Understand USD - INR and currency derivatives — Stock-Market notes

Overview

Currency derivatives are financial instruments whose value is derived from the exchange rate between two currencies. The USD/INR pair (US Dollar to Indian Rupee) is the most actively traded currency pair in India, allowing traders and businesses to hedge against currency risk or speculate on exchange rate movements.

Figure — Understand USD - INR and currency derivatives

Core Concepts

The Mathematics of Currency Derivatives

Interest Rate Parity - The Foundation

Derivation from First Principles:

Start with two investment strategies that must yield equal returns (no arbitrage):

Strategy A (Stay in India):

Invest ₹1 in India for time $t$
Final value: $₹(1 + r_d \times t)$

Strategy B (Go to USA and hedge back):

Convert ₹1 to dollars at spot rate $S$ : Get $\frac{1}{S}$ USD
Invest in USA at rate $r_f$ : Get $\frac{1}{S}(1 + r_f \times t)$ USD
Lock in forward contract to convert back at rate $F$ : Get $F \times \frac{1}{S}(1 + r_f \times t)$ INR

For no arbitrage: Strategy A = Strategy B

$1 + r_d \times t = F \times \frac{1}{S}(1 + r_f \times t)$

Solving for $F$ : $F = S \times \frac{1 + r_d \times t}{1 + r_f \times t}$

HOW to interpret: If Indian rates ( $r_d$ ) are higher than US rates ( $r_f$ ), the forward rate will be HIGHER than spot (USD appreciates forward). This compensates for the interest differential.

Worked example Calculating Forward Rate

Given:

Spot USD/INR = ₹83.00
India interest rate = 6.5% per annum
USA interest rate = 4.0% per annum
Contract period = 3 months (0.25 years) Find: 3-month forward rate

Solution: $F = 83.00 \times \frac{1 + 0.065 \times 0.25}{1 + 0.040 \times 0.25}$ Why this step? We're applying CIRP with $t = 0.25$ years.

$F = 83.00 \times \frac{1.01625}{1.01}$

Why this step? Computing the interest factors. India earns more interest (1.625% vs 1.0% for 3 months).

$F = 83.00 \times 1.00619 = 83.51$

Interpretation: The USD trades at a premium in the forward market (83.51 > 83.00) because Indian interest rates are higher. This premium of ₹0.51 exactly compensates for the 2.5% interest rate differential over 3 months.

Currency Futures Pricing

Derivation:

The cost of carry for currency is the interest rate differential.

Holding USD costs you:

You forego earning $r_d$ (India rate) on rupees
But you earn $r_f$ (USA rate) on dollars

Net cost = $r_d - r_f$ (what you give up minus what you gain)

By cost-of-carry model: $F_0 = S_0 \times e^{(\text{net carry cost}) \times T} = S_0 \times e^{(r_d - r_f) \times T}$

Worked example Currency Futures Contract Specifications (NSE)

USD/INR Futures on NSE:

Contract size: $1,000
Tick size: ₹0.0025 (one-fourth of a paisa)
Expiry: Last Thursday of the contract month (preceding trading day if Thursday is a holiday)
Settlement: Cash-settled in INR
Margin: ~3-5% (varies with volatility) Scenario: You expect USD to strengthen from ₹83 to ₹85 in one month.

Action: Buy 10 USD/INR futures contracts

Contract value: 10 × $1,000 × ₹83 = ₹8,30,000
Margin required (4%): ₹33,200 Outcome after 1 month:
USD/INR moves to ₹85
Profit per contract: $1,000 × (₹85 - ₹83) = ₹2,000
Total profit: 10 × ₹2,000 = ₹20,000
Return on margin: ₹20,000/₹33,200 = 60.2%

Why this works? Leverage. You control ₹8.3 lakh with ₹33,200. The 2.4% currency move translates to 60% return on your margin.

Currency Options - The Greeks

Worked example Hedging with Currency Options

Situation: Indian importer must pay $50,000 in 2 months for raw materials. Current spot = ₹83. Fear: rupee weakening to ₹86.

