51  Derivatives — Options, Forwards and Futures

51.1 What is a Derivative?

A derivative is a financial contract whose value is derived from an underlying asset (stock, bond, commodity, currency, interest rate, index). The Indian Securities Contracts (Regulation) Act 1956 defines a derivative as a “contract which derives its value from the prices or index of prices of underlying securities”. John Hull’s Options, Futures and Other Derivatives (1989+) is the canonical textbook.

TipWorking definitions
Author / body Definition
SCRA 1956 (India) “Security derived from a debt instrument, share, loan, risk instrument, or any contract for differences.”
IFRS 9 / Ind AS 109 “A financial instrument whose value changes in response to an underlying variable, requires little or no initial investment, and is settled at a future date.”
John Hull “A financial instrument whose value depends on the values of other, more basic underlying variables.”
Robert Kolb “An asset that derives its value from one or more underlying assets.”

51.2 History of Derivatives

TipMilestones in derivatives
Year Event
1630s Tulip mania, Netherlands — early option contracts
1848 Chicago Board of Trade (CBOT) founded; agricultural futures
1973 Chicago Board Options Exchange (CBOE) — first listed options; Black-Scholes-Merton option pricing model
1975 Interest rate futures launched
1982 Stock index futures (S&P 500)
2000 India — derivatives launched at NSE (Index futures, June 2000)
2001 India — Options on indices and individual stocks
2010s Currency, interest-rate, commodity derivatives in India
2024 SEBI tightens F&O retail regulations

51.3 Types of Derivatives — Classification

flowchart TB
  D[Derivatives]
  D --> F[Forwards]
  D --> FU[Futures]
  D --> O[Options]
  D --> S[Swaps]
  D --> EX[Exotics]
  EX --> Asia[Asian]
  EX --> Bar[Barrier]
  EX --> Lo[Lookback]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

TipFour basic derivative instruments
Type Nature
Forward OTC; customised; non-standardised; bilateral
Future Exchange-traded; standardised; cleared by clearing house
Option Right (not obligation) to buy/sell
Swap Exchange of cash flows over time

51.4 Forwards vs Futures

TipForward vs Future
Dimension Forward Future
Trading venue OTC (bilateral) Exchange
Standardisation Customised Standardised
Counterparty risk High Low (clearing house)
Margin / Mark-to-Market None Daily MTM
Settlement Physical (typical) Cash or physical
Regulation Light Heavy (SEBI / CFTC)
Liquidity Low High
Default risk High Low
Use Hedging by corporates Hedging, speculation, arbitrage

51.4.1 Forward Pricing — Cost of Carry

TipForward price formula

For an investment asset with no income: \[F_0 = S_0 \times e^{rT}\]

For an asset with continuous dividend yield q: \[F_0 = S_0 \times e^{(r-q)T}\]

For an asset with storage cost u and convenience yield y: \[F_0 = S_0 \times e^{(r+u-y)T}\]

The relationship is enforced by cash-and-carry arbitrage.

51.5 Margin and Mark-to-Market

TipMargin requirements in futures
  • Initial Margin — deposited at trade entry.
  • Maintenance Margin — minimum threshold.
  • Variation Margin — top-up if account falls below maintenance.
  • Mark-to-Market (MTM) — daily settlement of gains/losses.
  • SPAN Margin — Standard Portfolio Analysis of Risk; SEBI’s risk-based margin.
  • Exposure Margin — additional buffer.
  • Special Margin — exchange-imposed for volatility.

51.6 Options — Concept

An option is a contract that gives the buyer the right, but not the obligation, to buy (Call) or sell (Put) an underlying asset at a pre-agreed price (strike) on or before a specified date (expiration).

51.6.1 Call vs Put

TipCall vs Put
Right to BUY Right to SELL
Buyer of Call Yes — pays premium —
Buyer of Put — Yes — pays premium
Seller (Writer) of Call Obligation to sell —
Seller (Writer) of Put — Obligation to buy

51.6.2 Key Option Terms

TipKey option terms
  • Strike / Exercise Price (K) — the agreed price.
  • Premium — price paid by buyer to writer.
  • Expiration / Expiry — last date for exercise.
  • In-the-Money (ITM) — exercising would yield positive cash flow (S > K for Call; S < K for Put).
  • At-the-Money (ATM) — S ≈ K.
  • Out-of-the-Money (OTM) — exercising loses (S < K for Call; S > K for Put).
  • Intrinsic Value — Max(S − K, 0) for Call; Max(K − S, 0) for Put.
  • Time Value — Premium − Intrinsic Value.

