Chapter 3: Exchange Traded Currency Futures

Currency futures are standardized exchange-traded contracts that allow market participants to buy or sell a specific currency at a predetermined exchange rate on a future date. They are traded on recognized stock exchanges and settled through regulated clearing corporations.

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3.1 Currency Futures - Definition and Terminology

Definition

A Currency Futures Contract is a legally binding agreement to buy or sell a standardized quantity of a specific foreign currency pair on a recognized exchange at an agreed price (futures price) on a specified date in the future.

Core Terminology

• Underlying Asset / Currency Pair: The specific currency pair being traded (e.g., USD/INR, EUR/INR, GBP/INR, JPY/INR, EUR/USD, GBP/USD, USD/JPY).
• Contract Size / Lot Size: The fixed, standardized amount of the base currency delivered per contract.
  • For USD/INR, EUR/INR, GBP/INR: 1,000 units of base currency.
  • For JPY/INR: 100,000 units of Japanese Yen (quoted per 100 JPY).
• Price Quotation:
  • For INR pairs: Exchange rate expressed in Indian Rupees per 1 unit of foreign currency (per 100 units for JPY).
  • For Cross-currency pairs: Quoted in the price/quotation currency (e.g., USD for EUR/USD and GBP/USD; JPY for USD/JPY).
• Tick Size: The minimum permitted price increment:
  • For INR pairs: ₹ 0.0025 (0.25 paise).
  • For EUR/USD and GBP/USD: 0.0001 USD.
  • For USD/JPY: 0.01 JPY.
• Tick Value: The monetary change in contract value resulting from a single tick movement: 7918\text{Tick Value (USD/INR)} = 1,000 \times ₹ 0.0025 = ₹ 2.507918
• Contract Value: Total nominal monetary value of one contract: 7918\text{Contract Value} = \text{Futures Price} \times \text{Contract Size}7918
• Contract Trading Cycle:
  • Monthly Contracts: 12 serial monthly trading cycles.
  • Weekly Contracts (USD/INR): 11 serial weekly contracts (excluding the expiry week where a monthly contract expires on Friday).
• Expiry Date:
  • Monthly Contracts: Two working days prior to the last business day of the expiry month at 12:30 PM IST.
  • Weekly Contracts: Every Friday at 12:30 PM IST (if Friday is a holiday, the preceding trading day).
• Positions:
  • Long Position: An outstanding (unsettled) buy commitment in a futures contract. Benefits from price increases.
  • Short Position: An outstanding (unsettled) sell commitment in a futures contract. Benefits from price decreases.
  • Open Position / Open Interest: The total number of outstanding, active contracts that have not been settled by offset or final settlement.

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3.2 Payoff Diagrams for Futures Contracts

Futures contracts have a linear (symmetrical) payoff profile. Both the upside profit potential and downside loss risk are theoretically unlimited.

Long Futures Payoff

A buyer of a futures contract commits to purchase the currency at the contracted futures price ($): 7918\text{Profit / Loss} = (S_T - F_0) \times \text{Contract Size} \times \text{Lots}7918

• Where $ is the settlement price at expiration.
• Profit Zone: When > F_0$.
• Loss Zone: When < F_0$.
• Break-Even: = F_0$.

Short Futures Payoff

A seller of a futures contract commits to deliver the currency at the contracted futures price ($): 7918\text{Profit / Loss} = (F_0 - S_T) \times \text{Contract Size} \times \text{Lots}7918

• Profit Zone: When < F_0$.
• Loss Zone: When > F_0$.
• Break-Even: = F_0$.

Illustrative Payoff Table (Long & Short at ₹ 83.00, 1 Lot USD/INR = ,000)

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3.3 Contract Specifications of Exchange Traded Currency Futures

Exchange-traded currency futures in India are jointly regulated by SEBI and RBI. The standardized contract parameters are outlined below:

Currency Futures Involving Indian Rupee (INR Pairs)

IMPORTANT EXAM NOTE: All currency futures contracts in India are 100% Cash Settled in Indian Rupees. There is no physical delivery of foreign currency.

