Derivatives: futures and options basics

Commerce (General / Accounting and Finance / Banking and Insurance) (B.Com) · Finance and banking · free study notes for exams, placements and interviews

In short

A derivative is a contract whose value is *derived* from an underlying asset — a share, index, currency, bond, interest rate or commodity. Futures and options are the two exchange-traded workhorses: a future locks a price for a future date, an option gives a *right* (not an obligation) to buy or sell at a fixed price. In India they are defined in Section 2(ac) of the Securities Contracts (Regulation) Act, 1956, traded on NSE and BSE under SEBI regulation, and used daily for hedging portfolios, managing currency risk and taking leveraged views. The topic carries heavy weight in B.Com / M.Com financial-derivatives papers, NISM Series-VIII (Equity Derivatives) certification, CA/CS/CMA and CFA syllabi, and in placement interviews for broking houses, banks, treasury desks, mutual funds and risk/analytics roles.

Explained

What derivatives are and how the Indian market is organised

Definition (SCRA 2(ac)): a security derived from a debt instrument, share, loan, risk instrument or contract for differences, or any other form of security; includes commodity derivatives and such other instruments as notified.
Four families: *forwards* (OTC, customised), *futures* (exchange-traded, standardised), *options* (right without obligation), *swaps* (exchange of cash-flow streams, e.g. interest-rate or currency swaps — OTC).
Underlyings traded in India: equity indices (Nifty 50, Bank Nifty, Nifty Financial Services, Sensex), individual stocks (an eligibility-filtered list revised by SEBI/exchanges), currency pairs (USDINR, EURINR, GBPINR, JPYINR), interest rates (bond futures), and commodities on MCX/NCDEX.
Who regulates what: SEBI regulates exchange-traded securities and commodity derivatives (commodities moved to SEBI after the FMC merger in Sept 2015); RBI governs OTC rupee interest-rate and currency derivatives and bank exposures.
History for exams: L.C. Gupta Committee (1998) recommended derivatives, J.R. Varma Committee designed the risk-containment/margin system; index futures began on NSE in June 2000, index options 2001, stock options and stock futures 2001; *badla* was abolished in 2001.
Clearing and novation: trades are novated to a clearing corporation (NSE Clearing, ICCL) which becomes the counterparty to both sides — this, plus margins and a Core Settlement Guarantee Fund, removes counterparty risk.

Forwards and futures: mechanics, pricing and margining

Standardisation: exchange fixes underlying, lot size, expiry (last Tuesday/Thursday of the month — see regulation note), tick size and settlement method. Only price is negotiated.
Contract value = price × lot size. Since Nov 2024 SEBI requires index derivative contracts to have a value of at least about ₹15 lakh (to be kept in the ₹15–20 lakh band), so the Nifty 50 lot was reset to 75 units. Lot sizes are revised periodically — always check the exchange's contract specification.
Expiry cycle: three serial monthly contracts (near, next, far) trade simultaneously; weekly options exist on one index per exchange.
Margining (three layers): *initial margin* computed by the SPAN portfolio-risk system (covers a one-day 99% VaR move), *exposure/extreme loss margin (ELM)*, and *mark-to-market (MTM)* settled in cash every day. Margins are collected upfront; shortfall attracts penalty.
Mark to market: daily profit/loss is credited/debited against the day's settlement price, so a futures position is effectively re-priced every evening and there is no accumulation of unpaid gains.
Cost-of-carry pricing: F = S + cost of carrying the asset − income from holding it. For an index, carry cost is interest and income is dividend yield.
Basis and convergence: basis = spot − futures (the Indian convention; some texts use futures − spot). Basis shrinks to zero at expiry because the futures settles at spot. *Contango*: futures above spot (normal for equities). *Backwardation*: futures below spot — signals heavy selling, dividend accrual or borrowing stress.
Arbitrage: if futures > fair value → *cash-and-carry* (buy spot, sell futures, hold to expiry). If futures < fair value → *reverse cash-and-carry* (sell spot/short, buy futures). Transaction costs, STT, impact cost and margin funding define a no-arbitrage *band*, not a single price.
Rollover: closing the near-month and opening the next-month position near expiry; rollover percentage and cost are read as sentiment indicators.
Open interest (OI): number of contracts outstanding. Rising price + rising OI = fresh longs; rising price + falling OI = short covering. OI changes on every new contract created, unlike volume.