51.6.3 American vs European Options

TipAmerican vs European
Style Exercise
European Only at expiration
American Any time up to expiration
Bermudan Specified dates between

In India, stock options are European-style since 2010 (cash-settled).

51.7 Option Payoffs

TipOption payoffs at expiration
Position Payoff at expiration Max profit Max loss
Long Call Max(S − K, 0) − Premium Unlimited Premium
Short Call Premium − Max(S − K, 0) Premium Unlimited
Long Put Max(K − S, 0) − Premium K − Premium Premium
Short Put Premium − Max(K − S, 0) Premium K − Premium

51.8 Put-Call Parity

For European options on a non-dividend-paying stock:

\[C - P = S - K \times e^{-rT}\]

A relationship that links Call price, Put price, stock price and PV of strike. Violation → arbitrage.

51.8.1 Implications

  • Synthetic positions: Long Call + Short Put = Long Stock + Short Bond.
  • Conversion: Long Stock + Long Put + Short Call → risk-free bond.
  • Box Spread — arbitrage strategy combining four options.

51.9 Option Pricing — Black-Scholes-Merton (1973)

Fischer Black, Myron Scholes, and Robert Merton (1973) — the Black-Scholes formula for pricing European call options. Scholes and Merton won the Nobel Prize 1997 (Black had died in 1995).

51.9.1 Black-Scholes Formula

For a European call: \[C = S_0 \times N(d_1) - K \times e^{-rT} \times N(d_2)\]

Where: \[d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}; \quad d_2 = d_1 - \sigma\sqrt{T}\]

51.9.2 Five Inputs to Black-Scholes

TipFive drivers of option premium
  • Spot price (S) — Call ↑ as S ↑; Put ↓.
  • Strike (K) — Call ↓ as K ↑; Put ↑.
  • Time to expiry (T) — both Call and Put ↑ as T ↑.
  • Volatility (σ) — both Call and Put ↑ as σ ↑.
  • Risk-free rate (r) — Call ↑ as r ↑; Put ↓.
  • (Dividends — Call ↓, Put ↑.)

51.9.3 Black-Scholes Assumptions

TipBSM assumptions
  • European-style options.
  • Stock returns lognormally distributed.
  • Constant volatility.
  • No dividends (in basic form).
  • Continuous trading.
  • Constant risk-free rate.
  • No taxes or transaction costs.
  • No arbitrage.

51.10 Binomial Option Pricing — Cox-Ross-Rubinstein (1979)

John Cox, Stephen Ross, Mark Rubinstein (1979) — gave an alternative, intuitive lattice-based pricing model. Stock price evolves as a discrete binomial tree; option priced by working backwards.

\[p = \frac{e^{rT} - d}{u - d}\]

Where p = risk-neutral probability of an up-move; u, d = up/down factors.

Limit of binomial → Black-Scholes as steps → ∞.

51.11 The Greeks

TipOption Greeks — risk sensitivities
Greek Measures sensitivity to Range
Delta (Δ) Change in option price per ₹1 change in S Call: 0 to 1; Put: 0 to −1
Gamma (Γ) Change in Delta per ₹1 change in S Positive for long options
Theta (Θ) Time decay per day Usually negative for long options
Vega (ν) Change in price per 1 % change in volatility Positive for long options
Rho (ρ) Change in price per 1 % change in rate Positive for Call; negative for Put
Vanna, Volga Second-order Greeks Used in exotic books

51.12 Option Strategies

TipCommon option strategies
  • Covered Call — Long stock + Short call.
  • Protective Put — Long stock + Long put.
  • Bull Call Spread — Long lower-strike call + Short higher-strike call.
  • Bear Put Spread — Long higher-strike put + Short lower-strike put.
  • Straddle — Long call + Long put at same strike; bet on volatility.
  • Strangle — Long call + Long put at different strikes.
  • Butterfly Spread — Combination of three strikes; low volatility bet.
  • Iron Condor — Sell out-of-money call spread + put spread; range-bound bet.
  • Collar — Long stock + Long put + Short call.
  • Calendar Spread — Different expiries.
  • Diagonal Spread — Different expiries + strikes.
  • Risk Reversal — Sell put + buy call.

51.13 Swaps

A swap is an agreement between two parties to exchange cash flows over time.

