Equity Derivatives
CH4 · Introduction to Options
Option Greeks - Vega
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Theme 4
Learn call/put mechanics, premium, moneyness, Greeks and payoff calculations.
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Equity Derivatives
Option Greeks - Vega
Currency Derivatives
Currency options, moneyness, breakeven, Greeks
Interest Rate Derivatives
Bond options, premium, payoff, volatility, straddles and Greeks
Detailed notes
Equity Derivatives
Option Greeks - Vega
NISM Series VIII — Equity Derivatives | 20% weightage | ~20 exam questions
Options are the most important chapter in this exam — 20% weightage, 71 questions in the question bank, and the highest trap rate of any chapter. If you master this one chapter alone, you're more than a third of the way to passing.
The core idea is simple: an option gives you the right but not the obligation to buy or sell something at a fixed price. You pay a premium for that right. The seller receives the premium and takes on the obligation. Everything else in this chapter flows from that one sentence.
Call Option — right to BUY the underlying at the strike price on or before expiry. Buyer is bullish. Seller is bearish or neutral.
Put Option — right to SELL the underlying at the strike price on or before expiry. Buyer is bearish. Seller is bullish or neutral.
Strike Price (Exercise Price) — the fixed price at which you can buy (call) or sell (put). NOT the market price. This is the most common trap in the exam.
Option Premium — what the buyer pays to the seller for the right. Made up of two parts:
Moneyness — where the option sits relative to the market:
European vs American Options — In India, ALL index options (Nifty, Bank Nifty) are European — exercise only on expiry day. Stock options are physically settled. This comes up frequently.
Expiry — Last Thursday of the month (or day before if Thursday is a holiday). *Update: NSE shifted to Tuesday from September 2025.*
Think of Greeks as sensitivity meters. Each one measures how much the option premium moves when one specific thing changes.
| Greek | Measures sensitivity to | Direction for Calls | |-------|------------------------|-------------------| | Delta | Change in underlying price | 0 to +1 | | Gamma | Rate of change of Delta | Always positive | | Theta | Passage of time (time decay) | Negative (premium falls) | | Vega | Change in volatility | Positive | | Rho | Change in interest rates | Positive for calls |
Delta deep dive — the most tested Greek:
Vega — higher volatility = higher premium for BOTH calls and puts. Makes sense — more volatility = more chance of a big move = option worth more.
Theta — the silent killer. Every day that passes, the time value portion of the premium decays. This decay accelerates as expiry approaches. Theta hurts option buyers, benefits option sellers.
Rho — interest rate goes up → call premium goes up, put premium goes down. Think of it as cost of carry.
It's expiry week. Nifty is at 24,500. You buy a 24,500 CE (Call option, ATM) for ₹150 premium. Lot size = 75.
Your cost: ₹150 × 75 = ₹11,250
If Nifty rises to 24,800 by expiry:
If Nifty stays at 24,500 or falls:
For the seller of that same call:
This is the asymmetry of options — buyer has limited risk, unlimited upside. Seller has limited gain, unlimited risk.
| Position | Max Profit | Max Loss | View | |----------|-----------|---------|------| | Buy Call | Unlimited | Premium paid | Bullish | | Sell Call | Premium received | Unlimited | Bearish/Neutral | | Buy Put | Strike - Premium | Premium paid | Bearish | | Sell Put | Premium received | Strike - Premium | Bullish/Neutral |
Trap 1: "A call option gives the buyer the right to buy at MARKET price" → FALSE The right is to buy at the STRIKE price, not market price. The whole point of an option is locking in a price. If it was market price, why would you need the option?
Trap 2: "Vega measures change in delta" → FALSE. That's Gamma. Memory hook: Vega = Volatility. Gamma = Gradient of delta (rate of change).
Trap 3: "Theta measures sensitivity to volatility" → FALSE. That's Vega. Memory hook: Theta = Time. Vega = Volatility. Never mix these two.
Trap 4: "Delta is the change in option price for a 1% change in interest rates" → FALSE. That's Rho. Delta = price sensitivity. Rho = rate sensitivity.
Trap 5: "A long put can be closed by shorting a call with same strike and expiry" → FALSE. You close a long put by SELLING the same put (same strike, same expiry). You can only close an option position with the SAME type of option — put with put, call with call.
20% of the exam = ~20 questions. CH4 has 71 questions in the bank — highest of any chapter. The exam will heavily test: 1. Greeks (especially confusing Vega/Theta, Delta/Rho) — expect 6-8 questions 2. Payoff scenarios (who profits when price rises/falls) — expect 4-5 questions 3. Moneyness and intrinsic/time value — expect 3-4 questions 4. European vs American, closing positions — expect 2-3 questions
Priority order: Greeks → Payoffs → Moneyness → Contract specs → Pricing factors
Master CH4 and you've secured 20 marks before walking in.