Options: terminology, moneyness and payoffs

Call: right to *buy* the underlying at the strike. Put: right to *sell* at the strike. The buyer pays a premium and has limited loss; the writer (seller) receives the premium, posts margin and carries large/unlimited risk.
American vs European: American options can be exercised any time, European only at expiry. In India all index and stock options are European-style (stock options were converted from American to European in 2011), which is why put-call parity and Black-Scholes apply directly.
Strike price (K), premium (c or p), expiry, lot size are the four specification items; strikes are listed at fixed intervals around spot.
Moneyness: a call is ITM if S > K, ATM if S ≈ K, OTM if S < K; for a put the inequalities reverse. Only ITM options have intrinsic value.
Premium = intrinsic value + time value. Time value decays to zero at expiry (time decay accelerates in the final days) and is largest for ATM options.
Payoff shapes: long call — loss limited to premium, unlimited upside beyond K + c; long put — loss limited to premium, profit up to K − p (if the stock goes to zero); short call/put — mirror images, limited profit and large loss.
Settlement: index options and futures settle in cash against the closing spot (volume-weighted average of the last 30 minutes). All stock futures and options are physically settled — fully since the Oct 2019 expiry — so an un-squared ITM stock option results in actual delivery and needs full funds or shares.
Exercise, assignment and lapse: ITM options are exercised automatically at expiry (Do-Not-Exercise facility exists in limited cases); OTM options lapse worthless. Writers are assigned at random/pro-rata.

Option pricing, premium drivers and the Greeks

Six determinants of premium: spot, strike, time to expiry, volatility, risk-free rate, dividends. Higher volatility and longer time raise *both* call and put premiums; higher spot raises calls and lowers puts; higher rates raise calls and lower puts; expected dividends lower calls and raise puts.
Binomial model (Cox-Ross-Rubinstein): the underlying moves up by factor u or down by d; value the option by risk-neutral probability p and discount — extendable to multiple steps and American options.
Black-Scholes-Merton: closed-form value for a European option on a non-dividend stock; assumes lognormal prices, constant volatility and rate, no transaction costs, continuous trading. Limitations: ignores jumps, fat tails and the observed volatility smile/skew.
Greeks (sensitivities): *Delta* (∂premium/∂spot; 0 to 1 for calls, −1 to 0 for puts; ATM ≈ ±0.5; also the hedge ratio and a rough probability of expiring ITM). *Gamma* (rate of change of delta; peaks ATM near expiry). *Theta* (time decay; negative for buyers, positive for writers). *Vega* (sensitivity to volatility). *Rho* (sensitivity to interest rate).
Volatility: *historical* (from past returns) vs *implied* (back-solved from the market premium). India VIX is NSE's annualised implied volatility index computed from near-month Nifty option order books — it spikes in falling markets ("fear gauge").
Option chain reading: premiums, OI and change in OI at each strike; put-call ratio (PCR) = put OI / call OI, used as a contrarian sentiment measure; max-OI strikes act as perceived support/resistance.

Using derivatives: hedging, speculation, arbitrage and spreads

Hedging: reduce an existing exposure. A portfolio holder shorts index futures (beta hedge) or buys index puts (*protective put* — pays a premium but keeps upside). An exporter sells USDINR futures; an importer buys them.
Speculation: a directional view with leverage. Bullish — buy futures or calls, sell puts. Bearish — sell futures or buy puts.
Arbitrage: risk-free profit from mispricing — cash-and-carry, put-call parity violations, calendar and inter-exchange spreads.
Covered call: hold the share, write an OTM call — earns premium, caps upside. Cash-secured put: write a put against funds to buy lower.
Bull call spread example: buy a 24,000 call at ₹150 and sell a 24,300 call at ₹60 → net cost 90 points; maximum profit 300 − 90 = 210 points, maximum loss 90 points, break-even 24,090.
Straddle / strangle: buy both a call and a put (same strike / different strikes) to trade a big move either way; short straddle profits from a quiet market but has unlimited risk. Butterfly and iron condor are range strategies with capped risk.
Why derivatives matter economically: price discovery, risk transfer, liquidity and completeness of markets. Risks: leverage amplifies losses, basis risk, liquidity risk in far strikes, model risk, and systemic risk from concentrated positions.