TipCommon swap types
Type Cash flows exchanged
Interest Rate Swap (IRS) Fixed for floating (vanilla); MIBOR/OIS
Currency Swap Cash flows in two currencies
Equity Swap Returns on equity vs floating rate
Credit Default Swap (CDS) Premium for default protection (Blythe Masters at JPMorgan 1994)
Commodity Swap Fixed for floating commodity price
Total Return Swap Total return on asset vs floating rate

51.14 Uses of Derivatives

TipThree pillars of derivative usage
  • Hedging — risk management; locking in prices, rates, FX.
  • Speculation — directional bets; high leverage.
  • Arbitrage — exploiting price discrepancies for risk-free profit.
  • Asset-liability management — banks, insurers.
  • Price discovery.

51.15 Indian Derivatives Market

TipIndian derivatives — milestones
  • L.C. Gupta Committee 1998 — recommended derivatives.
  • J.R. Varma Committee 1998 — risk-containment measures.
  • SCRA Amendment 1999 — derivatives recognised as securities.
  • June 2000 — Index futures on Nifty at NSE.
  • June 2001 — Index options.
  • July 2001 — Stock options (US-style, then European 2010).
  • November 2001 — Stock futures.
  • 2008 — Currency derivatives.
  • 2009 — Interest rate futures (re-launched).
  • 2014 — RBI permits OTC FX options.
  • 2024 — SEBI tightens F&O retail rules (lot size hikes, fewer weekly expiries).

51.15.1 Indian Exchanges and Products

TipIndian derivative exchanges
  • NSE — dominant; F&O on Nifty 50, Bank Nifty, FINNIFTY, MIDCPNIFTY, individual stocks; currency F&O; IRF.
  • BSE — Sensex F&O; commodity F&O (via Asia Index).
  • MCX (Multi Commodity Exchange) — commodity futures.
  • NCDEX — agricultural commodities.
  • ICEX (now part of NSE).
  • MSEI (Metropolitan Stock Exchange of India).

51.15.2 Indian Regulatory Architecture

TipIndian regulatory framework for derivatives
  • SCRA 1956 — recognises derivatives as securities.
  • SEBI — equity and currency derivatives.
  • RBI — OTC interest-rate, currency derivatives.
  • FMC merged into SEBI 2015 — commodity derivatives now under SEBI.
  • SEBI (Stock Brokers) Regulations 1992.
  • SEBI Margin and Position Limits.
  • NSE/BSE Clearing Corporations — counterparty risk management.

51.16 OTC vs Exchange-Traded

TipOTC vs Exchange-traded
Dimension OTC Exchange
Standardisation Customised Standardised
Counterparty risk Bilateral Clearing house
Transparency Low High
Liquidity Variable High
Regulation Lighter Heavy
Volume Larger (notional) Smaller
Examples Forwards, IRS, CDS Futures, listed options

51.17 Famous Derivative Failures

TipNotable derivative-related losses
  • Barings Bank 1995 — Nick Leeson; Nikkei futures; £827 mn loss.
  • LTCM 1998 — Long-Term Capital Management; over-leveraged hedge fund.
  • Enron 2001 — energy derivatives, off-balance-sheet SPEs.
  • AIG 2008 — CDS on subprime mortgages.
  • JPMorgan London Whale 2012 — credit derivatives, $6.2 bn loss.
  • NSEL 2013 — India’s spot-derivative crisis ($1 bn investor loss).
  • Société Générale 2008 — Jérôme Kerviel; €4.9 bn unauthorised trades.

51.19 Practice Questions

Q 01 Derivative Easy

A derivative is a contract whose value:

  • AIs constant
  • BIs derived from an underlying asset
  • CHas no relation to other assets
  • DIs set by regulators
View solution
Correct Option: B
Value derived from underlying asset / index / rate.
Q 02 Forward vs Future Medium

Which is true of a future, not a forward?

  • ACustomised contract
  • BOTC traded
  • CStandardised + exchange-traded + MTM
  • DHigh counterparty risk
View solution
Correct Option: C
Futures: standardised, exchange-traded, daily MTM, clearing house.
Q 03 Call Easy

A Call Option gives the buyer the right to:

  • ASell at strike
  • BBuy at strike
  • CEither buy or sell
  • DReceive a dividend
View solution
Correct Option: B
Call = right to buy; Put = right to sell.
Q 04 Long Call payoff Medium

Max loss for buyer of a Call option is:

  • AUnlimited
  • BStrike price
  • CPremium paid
  • DZero
View solution
Correct Option: C
Max loss = premium paid; max profit unlimited.
Q 05 BSM Medium

