Exchange Traded Currency Futures — terminology, contract specifications, payoffs and pricing

Where this chapter sits

Chapter 3 carries 20% of the paper — a fifth of the whole exam, and the largest single chapter alongside Chapter 4.

Three things dominate: the contract specification tables, the payoff arithmetic, and interest rate parity.

3.1 What a currency future is

Futures markets were innovated to overcome the limitations of forwards.

A futures contract is an agreement made through an organized exchange to buy or sell a fixed amount of a commodity or a financial asset on a future date at an agreed price. Simply, futures are standardized forward contracts that are traded on an exchange. The Clearing Corporation associated with the exchange guarantees settlement of these trades.

A trader who buys futures contracts generally takes a long position and the one, who sells futures, takes a short position.

And a point worth pausing on: the words buy and sell are figurative only because no money or underlying asset changes hand, between buyer and seller, when the deal is executed.

The features:

Contract between two parties through Exchange · Centralised trading platform i.e. Exchange · Price discovery through free interaction of buyers and sellers · Margins are payable by both the parties · Expiry date decided today (standardized) · Quantity decided today (standardized lot size)

In the futures market, exchange decides all the contract terms of the contract other than price.

Everything but price is fixed by the exchange. Price is the one thing the market decides.

The definition: Currency Futures means a standardised foreign exchange derivative contract traded on a recognized stock exchange to buy or sell one currency against another on a specified future date, at a price specified on the date of contract, but does not include a forward contract.

The Indian timeline

The NSE launched its currency futures trading platform in August 2008, in a separate segment called currency derivatives segment.

Initially, futures contracts on USD-INR were introduced for trading and from February 2010, futures on EUR-INR, GBP-INR and JPY-INR were launched. Further in 2018, Cross Currency Futures contracts on EUR-USD, GBP-USD and USD-JPY were also introduced.

August 2008 → February 2010 → 2018. Three dates worth memorising.

And the meaning of "cross": in the exchange-traded currency derivatives context, cross currency derivatives means derivatives on currency pair not involving the Indian rupee.

3.1.1 The terminology

Underlying Asset — the value of the futures contract is derived from the value/price of the underlying asset, which in this case is the exchange rate in Indian Rupees for US Dollars, Euro, Pound Sterling, Japanese Yen. Further the underlying for cross currency futures may be the exchange rate in US Dollars for Euro and Pound Sterling and exchange rate in Japanese Yen for US Dollars.

Spot price/rate — the price at which the underlying asset (currency pairs) trades in the spot market.

Futures price — the current price of the specified futures contract. The future price can be higher or lower than the spot price. However, on the expiry date, the futures price converges with the spot price.

That convergence is the single most important idea in futures pricing.

Quotation — for USDINR future the price quotation is the exchange rate in Indian Rupees for one US Dollars and for JPYINR it is the exchange rate in Indian Rupees for 100 Japanese Yen.

Contract Cycle — it is a period over which a contract trades. The currency futures contracts on the SEBI recognized exchanges can be weekly, monthly and quarterly.

For monthly contracts: the contract maturing in the immediate month is called 'near month contract', the contract expiring in next month is called 'mid-month contract' and those expiring in subsequent months are called 'far month contracts'. These contracts can extend up to one year.

And the cycles differ by underlying: INR based currency futures have weekly and monthly contracts but cross currency futures may have only monthly contracts.

Expiry date — also called last trading day or maturity date of contract. It is the day on which trading ceases in the contract.

For all monthly currency futures contract the expiry date is two working days prior to the last business day of the expiry month at 12:30 PM.

The workbook's own worked example: if the last business day of April is 30th April (Tuesday), the expiry date for the April futures contract will be 26th April (Friday), assuming there are no holidays apart from Saturday and Sunday.

Count backwards two working days from the 30th: the 29th (Monday) is one, the 26th (Friday) is two — because Saturday and Sunday are not working days.

And note the earlier close: on the expiry date the trading in contract ceases at 12:30 pm and not at the regular trading close of 5:00 pm or 7:30 pm.

Tick Size — it is the minimum move allowed in the price quotations. The minimum trading increment or price differential at which traders are able to enter bids and offers is called the tick size.

