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NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Derivatives

Option Pricing and the Greeks for NISM PMS Distributors

Updated 11 October 2026 · Fact-checked

Option pricing explains why a premium is high or low. Premium = intrinsic value + time value. It depends on spot price, strike, time, volatility, interest rate and dividends. The Greeks (delta, gamma, theta, vega, rho) measure how premium reacts to each factor. Put-call parity links call and put prices.

Understand Option Pricing and the Greeks

An option premium is the price the buyer pays the seller (writer). It has two parts. Intrinsic value is the gain if exercised now: for a call, spot minus strike; for a put, strike minus spot; never below zero. Time value is the rest of the premium. It is what the buyer pays for the chance that the option becomes more valuable before expiry.

Six factors drive premium. For a call: a higher spot raises it, a higher strike lowers it, more time to expiry generally raises it, higher volatility raises it, a higher interest rate raises it slightly, and expected dividends lower it. For a put: higher spot lowers it, higher strike raises it, more time generally raises it, higher volatility raises it, higher interest rate lowers it, and dividends raise it. Treat "more time raises the premium" as the usual rule, not an absolute one. A deep in-the-money European put (or a European call on a dividend-paying stock) can lose value as time increases. Volatility raises both calls and puts, and more time generally does too, because they widen the range of possible outcomes and the option buyer's loss is limited to the premium.

Put-call parity says a European call and put on the same underlying, strike and expiry cannot be priced independently. If they were, traders could earn a risk-free profit (arbitrage) and would push prices back in line.

Models turn these inputs into a fair value. The Black-Scholes model gives a closed-form price for European options. It assumes constant volatility and interest rate, lognormal prices, no transaction costs, and no dividends in its basic form. The binomial model builds a tree where the price moves up or down each step. It works backward from expiry, and it can handle early exercise, so it suits American options.

The Greeks are sensitivities. Delta is the change in premium for a ₹1 move in the underlying. Gamma is the change in delta for a ₹1 move. Theta is the change in premium as one day passes. Vega is the change in premium for a 1 percentage point change in volatility. Rho is the change in premium for a 1 percentage point change in interest rate. Know the sign and size of each for long calls and puts.

Key formulas to remember

Intrinsic value of a call
Max(S − K, 0)
S is spot price, K is strike price. Never negative.
Intrinsic value of a put
Max(K − S, 0)
Out-of-the-money options have zero intrinsic value.
Premium
Premium = Intrinsic value + Time value
Time value = Premium − Intrinsic value. It is highest at the money and falls to zero at expiry.
Put-call parity (European, no dividends)
C + K × e^(−rT) = P + S
C and P are call and put premiums. With discrete compounding, use K ÷ (1 + r)^T. Applies to same strike and expiry.
Delta range
Call: 0 to +1; Put: −1 to 0
At-the-money options have delta near 0.5 (call) or −0.5 (put). Deep ITM approaches ±1.
Greek signs for a long option
Gamma +, Vega +, Theta −; Rho: call +, put −
Option buyers gain from volatility and lose from time decay. Sellers are the reverse.
Approximate premium change
ΔPremium ≈ Delta × ΔS
Gamma refines this for larger moves.

How to solve Option Pricing and the Greeks questions

Use this method for any question on premium factors, parity or the Greeks.

  1. 1Identify whether the option is a call or a put, and whether it is long (buyer) or short (writer).
  2. 2Compute intrinsic value using Max(S − K, 0) for a call or Max(K − S, 0) for a put, then find time value as premium minus intrinsic value.
  3. 3If the question asks how a factor changes the premium, recall the direction for that option type: spot, strike, time, volatility, interest rate, dividends.
  4. 4If a Greek is named, recall what it measures, its sign for the position, and where it is largest (gamma and theta peak at the money near expiry).
  5. 5For delta questions, multiply delta by the underlying's move to estimate the premium change.
  6. 6For parity questions, plug values into C + PV(K) = P + S and solve for the missing term.
  7. 7For model questions, match features: closed-form and European means Black-Scholes; tree and early exercise means binomial.
  8. 8Check the answer against sense: premium cannot be below intrinsic value, and delta must stay within its range.

Quickest way: Direction and sign shortcut

When to use it: Use for one-line MCQs asking what happens to premium or which Greek fits a description.

