This is a one-page reference for the calculations in NISM Series VIII. Each formula comes with a worked example. Practise them by hand and in a spreadsheet: test centre workstations have Microsoft Excel or LibreOffice Calc, and doing a calculation both ways is the best check you can have in the exam hall.
For the exam overview, see our NISM VIII Complete Guide.
#Futures
#Contract value
Contract value = Futures price × Lot size
The lot size is set by the exchange and differs for every stock and index, and it is revised from time to time, so always use the lot size given in the question.
#Cost of carry and futures price
Futures price = Spot price + Cost of carry
Cost of carry = Interest cost of financing the purchase − Dividend earned
Example: a stock trades at ₹100, financing it for a year costs ₹6, and it pays a ₹2 dividend. Net cost of carry = 6 − 2 = ₹4, so the futures price is ₹104.
#Futures fair value: two methods
NISM questions calculate the futures fair value in one of two ways. They give slightly different answers, so check which one the question asks for.
#Method 1: Annual compounding
F = S × (1 + r)^t
Where:
- F = futures fair value
- S = spot price = ₹1,500
- r = annual interest rate = 9% = 0.09
- t = time to expiry in years = 3 months = 3/12 = 0.25
F = 1,500 × (1.09)^0.25 = ₹1,532.67, so the cost of carry is ₹32.67.
In a spreadsheet: =1500*(1+0.09)^(3/12). The bracket trap here is calculating 1 + 0.09^0.25 instead of (1.09)^0.25.
#Method 2: Continuous compounding
F = S × e^(r × t), where S is the spot price, r the annual interest rate and t the time to expiry in years.
Example: spot ₹1,500, interest 9% a year, 3 months to expiry.
F = 1,500 × e^(0.09 × 3/12) = 1,500 × e^0.0225 = ₹1,534.13
The bracket trap: r × t must be calculated first, inside the exponent. Students who calculate e^0.09 and then multiply by 3/12 get a completely different (and wrong) number. In a spreadsheet, type =1500*EXP(0.09*3/12), and check you get 1,534.13.
#Mark-to-market
Daily MTM = (Today's settlement price − Previous settlement price) × Lot size × Number of lots
A long position gains when the price rises; a short position gains when it falls.
Example: you bought 1 lot (lot size 1,200) at ₹768 and squared off at ₹778. Gain = (778 − 768) × 1,200 = ₹12,000.
#Initial margin
Initial margin = Price × Number of lots × Lot size × Margin %
#Options
#Who has what
| Position | Pays or receives premium | Right or obligation | Gains when the price… |
|---|---|---|---|
| Long call (buy a call) | Pays | Right to buy | Rises |
| Short call (sell a call) | Receives | Obligation to sell | Falls or stays flat |
| Long put (buy a put) | Pays | Right to sell | Falls |
| Short put (sell a put) | Receives | Obligation to buy | Rises or stays flat |
Students find this counter-intuitive: buying a put is a bet that the price will fall. Learn this table before any payoff calculation.
#Intrinsic value and time value
Option premium = Intrinsic value + Time value
- Call intrinsic value = MAX(0, Spot − Strike)
- Put intrinsic value = MAX(0, Strike − Spot)
Intrinsic value is never negative. Example: spot ₹120, 110 call quoted at ₹24. Intrinsic value = 120 − 110 = ₹10; time value = 24 − 10 = ₹14.
#Payoffs at expiry (per unit)
| Position | Payoff at expiry | Break-even |
|---|---|---|
| Long call | MAX(0, S − K) − Premium | K + Premium |
| Short call | Premium − MAX(0, S − K) | K + Premium |
| Long put | MAX(0, K − S) − Premium | K − Premium |
| Short put | Premium − MAX(0, K − S) | K − Premium |
S is the spot price at expiry and K the strike price. Multiply by the lot size and the number of lots for the total. Note the sign: a long position's profit is exactly the short position's loss.
#Straddle and strangle
A long straddle (buy a call and a put at the same strike) has two break-even points: Strike − Total premium and Strike + Total premium. A strangle uses a lower-strike put and a higher-strike call, so its break-evens are Put strike − Total premium and Call strike + Total premium.
#Put-call parity
c + X × e^(−r × t) = p + S₀
c is the call premium, p the put premium, X the strike price, S₀ the spot price, r the interest rate and t the time to expiry in years.
#Hedging
#Hedge ratio with index futures
Number of index futures contracts = (Portfolio value × Portfolio beta) ÷ (Index futures price × Lot size)
Example: portfolio ₹9,00,000, beta 1.3, index at 8,000, lot size 75.
Contracts = (9,00,000 × 1.3) ÷ (8,000 × 75) = 11,70,000 ÷ 6,00,000 = 1.95, so about 2 contracts.
#Before every calculation, check three things
- Call or put?
- Bought or sold? The answer options usually include both signs, so a missed "sold" gives a wrong answer that looks right.
- How many lots? Sometimes the quantity is written in words ("two lots").
For a day-by-day plan to practise these, see How to Pass NISM VIII in Your First Attempt.