For example, if tick size for USDINR futures is Rs. 0.0025, the price entered by buyer and seller can be 82.9975, 83.0000, 83.0025 in multiples of Rs.0.0025.

Contract size / Lot Size — contract size specifies the amount of the asset that has to be delivered for a single contract. This is also called the 'lot size' or 'contract multiplier'. Trading always takes place in multiples of the lot size. For e.g. lot size for USDINR contract is 1000 USD.

Contract Value — to arrive at contract value, we multiply the futures price with the contract multiplier or lot size or contract size.

Trading Hours — exchanges currently have different market timings for contracts involving Indian rupee and those not involving Indian rupee. Further, on the contract expiry day, the specific currency futures and option contract stop trading earlier than normal trading hours i.e. 12:30 pm.

Base Price — base price generally acts as a reference price for trading for the start of the day. Generally, on the first day of trading (i.e. on introduction) of a futures contract, the base price is the theoretical futures price. The base price of the contracts on subsequent trading days is the daily settlement price of the futures contracts as computed by Clearing Corporation.

Theoretical price on day one; daily settlement price thereafter.

Price Band — the price range (maximum and minimum price) for the day within which contracts can be traded for that day. Generally, specify +/-% to base price. In many derivatives contracts there is no price band for contracts and in such cases a dummy operating range is set to avoid erroneous order entry at a non-genuine price.

Mark to Market (MTM) — the positions in the futures contracts for each member are marked-to-market to the daily settlement price of the futures contracts at the end of each trade day. The exchange/CC collects these margins (MTM margins) from the loss-making participants and pays to the gainers on a day-to-day basis.

Daily Settlement Price (DSP) — it is required mainly for MTM settlement. The settlement price is the weighted average futures price (VWAP) of the trades generally in the last 30 minutes of trading (i.e. close price). If the close price is not available then the daily settlement price is set equal to the theoretical price of the futures contracts.

Final Settlement Price (FSP) — all open positions on the last trading day of the currency futures contract are marked to the final settlement price for the relevant futures contract and settled on the final settlement day. The Final settlement price / rate is mainly derived from the underlying/spot market.

Note the difference in source: DSP comes from the futures market (VWAP of the last half hour); FSP comes from the spot market (the FBIL reference rate).

Final Settlement — can be cash settled or physical settled. In the case of cash settlement only the profit and loss resulting from positions is paid / received from the participants. In case of physical settlement, participants must physically give/take delivery of stocks/underlying asset.

And in India: currently, all exchange-traded currency futures and option contracts are cash settled in Indian rupees.

Open Interest — the open interest is the total number of contracts outstanding (yet to be settled) for an underlying asset.

The counting rule catches people out: it is important to understand that the number of long positions as well as number of short positions is equal to the Open Interest. This is because the total number of long positions is always equal to total number of short positions. Only one side is considered while calculating/mentioning the open interest.

And what it tells you: the level of open interest indicates depth in the market.

Positions

Long position — outstanding/ unsettled buy position in a contract is called "Long Position". For instance, if Mr. X buys 5 USDINR futures contracts then he would be long 5 USDINR futures contracts.

Short Position — outstanding/ unsettled sell position in a contract is called "Short Position".

Open position — outstanding/ unsettled either long (buy) or short (sell) position in various derivative contracts is called "Open Position."

The workbook's running example: if Mr. X shorts say 5 USDINR futures contracts and buys say 3 EURUSD futures contracts, he is said to have an open position, which is equal to short 5 contracts of USDINR and long 3 contracts of EURUSD futures. If on the next day, he sells 2 EURUSD futures contracts of the same maturity, his open position would be short 5 USDINR futures contracts and long 1 EURUSD futures contract.

Opening a position — means either buying or selling a contract, which increases the client's open position (long or short).

Closing a position — means either buying or selling a contract, which essentially results in the reduction of a client's open position... A client is said to close a position if he sells a contract which he had bought before or he buys a contract which he had sold earlier.

The same action — selling — opens a position for one trader and closes it for another. What matters is what you already held.

3.2 Payoffs

Pay off on a position is the profit/ loss that would accrue to a market participant with change in the price of the underlying asset at expiry. The pay-off diagram is a graphical representation showing the price of the underlying asset on the X-axis and profits / losses on the Y-axis.

