Theoretical Deviations: Real-World Prices

A theoretical price describes a world with no transaction costs, unlimited size available at every level, one volatility for every strike, and continuous trading. Not one of those five conditions holds on a live NSE option chain at 14:45. The model was never a claim about what the market will charge. It is a claim about what the contract is worth to somebody who could trade frictionlessly, and nobody can.

The gap opens up in four distinct places, and it is worth keeping them separate because they behave differently. Two of them are execution costs — the spread you pay to get in and out, and the depth available at the strike you chose. The other two are genuine pricing differences — the market charging a different implied volatility for different strikes, and cash flows such as dividends that the simple formula does not date properly. The first two you can reduce by choosing better strikes. The second two you cannot; you can only account for them.

One consequence is worth noting for anyone reading margin statements. For contracts that barely trade, the exchange itself falls back on a theoretical value rather than a stale last-traded price when it needs a closing figure for mark-to-market. So the model price is not a purely academic object — it becomes the official number precisely where the market stops providing one. Check the current NSE circular for the exact methodology before relying on it.

The bid is the highest price somebody is currently willing to pay. The ask is the lowest price somebody is currently willing to sell at. The theoretical value sits somewhere between them, usually near the middle. If you buy at the ask and later sell at the bid, you have paid the full spread even though the underlying did not move at all and your view was neither right nor wrong.

On a near-the-money NIFTY strike in the front expiry, that cost is trivial. The table below shows an illustrative chain with NIFTY at 24,500. The at-the-money call quotes 198.00 by 198.60. Sixty paise of spread across one lot of 75 is ₹45 — a rounding error against a ₹14,895 position. Walk out to the 26,500 call quoting 1.05 by 1.90 and the arithmetic inverts. The rupee cost is smaller, ₹64, but the position only costs ₹142.50, so you have handed over almost 45% of your capital before the trade has an opinion.

The right way to read that last row is in terms of what the underlying must do. With a delta of roughly 0.02 on a strike that far out, NIFTY has to travel more than 40 points just to earn back the spread. The trade is not break-even at entry; it starts deep in a hole that has nothing to do with your analysis. This is the single most common reason retail option buyers underperform their own backtests.

Somebody has to take the other side of your order, and on a far strike that is almost always a market maker who does not want the position. They will hold it only long enough to hedge it, and hedging a low-delta option means trading small quantities of the underlying repeatedly as the price moves. That hedging is expensive and imprecise. The spread is the fee charged for accepting that inconvenience, so the harder the hedge, the wider the quote.

Depth compounds the problem. A quote of 1.05 by 1.90 might be good for two lots. If you send an order for ten, the first two fill at 1.90 and the rest walk up the book to 2.20, 2.60, and whatever a reluctant seller wants. Your average fill is far worse than the screen suggested, and the screen never showed you that. Open interest and traded volume on the strike are the two columns that tell you in advance whether depth exists, which is why module 21 spends time on reading the chain properly.

The same effect appears across expiries, not just strikes. The front-month contract carries most of the activity. Go two or three expiries out and even at-the-money quotes widen noticeably, because far fewer participants are working those series. A calendar structure that looks attractive on theoretical values can be substantially less attractive once both legs are filled at real prices.

Because the people who need them are not price-sensitive. A fund holding a large Indian equity book has a mandate to limit drawdown. When it buys index puts as protection it is buying insurance, and insurance buyers accept a price above fair value — that is what insurance is. There is no equivalent standing demand for far out-of-the-money calls, so the two wings of the chain are not symmetric in who wants them.

The result shows up as different implied volatilities at different strikes for the same expiry. Downside strikes carry a higher implied volatility than at-the-money strikes on an equity index. Plot that across the chain and you get the downward-sloping curve known as skew. Black-Scholes assumes one flat volatility for the whole expiry, so relative to the model, the puts look permanently expensive and stay that way. It is not a temporary error waiting to be corrected.

There is a second reason beyond demand, and it is the more honest one. The lognormal assumption underlying the model treats a violent gap down as effectively impossible. Indian equity history says otherwise. The extra premium on downside strikes is the market pricing a risk that the formula excludes by construction. Traders who sell that premium because it looks rich against theory are collecting a real payment for a real exposure — module 32 covers what happens when the exposure is called.

On single-stock contracts, a dividend inside the life of the option matters. The share price falls on the ex-date by roughly the amount paid out, and that fall is entirely predictable. Options do not ignore it: call premiums on that name price the drop in advance, and put premiums price it too. If you value the call against a model that has not been told about the dividend, the call will look mysteriously cheap and the put mysteriously rich, and nothing is actually mispriced.

Index options are cleaner on this point, because a broad index absorbs the ex-dates of its constituents gradually rather than all at once. This is one of several reasons NIFTY and BANKNIFTY chains behave more like textbook examples than single-stock chains do, and one of the reasons most retail activity concentrates there.

The interest-rate input matters far less than beginners expect on short-dated contracts. Over a two-week NIFTY option, changing the rate assumption by half a percentage point moves the premium by a rupee or two, which is smaller than the spread you just paid. It grows with time to expiry, so it becomes a genuine consideration on long-dated positions and essentially never on weeklies. Rho, the Greek that measures it, is the one every trading desk checks last.

The check takes about fifteen seconds and it happens before the order is written, not after the fill disappoints. Read the bid and the ask, not the last traded price — the last trade may be twenty minutes stale on a quiet strike and tells you nothing about what you can transact at now. Compute the spread as a percentage of the ask. Then look at the quantity showing on each side and ask whether it covers the size you intend.

The second half of the check is about the exit, which is where most of the damage happens. A strike you can enter comfortably at 11:00 may have no bid at all at 15:15 on expiry day. Ask whether the position you are opening will still have a market when you want out of it, and if the honest answer is no, the plan has to be to hold to expiry and accept that outcome. Module 25 covers what actually happens to liquidity on an expiry session.

None of this is a substitute for having a view. It is what stops a correct view from being converted into a loss by the mechanics of getting in and out. The cheapest way to control every cost in this article at once is to trade near-the-money strikes in the front expiry, in size the book can absorb, using limit orders. That single habit removes most of the gap this module describes.

It is a reference point, not a target. Knowing the model value tells you roughly where the middle of the market should sit, which lets you judge whether a quote is reasonable or whether the strike is simply unloved. It tells you how the premium should respond to a move in the underlying, to a day passing, and to a shift in the volatility assumption. Those responses are the Greeks, and they remain useful even when the level is off.

It is also the language in which the market talks about price. When traders compare two strikes they do not compare rupee premiums, because those depend on moneyness and time. They compare implied volatilities, which is the model run in reverse. Without the model there is no common unit in which a 24,500 call and a 25,600 call can be discussed at all.

What it is not is an entitlement. A theoretical value of ₹15 against a market of ₹22 does not mean you are owed ₹7. It means either that the market is charging for something the model excludes, or that the strike is illiquid enough that no honest price exists there. Both readings lead to the same action, which is to trade somewhere the market is actually functioning.