Regulation, costs and the current Indian framework

Eligibility and limits: stocks must meet SEBI's liquidity/market-cap criteria to be in F&O. Market-wide position limit (MWPL) for a stock is 20% of free-float shares; when utilisation crosses 95% the stock enters a ban period where only position-reducing trades are allowed. Client-level and FPI/mutual-fund limits also apply; index-option limits are now monitored on a delta-adjusted "future equivalent" basis, and these thresholds have been revised more than once recently — verify against the latest SEBI circular.
SEBI's 2024-25 F&O measures (examinable as current practice): minimum index contract value raised to about ₹15 lakh; only one weekly expiry per exchange; extra 2% ELM on short options on expiry day; upfront collection of option premium from buyers; withdrawal of calendar-spread margin benefit on expiry day; intraday monitoring of position limits. SEBI also standardised expiry days (Tuesday/Thursday); the exact day for each index has changed more than once — check the exchange circular.
Costs: brokerage, exchange transaction charges, GST, stamp duty, SEBI fees and STT — since 1 Oct 2024 roughly 0.02% of traded value on the sale of futures and 0.1% of premium on the sale of options; exercised options attract STT on intrinsic value (about 0.125%, paid by the buyer). Rates can change in any Finance Act.
Taxation: income from exchange-traded equity derivatives is non-speculative business income (the proviso to Section 43(5) of the Income-tax Act excludes it from speculative transactions), so losses can be set off against other business income and carried forward 8 years; tax audit and turnover computation follow ICAI guidance, which has been revised — confirm the current method.
Accounting: derivatives are measured at fair value through profit or loss under Ind AS 109, with hedge accounting available for designated, documented and effective hedges (cash-flow, fair-value, net-investment hedges).

Key points

Derivative - a contract whose value depends on an underlying asset, index or rate; it creates no new capital, only transfers risk.
Forward vs future - forwards are OTC, customised, settled at maturity with counterparty risk; futures are standardised, exchange-traded, margined and marked to market daily.
Futures obligation - both buyer and seller must perform; profit/loss is symmetric and linear.
Option asymmetry - the buyer has a right and limited loss; the writer has an obligation, limited gain and large risk.
Premium = intrinsic value + time value; time value is zero at expiry.
Moneyness - call ITM when spot > strike; put ITM when spot < strike.
Cost of carry - futures price = spot plus financing cost minus dividend income; drives the no-arbitrage band.
Basis = spot − futures; converges to zero at expiry, which is what makes hedging work.
Margins - SPAN initial margin + exposure/ELM + daily MTM; option buyers pay full premium upfront, writers pay margin.
European style - all Indian index and stock options are European; index contracts settle in cash, all stock contracts settle physically.
Delta - change in premium per unit change in spot; also the hedge ratio (ATM ≈ 0.5).
Theta - time decay; works against buyers and for writers, accelerating near expiry.
Vega - sensitivity to implied volatility; long options are long volatility. India VIX tracks Nifty implied volatility.
Put-call parity - C + K·e^−rT = P + S for European options on the same underlying, strike and expiry; a violation is an arbitrage.
Beta hedge - number of index futures = β × portfolio value ÷ contract value.
MWPL ban - fresh positions in a stock are barred once 95% of the market-wide limit is used.
Open interest - outstanding contracts; read with price for position build-up or unwinding.
Leverage - a small margin controls a large exposure, so percentage gains and losses on capital are magnified several times.

Formulas and examples

Futures fair value (continuous compounding): F₀ = S₀ · e^{(r − q)T} — S₀ spot (₹ or index points), r risk-free rate p.a. (decimal), q dividend yield p.a., T time to expiry in years
Simple-interest / cost-of-carry form: F₀ = S₀ (1 + r·t/365) − dividends expected before expiry
Basis = S₀ − F₀ (→ 0 at expiry); Futures payoff per unit: long = S_T − F₀, short = F₀ − S_T; multiply by lot size
Intrinsic value: call = max(S − K, 0); put = max(K − S, 0); Time value = premium − intrinsic value
Long call P/L = max(S_T − K, 0) − c; break-even = K + c. Long put P/L = max(K − S_T, 0) − p; break-even = K − p
Short call P/L = c − max(S_T − K, 0); Short put P/L = p − max(K − S_T, 0)
Put-call parity (European, no dividend): C + K·e^−rT = P + S₀
Black-Scholes: C = S₀·N(d₁) − K·e^−rT·N(d₂); P = K·e^−rT·N(−d₂) − S₀·N(−d₁)
where d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ − σ√T; σ = annualised volatility, N(·) = standard normal CDF
One-step binomial: p = (e^rT − d)/(u − d); option value = e^−rT [p·f_u + (1 − p)·f_d]
Beta hedge contracts: N = (β × portfolio value) / (index futures price × lot size)
Minimum-variance hedge ratio: h* = ρ × (σ_S / σ_F)