In the case of futures contracts, the long as well as short position has unlimited profit or loss potential. This results into linear pay offs for futures contracts.

Long futures

Let us say a person goes long in a futures contract at Rs.100. This means that he has agreed to buy the underlying at Rs. 100 on expiry.

Now, if on expiry, the price of the underlying is Rs. 101, then this person will buy at Rs. 100, as per the futures contract and will immediately be able to sell the underlying in the cash market at Rs.101, thereby making a profit of Rs. 1.

Similarly, if the price of the underlying falls to Rs. 99 at expiry, he would have to buy at Rs. 100, as per the futures contract, and if he sells the same in the cash market, he will receive only Rs. 99, translating into a loss of Rs. 1.

And in India, only the difference moves: if it is a cash-settled futures contract then the participant will receive / pay only profit/loss amount i.e. Rs. 1 in the above example.

The chart convention: the X axis has the market price of the underlying at expiry. It increases on the Right-Hand Side (RHS). We do not draw the X axis on the Left-Hand Profit Side (LHS), as prices cannot go below zero. The Y axis shows profit & loss.

So, we can see that the long futures position makes profits when prices rise.

Short futures

Let us say a person goes short in a futures contract at Rs.100. This means that he has agreed to sell the underlying at Rs. 100 on expiry.

Now, if on expiry, the price of the underlying is Rs. 99, then the person will buy from underlying in cash market at Rs. 99 and will sell at Rs. 100, as per the futures contract thereby making a profit of Rs. 1.

Similarly, if the price of the underlying increases to Rs. 101 at expiry, he would have to buy at Rs. 101, in the underlying cash market and sell at Rs. 100 in the futures market, translating into a loss of Rs. 1.

So, we can see that a short futures position would make profits when prices fall.

The payoff graph for futures displays a linear or symmetrical style.

One formula covers both: long pays (expiry price − entry price); short pays (entry price − expiry price). Multiply by lot size and number of lots.

3.3 Contract specifications

Based on RBI and SEBI guidelines, various kinds of currency futures (including cross currency futures) have been launched by Exchanges. Currently Exchange traded currency futures are part of currency derivatives segment. Exchange traded currency futures are regulated by SEBI as well as RBI.

Contracts involving the Indian Rupee

Note the JPYINR asymmetry: the unit of trading is 100000 Japanese Yen but the price is quoted for 100 Japanese Yen — so contract value is still trade price × 1000, being trade price × 100000 / 100.

The rest of the specification, common to all four:

Base Price — theoretical price on the 1st day of contract, on all other day's daily settlement price of the contract.

Price Band — there shall be no daily price bands applicable for contracts. However, in order to prevent erroneous order entry by members, operating ranges will be kept at +/-3% of the base price for contracts with tenure up to 6 months and +/- 5% of the base price for contracts with tenure greater than 6 months. The dynamic price bands shall be relaxed in increments of 1% as and when a market-wide trend is observed.

Trading Hours — Monday to Friday: 9:00 a.m. to 5:00 p.m. And on contract expiry, the contract will be available for trading up to 12:30 pm.

Contract Trading Cycle — 11 serial weekly cycle (excluding expiry week wherein monthly contracts expires on a Friday) and 12 serial monthly trading cycle. New serial weekly/monthly futures contracts shall be introduced after expiry of the respective week's/month contract.

Expiry Day — two different rules:

For weekly contract: Every Friday at 12:30 pm. If the Friday of the expiring week is a trading holiday, then the expiry day is the previous trading day.

For monthly contract: Two working days prior to the last business day of the expiry month at 12:30 PM. For e.g. If last business day of the month is Thursday & there is no holiday, then expiry will be on Tuesday.

Mode of Settlement — Cash Settled in Indian Rupees.

Daily Settlement Price — Volume Weighted Average Futures Price of last half an hour across exchanges or theoretical futures price.

Final Settlement Price — FBIL reference rate on last trading day.

Daily MTM and Final Settlement — Daily Settlement: T+1. Final Settlement: T+2.

Cross currency contracts

Contract Value — Trade Price * 1000 (in quote currency).

Trading Hours — Monday to Friday: 9:00 a.m. to 7:30 p.m. — later than the INR contracts, with the same 12:30 pm expiry-day close.