Hedging Strategy: Buy USD/INR Call Options

Strike price (K): ₹84
Premium: ₹0.50 per dollar
Contracts: $50,000 worth Cost Analysis:
Premium paid: $50,000 × ₹0.50 = ₹25,000 Scenario 1 - Rupee weakens to ₹86:
Exercise the option, buy at ₹84
Cost of dollars: $50,000 × ₹84 = ₹42,00,000
Total cost with premium: ₹42,00,000 + ₹25,000 = ₹42,25,000
Cost if unhedged at spot: $50,000 × ₹86 = ₹43,00,000
Saved vs spot: ₹43,00,000 - ₹42,25,000 = ₹75,000

Why exercise? Strike (₹84) < Spot (₹86). Cheaper to use the option.

Scenario 2 - Rupee strengthens to ₹81:

Don't exercise (let option expire)
Buy at spot: $50,000 × ₹81 = ₹40,50,000
Total cost with premium: ₹40,50,000 + ₹25,000 = ₹40,75,000 Why not exercise? Spot (₹81) < Strike (₹84). Market is better than option.

Key insight: Options provide insurance. You're protected above ₹84, but can benefit if rupee strengthens. Premium is your insurance cost.

Common Pitfalls

Practical Applications

For Exporters (Receiving USD)

Risk: Rupee strengthening (USD/INR falling)

Solution: Sell USD futures or buy USD put options

Why futures? Lock in today's rate for future receivables
Why puts? Insurance if rupee strengthens; benefit if it weakens

For Importers (Paying USD)

Risk: Rupee weakening (USD/INR rising)

Solution: Buy USD futures or buy USD call options

Why futures? Fix your payment amount in rupees
Why calls? Cap maximum cost; benefit if rupee strengthens

For Speculators

Bullish on USD (expecting depreciation of INR):

Buy USD/INR futures
Buy USD/INR call options
Sell USD/INR put options (risky - unlimited loss potential)

Bearish on USD (expecting appreciation of INR):

Sell USD/INR futures
Buy USD/INR put options
Sell USD/INR call options (risky)

Recall Explain to a 12-year-old

Imagine you're going to America in 3 months and need $100. Today, each dollar costs ₹83, so you'd need ₹8,300.

But what if dollars become more expensive by the time you go? Maybe ₹90 each! Then you'd need ₹9,000. That's ₹700 more!

Currency derivatives are like buying a "coupon" today that says "I can buy $100 at ₹83 each anytime in the next 3 months, no matter what the market price is."

Futures are like a promise you MUST keep - you WILL buy at that price. Options are like paying a small fee for the CHOICE to buy at that price. If dollars actually get cheaper (₹80), you can ignore your coupon and just buy from the market. But if they get expensive (₹90), you use your coupon and save money!

Companies use this because they buy and sell stuff from other countries all the time. They don't want surprise costs, so they lock in prices using these tools. Some people also use them to bet on which way currency prices will move, like a game (but with real money).

Connections

Introduction to commodities, forex & crypto - Foundation of alternative markets
Gold, Silver, Crude basics - Commodity hedging uses similar futures
Options basics - Same principles, different underlying
Futures and forwards - Core derivative mechanics
Risk types - Currency risk is systematic
Macro indicators - Interest rates, inflation affect forex

#flashcards/stock-market

What does USD/INR = 83.50 mean? :: One US Dollar costs 83.50 Indian Rupees. It's a quote where USD is base currency and INR is quote currency.

What are the four main types of currency derivatives?

1. Currency Futures (standardized, exchange-traded), 2. Currency Options (rights to buy/sell), 3. Currency Forwards (customized OTC), 4. Currency Swaps (exchange principal and interest).

State the Covered Interest Rate Parity formula :: F = S × (1 + r_d × t) / (1 + r_f × t), where F is forward rate, S is spot rate, r_d is domestic rate, r_f is foreign rate, and t is time period.

Why does forward rate differ from spot rate?