Example 1 — Futures fair value and arbitrage. Nifty spot = 24,000; r = 6.5% p.a.; 73 days to expiry (T = 0.2 yr); dividend yield negligible.

Fair value F = 24,000 × e^{0.065 × 0.2} = 24,000 × e^0.013 = 24,000 × 1.013085 = 24,314 points (simple interest gives 24,000 × 1.013 = 24,312 — close enough for exams).
Market futures = 24,400 → overpriced by 86 points. Cash-and-carry: buy the index basket at 24,000, short futures at 24,400, hold to expiry → locked gain 86 points × 75 = ₹6,450 per lot, before brokerage, STT and impact cost.

Example 2 — Futures MTM and leverage. A stock future, lot size 500 shares, bought at ₹1,400. Contract value = 500 × 1,400 = ₹7,00,000. Initial margin at 15% = ₹1,05,000 → leverage = 7,00,000 ÷ 1,05,000 = 6.67×.

Price rises to ₹1,430 → MTM profit = 30 × 500 = ₹15,000, i.e. 15,000/1,05,000 = 14.3% on margin for a 2.1% move in the share.
Price instead falls to ₹1,370 → loss ₹15,000, debited the same evening; if the balance drops below the requirement, a margin call follows.

Example 3 — Option payoffs. Nifty 24,000 call bought at ₹150; lot 75; break-even = 24,000 + 150 = 24,150.

Spot at expiry	Call payoff (pts)	Buyer net (pts)	Buyer ₹ per lot	Writer ₹ per lot
23,700	0	−150	−11,250	+11,250
24,000	0	−150	−11,250	+11,250
24,150	150	0	0	0
24,400	400	+250	+18,750	−18,750
24,800	800	+650	+48,750	−48,750

Maximum buyer loss is the premium ₹11,250; writer's maximum profit is the same ₹11,250 with theoretically unlimited loss. A 24,000 put bought at ₹180 breaks even at 23,820; at 23,500 it earns (500 − 180) × 75 = ₹24,000.

Example 4 — Put-call parity arbitrage. S = 24,000, K = 24,000, T = 0.25 yr, r = 6%. Market: C = ₹600, P = ₹200.

Parity requires C − P = S − K·e^−rT = 24,000 − 24,000 × e^−0.015 = 24,000 − 23,642.69 = 357.31.
Actual C − P = 400 → the call is dear relative to the put. *Conversion:* buy stock, buy put, write call; net outflow = 24,000 + 200 − 600 = ₹23,600, financed by borrowing.
At expiry the combination is worth exactly K = 24,000 whatever the spot; repayment = 23,600 × e^0.015 = ₹23,956.67 → risk-free gain ₹43.33 per unit (= 42.69 points in present-value terms), about ₹3,250 per lot of 75.

Example 5 — Beta hedge with index futures. Portfolio value ₹1.20 crore, beta 1.25; Nifty futures 24,000, lot 75 → contract value ₹18,00,000.

N = (1.25 × 1,20,00,000) / 18,00,000 = 1,50,00,000 / 18,00,000 = 8.33 → short 8 contracts (rounding leaves a small unhedged residual).
If the market falls 5% (Nifty → 22,800): portfolio loses 1.25 × 5% = 6.25% = ₹7,50,000; futures gain = 1,200 × 75 × 8 = ₹7,20,000; net loss ₹30,000 — basis and rounding risk remain.