Contract Trading Cycle — 12 serial monthly trading cycle. No weekly contracts for cross currency.

Expiry Day — Two working days prior to the last business day of the expiry month at 12:30 PM.

Mode of Settlement — Cash Settled in Indian Rupees — even though neither leg is the rupee.

Final Settlement Price — the final settlement price for cross-currency futures contracts shall be computed using the FBIL reference rate for USD-INR and the corresponding exchange rate published by FBIL for EUR-INR, GBP-INR and JPY-INR, as applicable, on the last trading day of the contract.

Daily MTM and Final Settlement — Daily Settlement: T+1. Final Settlement: T+2.

3.4 Contract value in practice

Market lot / lot size is the minimum and multiple of trade size. Lot sizes may differ according to the underlying currency pair.

The workbook's worked table for INR pairs:

And the tick value, identical across all four: Change in contract value for each tick size change = INR 2.50 (110000.0025).

One tick on one lot of any INR currency future is Rs. 2.50.

For cross currency pairs:

How the INR value is derived: to arrive at the value of cross currency positions in INR for EUR-USD and GBP-USD contracts, the latest available FBIL reference rate for USD-INR shall be used. For USD-JPY contracts, the value in INR shall be arrived at using the latest available exchange rate published by FBIL for JPY-INR. And Reference Rate in respect of JPYINR will be for 100 units of JPY.

Why any of this matters: contract value is important for determining margin amount, transaction charges, regulatory charges etc.

3.5 Futures versus forwards

Forward contracts are often confused with futures contracts. The confusion is primarily because both serve essentially the same economic function of hedging risk in the face of price uncertainty in the future.

However, futures have some distinct advantages over forward contracts as they eliminate counterparty risk and offer more liquidity and price transparency. On the other hand, forwards enjoy the benefit of being customized to meet specific client requirements.

Forward advantages:

Can provide perfect hedge as it is a customized product Delivery-based settlement more helpful to importers and exporters Less operational issues related to margin and mark-to-market settlement

Futures advantages:

Price transparency Elimination of Counterparty credit risk as settlement guarantee is given by the clearing corporation of Exchanges Access to all types of market participants Access to futures contracts does not depend upon the credit profile of the participants Lower liquidity risk compared to forwards Generally lower impact cost Easy entry and exit

Forward limitations: Liquidity risk · Counter party risk · Limited market participants · Cancellation and rebooking are based on certain conditions.

Futures limitations:

May lead to imperfect hedge as the contract size and settlement dates are standardized Since it is cash settled, users need to access cash/spot market for actual delivery of currency Operational issues related to mark-to-mark settlement and margin

That fourth futures advantage is easy to miss and often examined: access to futures contracts does not depend upon the credit profile of the participants. A small firm with no banking line can still hedge.

3.6 Interest rate parity and pricing

The puzzle the chapter opens with: let us assume that risk free interest rate for one year deposit in India is 7% and in USA it is 3%. As a smart trader/ investor you will think about raising money from USA and deploying it in India to try and capture the spread of 4%. You could continue to do so and make this transaction as a non-stop money-making machine. Life is not that simple! And such arbitrages do not exist for very long.

The derivation

Assumptions:

1. Spot exchange rate of USDINR is 83 (S) 2. One year future rate for USDINR is "F" 3. Risk free interest rate for one year in USA is 5% (RUSD) 4. Risk free interest rate for one year in India is 7% (RINR) 5. Money can be transferred easily from one country into another without any restriction of amount, without any taxes etc.

The trade: you decide to borrow one USD from USA for one year, bring it to India, convert it in INR and deposit for one year in India. After one year, you return the money back to the USA.

Step by step: you borrow 1 USD in US at the rate of 5% and agree to return 1.05 USD after one year (including interest of 5 cents or 0.05 USD). This 1 USD is converted into INR at the prevailing spot rate of 83. You deposit the resulting INR 83 for one year at interest rate of 7%. At the end of one year, you receive INR 5.81 (7% of 83) as interest on your deposit and also get back your principal of INR 83 i.e., you receive a total of INR 88.81.

The two questions the workbook poses:

The loan taken in the US was in USD and currently you have INR. Therefore, you need to convert INR into USD What exchange rate do you use to convert INR into USD?