Interest rate differentials between countries. If domestic rates > foreign rates, forward rate > spot rate (currency depreciates forward). This prevents arbitrage.

If India rates = 6%, US rates = 4%, and spot USD/INR = 80, will the forward be higher or lower than 80?

Higher. Forward = 80 × (1.06/1.04) ≈ 81.54. Higher domestic rates mean forward premium on USD.

What is the contract size of USD/INR futures on NSE?

$1,000 per contract, settled in INR at expiry.

What is the tick size of USD/INR futures on NSE?

₹0.0025 (one-fourth of a paisa) per dollar.

When do USD/INR futures on NSE expire?

Last Thursday of the contract month (or the preceding trading day if Thursday is a holiday).

What is the payoff formula for a currency call option at expiry?

Profit = max(S_T - K, 0) - Premium, where S_T is spot at expiry and K is strike price. You subtract the premium paid upfront.

An importer must pay $10,000 in 2 months. Current spot = ₹83. How to hedge?

Buy USD/INR call options or buy USD/INR futures. This locks in maximum payment if rupee weakens, protects against upside risk.

If USD/INR falls from 84 to 80, which currency strengthened?

Indian Rupee strengthened. You need fewer rupees (80 vs 84) to buy one dollar, so rupee gained value.

What is the margin requirement typically for currency futures?

Around 3-5% of contract value, varies with market volatility. Much lower than equity futures due to lower volatility.

Why is the forward rate NOT a prediction of future spot rate?

Forward rate is calculated from interest rate parity (arbitrage-free condition), not market expectations. Expectations are in the spot rate; forward premium/discount is mechanical interest adjustment.

What does it mean if forward rate > spot rate?

Forward premium on the base currency (USD). Indicates domestic interest rates > foreign rates. Base currency is expected to cost more in the forward market.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Chalo ek simple si baat samajhte hain — currency derivatives ka core intuition. Socho tum ek Indian exporter ho jo US company ko software bech rahe ho, aur tumhe 3 mahine baad $100,000 milne hain. Aaj ka rate ₹83/$ hai, toh tum ₹83 lakh expect kar rahe ho. Lekin agar rupee strong ho gaya aur rate ₹80/$ ho gaya, toh tumhe sirf ₹80 lakh milenge — ₹3 lakh ka nuksaan! Yahi problem solve karti hain currency derivatives — ye tumhe aaj hi ka rate future transaction ke liye "lock" karne dete hain. Matlab uncertainty ko certainty mein convert kar dete hain. Isliye ye exist karte hain: risk se bachne ke liye (hedging) aur profit kamane ke liye (speculation).

Ab USD/INR pair ko samjho — ye simply batata hai ki 1 US Dollar ki kimat kitne rupees hai. Agar USD/INR = 83.50, toh 1 dollar = ₹83.50. Ismein USD "base" hai (jo tum kharid rahe ho) aur INR "quote" hai (jisse tum pay kar rahe ho). Currency derivatives ki four main types hain: futures, options, forwards, aur swaps. Isme se USD/INR India mein sabse zyada trade hone wala pair hai, isliye iski samajh zaroori hai.

Ab ek dilchasp baat — forward rate randomly decide nahi hota, ye do deshon ke interest rates par depend karta hai. Isko Interest Rate Parity formula batata hai: $F = S \times \frac{1 + r_d \times t}{1 + r_f \times t}$ . Iske peeche logic ye hai ki agar forward rate galat hota, toh log ek currency mein borrow karke, doosri mein invest karke risk-free profit (arbitrage) kama lete. Market ye opportunity allow nahi karti, isliye rate automatically balance ho jata hai. Jaise humare example mein India ka interest rate (6.5%) US se zyada hai, toh forward rate spot se thoda upar aata hai — ₹83.51 — kyunki ye interest ka difference compensate karta hai. Yahi maths samajhna important hai kyunki isse tum predict kar sakte ho ki future rate kis direction mein move karega, aur apni hedging ya trading strategy smartly bana sakte ho.

Test yourself — Commodities, Forex & Crypto

Connections