NISM Series VIII Formula Sheet
Ten formulas, what each one is for, and a worked example.
Series VIII questions are full of numbers: fair futures prices, option payoffs, break-evens and hedge sizes. These ten formulas cover nearly all of them.
A worked beta-hedge example follows the table.
The 10 Formulas
1
Formula
Futures fair price (cost of carry)
Expression
F = S × (1 + r × t) − Dividends
Use it for
Theoretical price of a stock or index future.
2
Formula
Basis
Expression
Basis = Futures price − Spot price
Use it for
Premium or discount of futures over spot.
3
Formula
Call intrinsic value
Expression
max(S − K, 0)
Use it for
How much a call is in the money.
4
Formula
Put intrinsic value
Expression
max(K − S, 0)
Use it for
How much a put is in the money.
5
Formula
Time value
Expression
Option premium − Intrinsic value
Use it for
The part of the premium that decays to zero at expiry.
6
Formula
Break-even, long call
Expression
Strike + Premium
Use it for
Price at expiry where a call buyer breaks even.
7
Formula
Break-even, long put
Expression
Strike − Premium
Use it for
Price at expiry where a put buyer breaks even.
8
Formula
Put-call parity
Expression
C + K ÷ (1 + r)ᵗ = P + S
Use it for
Linking call and put prices on the same strike and expiry.
9
Formula
Contracts to hedge a portfolio
Expression
Portfolio value × β ÷ (Futures price × Lot size)
Use it for
Index futures needed to hedge market risk.
10
Formula
Futures P&L
Expression
(Exit price − Entry price) × Lot size × Contracts
Use it for
Profit or loss on a long futures position. Reverse the sign for short.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Futures fair price (cost of carry) | F = S × (1 + r × t) − Dividends | Theoretical price of a stock or index future. |
| 2 | Basis | Basis = Futures price − Spot price | Premium or discount of futures over spot. |
| 3 | Call intrinsic value | max(S − K, 0) | How much a call is in the money. |
| 4 | Put intrinsic value | max(K − S, 0) | How much a put is in the money. |
| 5 | Time value | Option premium − Intrinsic value | The part of the premium that decays to zero at expiry. |
| 6 | Break-even, long call | Strike + Premium | Price at expiry where a call buyer breaks even. |
| 7 | Break-even, long put | Strike − Premium | Price at expiry where a put buyer breaks even. |
| 8 | Put-call parity | C + K ÷ (1 + r)ᵗ = P + S | Linking call and put prices on the same strike and expiry. |
| 9 | Contracts to hedge a portfolio | Portfolio value × β ÷ (Futures price × Lot size) | Index futures needed to hedge market risk. |
| 10 | Futures P&L | (Exit price − Entry price) × Lot size × Contracts | Profit or loss on a long futures position. Reverse the sign for short. |
Worked Example: Hedging a Portfolio With Nifty Futures
A ₹50,00,000 portfolio with a beta of 1.2 is to be hedged. Nifty futures trade at 24,000, with a lot size of 65 (NSE revises lot sizes from time to time).
- 1
Beta-adjusted exposure
50,00,000 × 1.2 = ₹60,00,000.
- 2
Value of one contract
24,000 × 65 = ₹15,60,000.
- 3
Contracts to sell
60,00,000 ÷ 15,60,000 ≈ 3.85, so about 4 contracts short.
Free account, this exam preselected.
Only Time Value Decays
At expiry an option is worth exactly its intrinsic value. If a question asks what an option is worth on expiry day, ignore the premium paid and compute the intrinsic value.
FAQs
Why is the futures price usually above spot?expand_more
Because of the cost of carry: interest on the money you'd otherwise need to buy the shares, less any dividends.
Is put-call parity tested with numbers?expand_more
Yes. Questions give three of the four values and ask for the fourth, or ask whether an arbitrage exists.
Are Indian equity options American or European?expand_more
European. Index and stock options on Indian exchanges can be exercised only on expiry.
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