Currency Derivatives
Currency options, moneyness, breakeven, Greeks
NISM Series I — Currency Derivatives | ~11% weightage | ~70 questions
Currency options work exactly like equity options — same Greeks, same moneyness concepts, same payoff logic. If you've done CH4 of Series VIII, this is largely review with one critical difference: the underlying is an exchange rate instead of a stock price. The exam tests the same traps (selling call = obligation to SELL not buy), the same breakeven formulas, and the same volatility logic. Master this chapter and it compounds with Series VIII knowledge.
Call option — right to BUY the underlying (currency pair) at the strike price. Buyer is bullish on the underlying (expects USDINR to rise = expects USD to appreciate).
Put option — right to SELL the underlying at the strike price. Buyer is bearish (expects USDINR to fall = expects INR to appreciate).
Only European style options on Indian exchanges — exercise only on expiry date. Both OTC and exchange-traded currency options in India are European.
Lot size same as futures — USDINR = 1,000 USD, EURINR = 1,000 EUR, GBPINR = 1,000 GBP, JPYINR = 1,00,000 JPY
Premium settlement — option premium is cash-settled in INR upfront (buyer pays, seller receives). Quoted in INR per unit of base currency.
Expiry time — 12:30 PM on expiry day (same as futures). Trading stops at 12:30 PM.
Operating range for options — based on DELTA of the option (not a fixed ±3% like futures).
| | Call Option | Put Option | |--|------------|-----------| | ITM | Spot > Strike | Spot < Strike | | ATM | Spot = Strike | Spot = Strike | | OTM | Spot < Strike | Spot > Strike |
Intrinsic value = amount by which option is ITM (minimum zero, never negative)
Time value = Option premium − Intrinsic value
Option value = Intrinsic Value + Time Value ← tested as True/False constantly
Call buyer breakeven = Strike + Premium paid
Put buyer breakeven = Strike − Premium paid
Call seller breakeven = Strike + Premium received
Put seller breakeven = Strike − Premium receivedExample: Buy USDINR call at strike 84, pay premium 0.35 Breakeven = 84 + 0.35 = 84.35 You start profiting only when USDINR > 84.35
Sell USDINR put at strike 84, receive premium 0.40 Breakeven = 84 − 0.40 = 83.60 You start losing only when USDINR < 83.60
| Position | Market View | Max Profit | Max Loss | |----------|------------|-----------|---------| | Buy Call | Bullish (USDINR rises) | Unlimited | Premium paid | | Sell Call | Bearish/Neutral | Premium received | Unlimited | | Buy Put | Bearish (USDINR falls) | Unlimited | Premium paid | | Sell Put | Bullish/Neutral | Premium received | Strike − Premium |
Option writer (seller): Always limited profit (premium), potentially unlimited loss.
| Factor | Call Premium | Put Premium | |--------|-------------|------------| | Spot price increases | Increases | Decreases | | Volatility increases | Increases | Increases | | Time to expiry increases | Increases | Increases | | Interest rate (India) increases | Increases | Decreases | | ITM vs OTM | ITM > ATM > OTM | ITM > ATM > OTM |
Key rule: Higher volatility = higher premium for BOTH calls and puts. Volatility measures magnitude of price movement (direction-neutral).
Black-Scholes — analytical, faster, used for EUROPEAN options
Binomial model — iterative (uses repeated calculation), more flexible, used for AMERICAN options. More computing power required, more accurate but slower.
Delta — rate of change of option price per unit change in spot. Used to determine operating range for currency options (unlike futures which use fixed ±3%).
Vega — sensitivity to volatility. Higher volatility → premium rises.
Theta — time decay. As time passes, premium falls (benefits seller).
Example: USDINR spot = 75. Buy 1 lot put at strike 75.50, pay premium 0.28. Sell 1 lot call at strike 75.25, receive premium 0.35. Expiry settlement = 75.50.
Put (bought): Strike 75.50, settlement 75.50 → exactly ATM → zero intrinsic value. Loss = premium paid = 0.28 × 1,000 = Rs 280 loss
Call (sold): Strike 75.25, settlement 75.50 → ITM for buyer → seller pays (75.50 − 75.25) = 0.25. Net = 0.35 received − 0.25 paid = 0.10 × 1,000 = Rs 100 profit
Net = Rs 280 loss − Rs 100 profit = Rs 180 net loss
An Indian IT company will receive USD 10 lakh in 3 months. They fear INR might appreciate (USDINR might fall from 84 to 82). They buy USDINR put options at strike 84, paying premium Rs 0.40 per USD.
