NISM Series I Formula Sheet
Ten formulas, what each one is for, and a worked example.
Series I tests how currency futures and options are priced and settled on Indian exchanges. The arithmetic is short, but the questions depend on getting the quote convention and the contract size right.
These ten formulas cover pricing, payoffs and margins, with a worked fair-value example.
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The 10 Formulas
1
Formula
Futures fair value (interest parity)
Expression
F = S × (1 + r_INR × t) ÷ (1 + r_USD × t)
Use it for
Theoretical USD/INR futures price from spot and the two interest rates.
2
Formula
Forward premium (annualised)
Expression
(F − S) ÷ S × 365 ÷ Days × 100
Use it for
Comparing the futures premium with the interest-rate differential.
3
Formula
Contract value
Expression
Futures price × Lot size
Use it for
Exposure per contract. USD/INR lot size is USD 1,000.
4
Formula
Mark-to-market
Expression
(Today's settlement price − Previous settlement price) × Lot size × Contracts
Use it for
Daily profit or loss settled in cash.
5
Formula
Basis
Expression
Basis = Spot − Futures
Use it for
Gap between cash and futures; it narrows to zero at expiry.
6
Formula
Call option payoff (long)
Expression
max(S_T − K, 0) − Premium
Use it for
Importer hedging against rupee depreciation.
7
Formula
Put option payoff (long)
Expression
max(K − S_T, 0) − Premium
Use it for
Exporter hedging against rupee appreciation.
8
Formula
Break-even for a long call
Expression
Strike + Premium
Use it for
Spot rate at which a call buyer neither gains nor loses.
9
Formula
Hedge contracts needed
Expression
Exposure in USD ÷ Lot size
Use it for
Number of contracts to hedge a foreign currency payable or receivable.
10
Formula
Cross rate
Expression
EUR/INR = EUR/USD × USD/INR
Use it for
Checking whether EUR/INR futures are in line with USD/INR and EUR/USD.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Futures fair value (interest parity) | F = S × (1 + r_INR × t) ÷ (1 + r_USD × t) | Theoretical USD/INR futures price from spot and the two interest rates. |
| 2 | Forward premium (annualised) | (F − S) ÷ S × 365 ÷ Days × 100 | Comparing the futures premium with the interest-rate differential. |
| 3 | Contract value | Futures price × Lot size | Exposure per contract. USD/INR lot size is USD 1,000. |
| 4 | Mark-to-market | (Today's settlement price − Previous settlement price) × Lot size × Contracts | Daily profit or loss settled in cash. |
| 5 | Basis | Basis = Spot − Futures | Gap between cash and futures; it narrows to zero at expiry. |
| 6 | Call option payoff (long) | max(S_T − K, 0) − Premium | Importer hedging against rupee depreciation. |
| 7 | Put option payoff (long) | max(K − S_T, 0) − Premium | Exporter hedging against rupee appreciation. |
| 8 | Break-even for a long call | Strike + Premium | Spot rate at which a call buyer neither gains nor loses. |
| 9 | Hedge contracts needed | Exposure in USD ÷ Lot size | Number of contracts to hedge a foreign currency payable or receivable. |
| 10 | Cross rate | EUR/INR = EUR/USD × USD/INR | Checking whether EUR/INR futures are in line with USD/INR and EUR/USD. |
Worked Example: Fair Value of a 3-Month USD/INR Future
Spot is ₹84.20, the rupee interest rate is 6.5% and the dollar rate is 4.5%.
- 1
Rupee leg
1 + 0.065 × 0.25 = 1.01625.
- 2
Dollar leg
1 + 0.045 × 0.25 = 1.01125.
- 3
Fair value
84.20 × 1.01625 ÷ 1.01125 ≈ ₹84.62. The dollar trades at a premium because rupee rates are higher.
Free account, this exam preselected.
Higher Interest Rate, Forward Discount
The currency with the higher interest rate trades at a forward discount. In USD/INR that's the rupee, so the dollar is at a premium. Use this to check your answer's direction before choosing an option.
FAQs
Are currency futures in India settled in dollars?expand_more
No. Exchange-traded currency futures in India are cash-settled in rupees.
Why does basis narrow to zero?expand_more
At expiry the futures contract settles at the reference rate, so spot and futures converge.
Do options in Series I use premiums in rupees?expand_more
Yes. Currency option premiums are quoted in rupees per unit of foreign currency.
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