Feature	Futures	Options
Right or obligation	Obligation on both sides	Right for buyer, obligation for writer
Upfront payment	Margin only	Buyer pays full premium; writer pays margin
Payoff	Linear, symmetric	Non-linear, asymmetric
Maximum loss	Unlimited (both sides)	Buyer: premium; writer: large/unlimited
Time decay	None	Erodes the buyer's premium daily
Best for	Full hedge, directional view	Insurance, defined-risk and volatility views

Where it is used

Broking and trading desks (Zerodha, Angel One, ICICI Direct, Kotak Securities, Motilal Oswal): dealing, option-chain analysis, margin and risk-management roles; NISM Series-VIII certification is a hiring condition.
Mutual funds, insurers and PMS/AIFs: index futures and puts to hedge equity portfolios, arbitrage funds that run cash-and-carry between spot and futures as their core strategy.
Bank treasuries and corporate finance: USDINR forwards and futures to hedge import/export exposure, interest-rate futures and swaps for ALM; Ind AS 109 hedge documentation handled by finance teams.
Corporates with commodity exposure: MCX hedges on gold, crude, aluminium, cotton and agri contracts by jewellers, refiners, textile mills and FMCG buyers.
Clearing corporations and risk/analytics roles: SPAN margin computation, stress testing, MWPL and position-limit surveillance at NSE Clearing, ICCL, CDSL/NSDL-linked operations.
Audit, taxation and compliance: classifying F&O income as business income, turnover and audit determination, STT reconciliation, and derivative disclosures in company accounts.

Interview questions

Q: How does a futures contract differ from a forward? A: Futures are standardised, exchange-traded, cleared with daily mark-to-market and margins, so counterparty risk sits with the clearing corporation; forwards are customised OTC contracts settled at maturity with direct counterparty risk.
Q: Why can an option buyer lose only the premium? A: The buyer holds a right, not an obligation — if the option is OTM at expiry it simply lapses, and the maximum sacrifice is the premium already paid.
Q: What is the cost-of-carry model and when does futures trade below spot? A: Fair futures = spot + financing cost − income; futures trade below spot (backwardation) when expected dividends or borrowing returns exceed the interest cost, or when heavy short-selling pressure exists.
Q: An ATM call has delta 0.5 — what does that tell you? A: The premium changes about ₹0.50 for a ₹1 move in the underlying, 2 lots of the option roughly hedge 1 lot of futures, and the market implies roughly a 50% chance of expiring ITM.
Q: Which Greek hurts an option buyer most and why? A: Theta — time value decays every day and the decay accelerates near expiry, so a buyer loses money even if the underlying does not move.
Q: Volatility rises sharply but the index is flat. What happens to a long straddle? A: It gains, because both legs are long vega and the premiums expand with implied volatility even with no directional move.
Q: State put-call parity and its use. A: C + K·e^−rT = P + S for European options on the same underlying, strike and expiry; a deviation allows a risk-free conversion/reversal arbitrage, and it lets one option be priced from the other.
Q: How would you hedge a ₹5 crore equity portfolio with beta 1.1? A: Short index futures worth β × portfolio = ₹5.5 crore, i.e. 5.5 crore ÷ (index level × lot size) contracts, accepting basis and rounding risk.
Q: Why does a short OTM option require margin when it looks safe? A: The writer's loss is open-ended; SPAN margin is sized to a worst-case one-day move in price and volatility, which can be many times the premium received.
Q: What happens if you hold an ITM stock option to expiry in India? A: It is exercised and physically settled — delivery of shares with full funds or shares required, plus exercise STT — which is why most traders square off before expiry.
Q: Are F&O losses speculative losses for tax? A: No — exchange-traded equity derivatives are excluded from "speculative transaction" by Section 43(5), so the loss is a non-speculative business loss, set off against business income and carried forward 8 years.
Q: Do derivatives increase or reduce risk in a market? A: They transfer and price risk and improve price discovery and liquidity; the risk arises from leverage and concentration, which is why SEBI imposes position limits, margin rules and larger contract sizes.

Common mistakes

Treating a buyer's limited loss as symmetric to the writer's position — writing options is a high-risk, margin-intensive trade, not "free premium".
Forgetting to multiply the per-unit payoff by the lot size, or quoting profit in index points as if it were rupees.
Computing break-even for a long call as the strike instead of strike + premium (and strike − premium for a put).
Mixing up moneyness for puts, and so assigning intrinsic value to an OTM option (intrinsic value can never be negative).
Using simple interest and continuous compounding interchangeably in futures pricing, or leaving T in days instead of years in Black-Scholes.
Ignoring dividends, STT and transaction costs in an "arbitrage", which usually wipes out a small theoretical mispricing.
Assuming an Indian stock option can be exercised early (they are European) or that it settles in cash (stock contracts are physically settled).