Cost of hedge = 0.40 × 10,00,000 = Rs 4,00,000
If USDINR falls to 82 at expiry:
The hedge worked. This is how exporters use put options.
Trap 1: "Selling a call = obligation to BUY" — FALSE Selling a call = obligation to SELL (deliver) the underlying to the buyer if exercised.
Trap 2: "Selling a put = obligation to SELL" — FALSE Selling a put = obligation to BUY (take delivery of) the underlying from the buyer if exercised.
Trap 3: "Buying a put = right to buy" — FALSE Buying a put = right to SELL. Only buying a call = right to buy.
Trap 4: "American options are traded on Indian exchanges" — FALSE Only European options on Indian exchanges (both OTC and exchange-traded in India are European).
Trap 5: "ATM premium > ITM premium for same tenor" — FALSE ITM premium > ATM premium > OTM premium (ITM has intrinsic value).
Trap 6: "Volatility only affects call premium, not put premium" — FALSE Higher volatility → higher premium for BOTH calls AND puts.
~11% = ~70 questions. Heavy on True/False traps around call/put rights and obligations. Breakeven calculations appear 2-3 times per exam. Complex multi-leg P&L (buy put + sell call type) appears 1-2 times. Option pricing factors (volatility, time) are standard True/False questions.
Interest Rate Derivatives
Bond options, premium, payoff, volatility, straddles and Greeks
NISM Series IV — Interest Rate Derivatives | ~8% weightage | ~32 questions
Options on interest rate instruments — same framework as Series VIII equity options but with bond prices as the underlying. Call options, put options, Greeks, breakeven, P&L calculations. Heavy overlap with Series I (Currency) CH4. The new addition for IRD: option P&L calculations involving bond prices as the underlying, and the short straddle/strangle strategies.
Call option: Right to BUY the underlying bond at the strike price.
Put option: Right to SELL the underlying bond at the strike price.
Only European style options on Indian exchanges.
Premium settlement: Cash settled (upfront by buyer to seller).
Option expiry for interest rate options: Last Thursday of the month.
Long Call:
Long Put:
Short Call (sold call):
Short Put (sold put):
Example 1: Buy Rs 21.50 call at Rs 0.20 premium. Bond closes at Rs 21.70.
Example 2: Sell Rs 40.50 put at Rs 0.35 premium. Bond at Rs 40.50 at expiry.
Example 3: Buy Rs 21.50 call (Rs 0.20 premium) + sell Rs 39.50 call (Rs 0.60 premium). Underlying = Rs 39.50 at expiry.
Example 4 (Covered call): Buy bond at Rs 54.50, sell Rs 55 call at Rs 0.10. Bond = Rs 55.50 at expiry.
Example 5 (Long straddle): Buy call Rs 150 (Rs 0.30) + buy put Rs 150 (Rs 0.20). Bond = Rs 149.50.
Delta: Rate of change of option price per unit change in underlying. Used for hedging.
Theta: Measures TIME DECAY. Negative for option buyers — premium falls as expiry approaches. Time value of option is directly proportional to time to expiry.
Gamma: Rate of change of Delta. Second-order measure.
Vega: Sensitivity to volatility. Higher volatility → higher premium for both calls and puts.
Rho: Sensitivity to interest rates.
Historical volatility: Calculated from past closing prices. Implied volatility: Derived from current option prices. Rise in implied volatility = advantageous for BOTH call buyers and put buyers.
| Factor | Call premium | Put premium | |--------|-------------|------------| | Bond price rises | Increases | Decreases | | Volatility rises | Increases | Increases | | Time to expiry increases | Increases | Increases | | Strike price increases | Decreases | Increases |
Short straddle: Sell both call and put at SAME strike. Profit from low volatility. Short strangle: Sell call at higher strike + sell put at lower strike (both OTM). Profit from low volatility. Bull call spread (bullish vertical): Buy lower strike call + sell higher strike call. Bull put spread (bullish vertical using puts): Buy lower strike put + sell higher strike put. Butterfly: Long call at lower strike + long call at higher strike + 2 short calls at middle strike.
Butterfly P&L example:
Trap 1: "Theta is positive for option buyers" — FALSE Theta is negative for buyers (time decay erodes premium). Positive for sellers.
Trap 2: "Rising volatility only benefits call buyers" — FALSE Rising volatility increases premium for BOTH calls and puts. Benefits all option buyers.
Trap 3: "Option value = Intrinsic value × Time value" — FALSE Option value = Intrinsic value + Time value (ADDITION, not multiplication)
Trap 4: "Interest rate options expiry = Last Wednesday" — FALSE IRD options expiry = Last Thursday (same as G-Sec bond futures, unlike T-bill futures which is Wednesday)
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