The answer: at the beginning of the transaction, you would lock the conversion rate of INR into USD using the one-year future prices of USDINR. To ensure that the transaction does not result into any risk-free profit, the money which you receive in India after one year should be equal to the loan amount that you have to pay in USD.

S(1+RINR) = F(1+RUSD)

Or F/S = (1+RINR) / (1+RUSD)

Another way to illustrate the concept is to think that the INR 88.81 received after one year in India should be equal to USD 1.05 when converted using the one-year future exchange rate.

F/83 = (1+0.07) / (1+0.05)

F = 84.5809

And the approximation: *approximately, F is equal to the interest rate differential between two currencies i.e., F = S + (RINR − RUSD)S.

This concept of difference between future exchange rate and spot exchange rate being approximately equal to the difference in domestic and foreign interest rate is called the "Interest rate parity".

Stated generally: interest rate parity says that the spot price and futures price of a currency pair incorporate any interest rate differentials between the two currencies assuming there are no transaction costs or taxes.

The formulas

The accurate one:

F = S × (1 + RQC × Period) / (1 + RBC × Period)

Where F = forward price · S = spot price · RBC = interest rate on base currency · RQC = interest rate on quoting currency · Period = forward period in years.

Quote currency on top, base currency below.

The quick estimate:

F = S + (S × (RQC – RBC) × Period)

Worked illustration

Suppose the 6-month interest rate in India is 3.5% (or 7% per annum) and in the USA it is 2.5% (5% per annum). The current USDINR spot rate is 83. What is the likely 6-month USDINR futures price?

Approximate: Spot + 6-month interest difference = 83 + 1% of 83 = 83 + 0.83 = 83.83.

Exact: 6-month futures price = 83 × (1+0.070.5) / (1+0.050.5) = 83.8097.

Now change one variable. Suppose traders expect the USD interest rate to go up (say from 5% to 5.25%) and INR interest rate to remain constant. What will happen to the 6-month forward rate?

6-month forward rate = 83 × (1+0.070.5) / (1+0.05250.5) = 83.7076.

You can see that the 6-month forward USDINR rate will fall from the earlier 83.8097 to 83.7076. Hence, a trader would initiate a short position in the USDINR futures contract.

The general rule: in the above example, if the USD interest rate were to go up and INR interest rate were to remain at 7%, the one year futures price of USDINR would decline as the interest rate difference between the two currencies has narrowed and vice versa.

And traders act on it: everything else remaining the same, if the USD interest rate is expected to rise (say from 3.0% to 4.0%) and INR interest rate is expected to remain constant say at 7%; a trader would initiate a short position in the USDINR futures contract.

Premium and discount

You can observe that the 6-month future price of USDINR pair is 83.8097 when the spot price is 83. It means that INR trades at a discount to USD and USD quotes at a premium to INR.

The intuition: to buy 1 USD you had to pay INR 83 now but you have to pay 83.8097 after 6 months i.e., you have to pay more INR to buy the same 1 USD. Hence the future value of INR is at a discount to USD.

A second worked case, deliberately in the opposite direction. Assume that the risk-free interest rate for one year in JPY is 0.25% and in EUR is 1%. The current EURJPY spot rate is 123.4. Would the future value of EUR be at discount or premium to JPY? What is it likely to be: towards 124 or towards 122?

The 1 year forward rate for EURJPY will be 122.4837.

122.4837 = 123.40 × (1+0.00251) / (1+0.011)

EUR has the higher rate, so EUR falls to a discount — towards 122, not 124.

Key Conclusion: The future value of a currency with a high interest rate is at a discount to the value of the currency with a low interest rate or future value of a currency with a low interest rate is at a premium to value of the currency with a high interest rate.

High interest rate currency → discount. Low interest rate currency → premium. Learn it in that direction and every premium/discount question answers itself.

The theoretical price

The theoretical price of a currency futures contract shall be computed as per the following formula:

F = S × e^((r − rf) × t)

Where F = Theoretical futures price · S = Value of the underlying · r = Correspondence to interest rate for quote currency · rf = Correspondence to interest rate for base currency · t = Time till expiration · e = 2.71828.

This is the continuous-compounding version of the same idea — and it is the price used as the base price on a contract's first day and as the daily settlement price when a close price is unavailable.