The Black-Scholes option-pricing model was developed in:

  • A1952
  • B1973
  • C1990
  • D2000
View solution
Correct Option: B
1973 — Black, Scholes, Merton; Nobel 1997 to Scholes & Merton.
Q 06 Inputs Medium

Black-Scholes uses all the following inputs EXCEPT:

  • ASpot price
  • BStrike
  • CTime to expiry
  • DExpected return on stock
View solution
Correct Option: D
Expected return is NOT an input; risk-neutral pricing uses Rf instead. The 5 inputs are S, K, T, σ, r (+ dividends).
Q 07 PCP Hard

Put-Call Parity for European options is:

  • AC + S = P + K e^(-rT)
  • BC − P = S − K e^(-rT)
  • CC × P = S × K
  • DC + P = S + K
View solution
Correct Option: B
C − P = S − K e^(−rT).
Q 08 Delta Medium

"Delta" of an option measures:

  • ASensitivity to volatility
  • BSensitivity to underlying price
  • CTime decay
  • DSensitivity to interest rate
View solution
Correct Option: B
Δ = ∂C/∂S; range 0 to 1 for Calls, 0 to −1 for Puts.
Q 09 Theta Medium

"Theta" of an option captures:

  • ATime decay
  • BDelta change
  • CVolatility
  • DInterest rate
View solution
Correct Option: A
Θ = ∂Premium/∂time; usually negative for long options.
Q 10 Binomial Hard

The Binomial option pricing model was developed in 1979 by:

  • ACox-Ross-Rubinstein
  • BBlack-Scholes
  • CMarkowitz
  • DSharpe-Lintner
View solution
Correct Option: A
John Cox, Stephen Ross and Mark Rubinstein (1979).
Q 11 Straddle Medium

A "Straddle" strategy is a bet on:

  • AStable price
  • BLarge price movement (high volatility)
  • CHigher dividends
  • DLower volatility
View solution
Correct Option: B
Long call + Long put at same strike; profit if price moves a lot in either direction.
Q 12 India derivative Medium

Derivatives were launched on Indian stock exchanges in:

  • A1995
  • B2000
  • C2005
  • D2010
View solution
Correct Option: B
June 2000 — Index futures on Nifty 50 (NSE).
Q 13 Barings Medium

Barings Bank collapsed in 1995 because of:

  • ANikkei futures losses by Nick Leeson
  • BFX losses
  • CReal estate losses
  • DCDS exposures
View solution
Correct Option: A
Nick Leeson's unauthorised Nikkei trades; £827 mn loss.
Q 14 FMC merger Hard

FMC (Forward Markets Commission) was merged into SEBI in:

  • A2010
  • B2013
  • C2015
  • D2018
View solution
Correct Option: C
2015 — commodity derivatives moved under SEBI.
Q 15 CDS Hard

Credit Default Swaps (CDS) were pioneered in 1994 by:

  • AGoldman Sachs
  • BBlythe Masters at JPMorgan
  • CMorgan Stanley
  • DCiti
View solution
Correct Option: B
Blythe Masters at JPMorgan (1994).
Q 16 SPAN Medium

SPAN margin is:

  • AA risk-based portfolio margin system
  • BA 10 % flat margin
  • CAn anti-money-laundering rule
  • DA type of swap
View solution
Correct Option: A
Standard Portfolio Analysis of Risk — risk-based margin computation.
Q 17 Volatility Medium

An increase in volatility (σ):

  • AIncreases Call price only
  • BIncreases Put price only
  • CIncreases both Call and Put prices
  • DDecreases both
View solution
Correct Option: C
Higher uncertainty → higher option value for both Calls and Puts (positive Vega).
Q 18 American Hard

An American option can be exercised:

  • AOnly at expiration
  • BAt any time up to expiration
  • COn specified dates only
  • DOnly in the US
View solution
Correct Option: B
American = any time before/at expiration; European = only at expiration; Bermudan = specified dates.
Q 19 Hedge motive Easy

An Indian exporter buying USD-INR put options is:

  • ASpeculating
  • BHedging
  • CArbitraging
  • DDoing M&A
View solution
Correct Option: B
Locks in floor INR-value of future USD receivable — hedging.
Q 20 Match Greeks Hard

Match the Greek with what it measures:

(i) Delta (a) Volatility
(ii) Gamma (b) Time decay
(iii) Theta (c) Price sensitivity
(iv) Vega (d) Delta sensitivity
  • A(i)-(c), (ii)-(d), (iii)-(b), (iv)-(a)
  • B(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
  • C(i)-(b), (ii)-(a), (iii)-(d), (iv)-(c)
  • D(i)-(d), (ii)-(c), (iii)-(a), (iv)-(b)
View solution
Correct Option: A
Delta — price; Gamma — delta sensitivity; Theta — time decay; Vega — volatility.