  1. Match the keyword to the Greek: price move is delta, delta change is gamma, time is theta, volatility is vega, interest rate is rho.
  2. For a long option remember: gamma and vega positive, theta negative.
  3. Volatility up means both call and put premium up. More time generally does the same, except for some deep in-the-money European options.
  4. Spot up helps calls and hurts puts; strike up does the opposite.
  5. Eliminate options that break limits such as delta above 1 or negative time value.

Common mistakes in Option Pricing and the Greeks

  • Saying higher volatility lowers one of the premiums, such as the put.

    Students link volatility with direction instead of range of outcomes.

    Fix: Volatility raises both call and put premiums because the buyer's loss is capped at the premium while gains can grow.

  • Treating theta as positive for an option buyer.

    Time passing feels like progress.

    Fix: Time decay erodes the buyer's premium, so theta is negative for long positions and positive for writers.

  • Confusing delta and gamma.

    Both relate to price moves.

    Fix: Delta is the change in premium per ₹1 move in the underlying; gamma is the change in delta per ₹1 move. Gamma is the second-order measure.

  • Giving a put delta of +0.5.

    Students remember at-the-money as 0.5 and drop the sign.

    Fix: A long put loses value when spot rises, so its delta is negative, between −1 and 0.

  • Computing intrinsic value as negative for out-of-the-money options.

    Subtracting strike and spot mechanically.

    Fix: Use Max(…, 0). An out-of-the-money option has zero intrinsic value, and its whole premium is time value.

  • Applying Black-Scholes to American options without caution.

    Both models are called pricing models.

    Fix: Black-Scholes is for European options; the binomial model handles early exercise.

Worked examples

Example 1

Nifty spot is 22,000. A call with strike 21,800 trades at a premium of ₹350. A put with strike 22,200 trades at ₹260. Find the intrinsic value and time value of each.

Show the solution
  1. Call intrinsic value = Max(22,000 − 21,800, 0) = ₹200.
  2. Call time value = 350 − 200 = ₹150.
  3. Put intrinsic value = Max(22,200 − 22,000, 0) = ₹200.
  4. Put time value = 260 − 200 = ₹60.

Answer: Call: intrinsic ₹200, time value ₹150. Put: intrinsic ₹200, time value ₹60.

Example 2

A call option has a delta of 0.6 and a gamma of 0.04. The underlying rises by ₹2. Estimate the new delta and the approximate change in premium.

Show the solution
  1. Approximate premium change = delta × move = 0.6 × 2 = ₹1.20.
  2. Change in delta = gamma × move = 0.04 × 2 = 0.08.
  3. New delta = 0.6 + 0.08 = 0.68.
  4. The premium rises by about ₹1.20 (a more precise figure would adjust for the delta change during the move).

Answer: Premium rises by about ₹1.20 and delta becomes 0.68.

Exam tips

  • Expect direct recall questions on the direction of premium for each of the six factors; memorise the call and put table.
  • Greek questions usually ask for a definition or sign. Learn who gains and loses from each Greek, buyer or writer.
  • Know which model fits which option style: Black-Scholes for European, binomial for American.
  • Put-call parity questions apply to European options with the same strike and expiry; check these conditions in the stem.
  • This paper has negative marking of 10% of the marks assigned to a question (0.1 mark per wrong 1-mark answer). Guess only when you can eliminate at least one option.

Practice questions from Derivatives

Option Pricing and the Greeks in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Option Pricing and the Greeks: frequently asked questions

What are the factors affecting option premium?

Spot price, strike price, time to expiry, volatility, risk-free interest rate and expected dividends. Volatility raises both call and put premiums, and more time to expiry generally does too, with exceptions such as some deep in-the-money European options. Spot and strike move calls and puts in opposite directions.

What is the put-call parity formula?

For European options with the same strike and expiry and no dividends, C + K × e^(−rT) = P + S. It shows that a call plus the present value of the strike equals a put plus the spot price. Breaches create arbitrage.

What do delta, gamma, theta, vega and rho measure?

Delta is premium change per ₹1 move in the underlying. Gamma is change in delta. Theta is premium change over time, vega is for volatility and rho is for interest rates.

Do I need to calculate Black-Scholes for the NISM PMS Distributors exam?

Expect conceptual questions on its assumptions, inputs and the type of option it prices, not long calculations. Know the inputs and that it prices European options. Check the current NISM workbook for scope.