreads
They are larger than in spot markets, and widen as the maturity increases
->In order to compensate forward market dealers for the counter party default risk
FX swap
FX swap contract is the simultaneous purchase and sale of a certain amount of foreign currency for two different dates
Typically involves the spot sale of a currency combined with a simultaneous forward repurchase (or vice versa) of that same currency
Forward premiums and discounts
When the forward rate of USDJPY (¥/$) is less than the spot rate, there is a forward discount on the dollar
-> because its less expensive to purchase dollars in the forward market than the spot
The Bid price of GBPEUR
The Bid price of GBPUSD × The Bid price of USDEUR
The Ask price of GBPEUR
The Ask price of GBPUSD × The Ask price of USDEUR
Spot FX dealers (e.g., banks) buy £ at…
…the bid price of GBPUSD and sell £ at the ask price of GBPUSD
Spot FX dealers (e.g., banks) buy $ at …
…the bid price of USDGBP and sell $ at the ask price of USDGBP
“$/£” in this course indicates…
“GBPUSD”
Appreciation/depreciation on £
CH = S(t+1, $/£)−S(t, $/£)/ S(t, $/£)
→ S(t+1, $/£) =
S(t, $/£) × (1+ CH)
Distribution of S(t+1, $/£) - Mean
Et[S(t+1, $/£)] = S(t, $/£) × (1+ Et[CH])
Distribution of S(t+1, $/£) - STD
STDt[S(t+1, $/£)] = S(t, $/£) × STDt[CH]
68-95-99 rule on the distribution of
S(t+1, $/£)
95% bounds: Et[S(t+1, $/£)] ± 2 × STDt[S(t+1, $/£)]
Forward premium/discount on £
100 x (360/N) x [F(t, $/£)−S(t, $/£) / S(t, $/£)]
where N is the maturity