51.19.1 Advanced Format Questions

AR 1Assertion-ReasonHard

A: Black-Scholes-Merton (1973) prices European options.
R: The model assumes constant volatility and risk-free rate.

  • ABoth true; R explains A
  • BBoth true; R does not explain A
  • CA true, R false
  • DA false, R true
View solution
Correct Option: B
S 1Statement-basedMedium

Derivatives types: (i) Forwards. (ii) Futures. (iii) Options. (iv) Swaps.

  • AAll four
  • B(i) and (ii) only
  • C(iii) and (iv) only
  • D(iii) only
View solution
Correct Option: A
N 1NumericalMedium

Call option: Strike ₹100; Premium ₹5; Spot at expiry ₹115. Net profit/share:

  • A₹10
  • B₹15
  • C−₹5
  • D₹5
View solution
Correct Option: A
Intrinsic 15 − Premium 5 = ₹10.
N 2NumericalHard

Put option: Strike ₹100; Premium ₹3; Spot at expiry ₹90. Net P/L:

  • A₹7
  • B₹10
  • C−₹3
  • D₹13
View solution
Correct Option: A
Intrinsic (100−90)=10; minus premium 3 = ₹7.

51.20 Quick Recall

ImportantQuick recall
  • Derivative = contract whose value derives from underlying. SCRA 1956 Indian definition.
  • Milestones: CBOT 1848 · CBOE 1973 · Black-Scholes 1973 · India NSE F&O June 2000.
  • Four basic types: Forwards · Futures · Options · Swaps.
  • Forward vs Future: OTC/customised/no MTM/high counterparty risk vs Exchange/standardised/daily MTM/clearing house.
  • Forward pricing: F₀ = S₀ × e^(rT); cost-of-carry; arbitrage-enforced.
  • Margins: Initial · Maintenance · Variation · MTM · SPAN · Exposure · Special.
  • Option = right (not obligation). Call = right to buy; Put = right to sell.
  • Option terms: Strike · Premium · Expiry · ITM/ATM/OTM · Intrinsic + Time value.
  • Style: European (expiry only) · American (anytime) · Bermudan (dates). India = European since 2010.
  • Option payoffs: Long Call max loss = Premium, max profit = Unlimited; Short Call vice versa; Put symmetric.
  • Put-Call Parity (European): C − P = S − K × e^(−rT).
  • Black-Scholes-Merton (1973, Nobel 1997) — pricing European options; 5 inputs: S, K, T, σ, r (+ dividends). Expected return NOT an input.
  • Binomial — Cox-Ross-Rubinstein (1979); converges to BSM as steps → ∞.
  • Greeks: Δ Delta (price) · Γ Gamma (delta sensitivity) · Θ Theta (time decay) · ν Vega (volatility) · ρ Rho (rate); Vanna, Volga (2nd order).
  • Option strategies: Covered Call · Protective Put · Bull/Bear Spread · Straddle (vol bet) · Strangle · Butterfly · Iron Condor · Collar · Calendar · Diagonal · Risk Reversal.
  • Swaps: IRS · Currency · Equity · CDS (Blythe Masters JPMorgan 1994) · Commodity · Total Return.
  • Uses: Hedging · Speculation · Arbitrage · ALM · Price discovery.
  • India: L.C. Gupta & J.R. Varma Committees 1998; SCRA Amendment 1999; NSE Index Futures June 2000; Options 2001; Currency 2008; FMC merged into SEBI 2015; SEBI 2024 F&O retail tightening.
  • Indian exchanges: NSE · BSE · MCX · NCDEX · MSEI.
  • OTC vs Exchange-traded comparison.
  • Famous failures: Barings 1995 (Leeson) · LTCM 1998 · Enron · AIG 2008 · JPM London Whale 2012 · NSEL 2013 · SocGen Kerviel 2008.
  • Modern trends: Crypto derivatives · ESG/carbon derivatives · VIX · weather · ILS · algo dominance · CCP central clearing · SOFR (post-LIBOR) · AI pricing · tokenised DeFi · India F&O retail rules 2024.