Cross-Currency Futures (Contracts Involving Non-INR Pairs)

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3.4 Contract Value Calculation

The total contract value dictates margin requirements and position sizing: 7918\text{Contract Value} = \text{Trade Price} \times \text{Contract Size} \times \text{Number of Lots}7918

Worked Examples:

1. USD/INR:
   • Bought 10 lots at ₹ 83.2500.
   • Contract Value $= 83.2500 \times 1,000 \times 10 = ₹ 8,32,500$.
2. JPY/INR:
   • Bought 5 lots at ₹ 54.5000 (rate per 100 JPY).
   • Contract Value $= \left(\frac{54.5000}{100}\right) \times 100,000 \times 5 = ₹ 2,72,500$.
3. EUR/USD:
   • Sold 5 lots at 1.0850.
   • Contract Value $= 1.0850 \times 1,000 \times 5 = 5,425 \text{ USD}$.
   • Converted to INR for margin using prevailing USD/INR rate.

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3.5 Comparison: Currency Futures vs. OTC Forward Contracts

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3.6 Interest Rate Parity (IRP) and Pricing of Currency Futures

The theoretical price of a currency futures contract is governed by the Covered Interest Rate Parity (CIRP) theorem.

Concept of Covered Interest Rate Parity

CIRP states that under arbitrage-free conditions, the forward/futures exchange rate differential must equal the nominal interest rate differential between the two countries. If this relationship is violated, riskless arbitrage profits can be generated.

Mathematical Pricing Formulas

1. Simple Interest (Money Market Convention): 7918F = S \times \left[ \frac{1 + \left( r_{\text{quote}} \times \frac{t}{365} \right)}{1 + \left( r_{\text{base}} \times \frac{t}{365} \right)} \right]7918
   • Where:
     • $ = Theoretical Futures Price
     • $ = Spot Exchange Rate
     • {\text{quote}}$ = Risk-free interest rate of Quotation Currency (e.g., INR)
     • {\text{base}}$ = Risk-free interest rate of Base Currency (e.g., USD)
     • $ = Number of days to contract expiration
2. Continuous Compounding Convention: 7918F = S \times e^{(r_{\text{quote}} - r_{\text{base}}) \times T}7918
   • Where = \frac{t}{365}$ and \approx 2.71828$.
3. Quick Rule of Thumb (Linear Approximation): 7918F \approx S + \left[ S \times (r_{\text{quote}} - r_{\text{base}}) \times \frac{t}{365} \right]7918

Forward Premium and Forward Discount

• Forward Premium: A currency is at a premium when its futures price is higher than its spot price ( > S$).
• Forward Discount: A currency is at a discount when its futures price is lower than its spot price ( < S$).
• Golden Rule of IRP: 7918\text{The currency with the HIGHER interest rate trades at a forward DISCOUNT.}7918 7918\text{The currency with the LOWER interest rate trades at a forward PREMIUM.}7918
  • Example: In USD/INR, the Indian Rupee interest rate (~6.5-7%) is higher than the US Dollar interest rate (~5%). Therefore:
    • The US Dollar (base currency) trades at a forward premium ( > S$).
    • The Indian Rupee (quote currency) trades at a forward discount.

Annualized Forward Premium Calculation Formula

7918\text{Annualized Premium (%)} = \left( \frac{F - S}{S} \right) \times \left( \frac{365}{\text{Days to Expiration}} \right) \times 1007918

• Numerical Example:
  • Spot Rate ($) = ₹ 83.00
  • 90-Day Futures Rate ($) = ₹ 83.50 7918\text{Annualized Premium} = \left( \frac{83.50 - 83.00}{83.00} \right) \times \left( \frac{365}{90} \right) \times 100 = \left( \frac{0.50}{83.00} \right) \times 4.0556 \times 100 = 2.44%7918

Concept of Basis

• Basis: The difference between the spot price and the futures price: 7918\text{Basis} = \text{Spot Price} - \text{Futures Price} = S - F7918
• Convergence: As the contract approaches expiration ( \rightarrow 0$), the time value and interest rate differential decay. On the expiration date, Basis converges to zero ( = S$).

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Key Exam Takeaways for NISM Series I

• Mode of Settlement: Cash Settled in Indian Rupees for both INR pairs and Cross-Currency pairs.
• Lot Sizes: 1,000 units for USDINR, EURINR, GBPINR; 100,000 units for JPYINR.
• Tick size for all INR pairs is ₹ 0.0025; Tick value is ₹ 2.50.
• Monthly contracts expire two working days prior to the last business day of the expiry month at 12:30 PM IST.
• Final settlement price is the FBIL Reference Rate published on the last trading day.
• Trading hours: 9:00 AM to 5:00 PM IST for INR pairs; 9:00 AM to 7:30 PM IST for Cross-currency pairs.
• According to Interest Rate Parity, the currency with the higher interest rate trades at a forward discount.
• On contract expiry, the futures price converges to the spot price, and basis becomes zero.