Theoretical Price

Q: What is the theoretical price of an option?

The theoretical price is the value a pricing model such as Black-Scholes or a binomial tree assigns to an option from five inputs: the underlying's price, the strike, the time to expiry, the risk-free interest rate and an assumed volatility. It is a model output, not a market quote. The market price is whatever buyers and sellers agree on; the theoretical price is what the model says that should be under its assumptions.

Q: Why does the theoretical price differ from the market price?

Almost entirely because of the volatility input. Four of the five inputs are observable; the fifth, volatility, is an assumption. If you use historical volatility the model will usually produce a price below the market, because index options embed a premium over realised volatility. If you use the market's own implied volatility the theoretical price equals the market price by construction. The gap therefore measures the difference between your volatility view and the market's, not a mispricing.

Q: Is an option trading above its theoretical price overvalued?

Only relative to the volatility you assumed. The market may know something the assumption does not: an event inside the option's life, a persistent demand for protection, or simply that realised volatility is about to rise. A gap is a prompt to ask why, not a verdict. Traders who sell options above their theoretical price profit on average only if their volatility assumption turns out closer to reality than the market's.

Q: Which model is used for theoretical prices on NSE options?

NSE index and stock options are European, so the Black-Scholes model is the standard; it is what NSE uses to publish implied volatility on the option chain, and what most brokers and platforms use for theoretical values and Greeks. A binomial model gives the same answer for European options and is needed only where early exercise matters, which does not apply on NSE.

Q: How is the theoretical price used in practice?

Three ways. To check a quote at an illiquid strike where the last traded price is stale. To price a position under a scenario, by changing the spot, time or volatility input and seeing what the option would be worth. And to compare strikes and expiries on the same volatility assumption, which shows which contracts the market prices rich or cheap relative to one another.

What an option should cost, according to a model and an assumption. The number is useful exactly as far as the assumption is, and the gap to the market price is where the information lives.

In short: the theoretical price (also model price or theoretical value) is what a pricing model, usually Black-Scholes for Indian options, says an option is worth given the spot, strike, time to expiry, interest rate and an assumed volatility. Four inputs are facts; the volatility is a view. If the view is the market's own implied volatility, the theoretical price is the market price. If it is anything else, the gap between the two prices is the gap between your volatility view and the market's.

The intuition

An option's value is the expected payoff at expiry, discounted to today, under some assumption about how the underlying will move. A pricing model makes that assumption explicit: the underlying's returns are random with a particular spread, and the spread is the volatility input. Feed in a spread and the model integrates over every possible ending to produce one number. That number is the theoretical price. It is exact for the assumption and only as good as the assumption.

This is why two traders can compute different theoretical prices for the same contract and both be right about the arithmetic. One used 12% volatility and got ₹373; the other used 14% and got ₹424. The model did not disagree with itself; the traders disagreed about the future. The market price is a third opinion, the one that clears.

The inputs

Input	Source	Effect on a call
Spot price	Observed	Higher spot, higher call
Strike	Contract term	Higher strike, lower call
Time to expiry	Contract term	More time, higher call
Risk-free rate	Observed (T-bill or MIBOR)	Higher rate, slightly higher call
Volatility	Assumed	Higher volatility, higher call and put

Dividends enter for stock options; for index options the expected dividend yield is small and usually folded into the rate. The rate itself matters less than beginners expect: in the example below, dropping it from 6.5% to zero moves the 27-day at-the-money call from ₹424 to about ₹365, while dropping volatility from 14% to 12% moves it to ₹373. Over a month, two volatility points are worth about as much as the entire interest rate.

Worked example (illustrative numbers)

Suppose NIFTY is at 24,000, the 24,000 call has 27 days to expiry, the risk-free rate is 6.5%, and the call is quoted in the market at ₹450. Running Black-Scholes at different volatility assumptions:

Volatility assumed	Theoretical call price	Versus market ₹450
12% (a quiet recent month)	₹373	market ₹77 above model
14% (a typical level)	₹424	market ₹26 above model
15.0% (the implied volatility)	₹450	equal, by construction

Read the table backwards. The market is paying ₹450, which means it is pricing 15% volatility for the next 27 days. Whether ₹450 is "too much" depends on whether you believe the coming month will realise less than 15%. If the last month realised 12% and nothing is scheduled, the three-point gap is the normal premium sellers demand. If an RBI policy meeting and a budget sit inside the window, 15% may be modest. The theoretical price turned a rupee quote into a volatility statement that can be argued with; it did not settle the argument.

One contract, one model, many theoretical prices. The market price picks out a single volatility on the line: the implied volatility.

Why it matters to an options trader

It converts prices into volatility, which is comparable. ₹450 on a 24,000 call and ₹207 on a 24,500 call cannot be compared directly; 15% and 14% can.
It is the basis of every Greek. Delta, gamma, theta and vega are the sensitivities of the theoretical price to its inputs; without a model there are no Greeks.
It prices what has not traded. At a strike with no trades for an hour, the theoretical price at the neighbouring strikes' IV is a better guide than the stale last print.
It runs scenarios. Move the spot by 300 points and the clock by three days, and the model tells you what the position will be worth, which is how risk is managed before it happens.

Common mistakes

Calling the theoretical price "fair value". It is fair under the assumption. The market disagreeing with your assumption is not a market error.
Using one volatility for every strike. The market prices a smile; a flat-volatility theoretical price will show every far put as overvalued, always, and be wrong about it.
Using historical volatility and selling every "overpriced" option. The gap to historical is the volatility risk premium; it is the seller's expected income and also the reason sellers get hurt when realised volatility jumps.
Ignoring the rate and dividends on long-dated or stock options. On a month they are small; on a six-month stock option with a dividend inside the window they are not.
Trusting a platform's theoretical price without knowing its volatility input. Two platforms showing different theoretical values are usually using different IV sources, not different models.

Indian-market specifics

NSE options are European since 2011 for stocks and from inception for indices, so Black-Scholes is the appropriate model and the binomial model adds nothing for them.
NSE's published implied volatility on the option chain is the volatility at which the Black-Scholes theoretical price equals the last traded price; it is blank where there is no trade.
The risk-free input used in India is typically the 91-day T-bill yield or MIBOR; NSE's own calculations for margin use a prescribed rate. Across a one-month option the choice barely moves the price.
For physically settled stock options, the theoretical price near expiry is the same as for a cash-settled one; settlement mechanics change what you receive, not what the model says the right is worth.

FAQ

What is the theoretical price of an option?

The value a pricing model assigns from spot, strike, time, rate and an assumed volatility; a model output, not a quote.

Why does the theoretical price differ from the market price?

Because of the volatility input; at the market's implied volatility the two are equal.

Is an option trading above its theoretical price overvalued?

Only relative to your volatility assumption; the gap is a question, not an answer.

Which model is used for theoretical prices on NSE options?

Black-Scholes, since NSE options are European.

How is the theoretical price used in practice?

To check stale quotes, run scenarios and compare contracts on one volatility assumption.

The implied volatility behind every quote

The NIFTY option-chain page shows the implied volatility at every strike, which is the volatility at which the theoretical price matches the market. In the app, the option chain shows the Greeks at each strike alongside the premium.

NIFTY option chain Option Greeks explained

Related terms

Black-Scholes Model, the model behind the number
Implied Volatility, the volatility at which theory meets market
Historical Volatility, the usual alternative input
Volatility Smile, why one volatility does not fit every strike