Theoretical Deviations: Real-World Prices

A theoretical price describes a world with no costs, unlimited quantity at every level, one volatility for every strike, and continuous trading. None of these holds on a live NSE option chain at 2:45 pm. The model never claimed to tell you what the market will charge. It tells you what a contract is worth to someone who could trade without friction, and nobody can.

The gap opens in four places. Two are costs of execution: the spread you pay to get in and out, and the quantity available at your strike. The other two are real differences in price: the market charging a different implied volatility for different strikes, and cash flows such as dividends that the simple formula does not date properly. You can reduce the first two by choosing better strikes. You cannot avoid the second two. You can only understand them.

The picture shows the path from the model price to what you actually pay. Look at each stage and ask whether it is something you can shrink. Keep in mind the other side of the story too. A gap between model and market is not automatically an opportunity. Usually the market is charging for something the model leaves out.

The bid is the highest price a buyer is offering right now. The ask is the lowest price a seller will accept right now. The theoretical value usually sits somewhere between them. If you buy at the ask and sell later at the bid, you have paid the full spread even if the index did not move and your view was neither right nor wrong.

On a near-the-money Nifty strike in the nearest expiry, this cost is small. The table shows an illustrative chain with Nifty at 24,500. The at-the-money call quotes 198.00 to 198.60. Sixty paise on a lot of 65 is ₹39, small against a position of about ₹12,909. Now move to the 26,500 call quoting 1.05 to 1.90. The rupee cost is similar, about ₹55, but the whole position costs only 1.90 × 65 = ₹123.50. You have handed over about 45% of your money before the trade has done anything.

Read the last row in terms of what the index must do. At a delta of about 0.02, which is an assumed illustrative value for a strike that far out, Nifty has to move roughly 40 points just to earn back the spread (0.85 ÷ 0.02 = 42.5). The trade does not begin at breakeven. It begins in a hole that has nothing to do with your analysis. This is one of the commonest reasons that small traders do worse than their own back-tests.

To be fair to the other side: a wide spread on a far strike is not always a bad sign for holding it. It is a warning about entering and leaving. If you plan to hold to expiry and the option is a small part of a hedged position, the spread may matter little. The cost matters most when you trade often or in size.

Someone has to take the other side of your order. On a far strike that is usually a market maker who does not want the position. The market maker will hold it only long enough to hedge it. Hedging a low-delta option means trading small amounts of the underlying again and again as the price moves. This is costly and never exact. The spread is the fee for this trouble, so the harder the hedge, the wider the quote.

Quantity adds to the problem. A quote of 1.05 to 1.90 might be good for two lots. If you send an order for ten, the first two lots fill at 1.90 and the rest climb the queue to 2.20, 2.60 and whatever a reluctant seller wants. Your average price is worse than the screen suggested, and the screen did not warn you. Open interest and traded volume on the strike tell you in advance whether depth exists. The option chain article in this series shows how to read them.

The same effect appears across expiries. The nearest expiry has most of the activity. Two or three expiries further out, even at-the-money quotes widen, because fewer people trade those series. A structure that looks attractive at model prices may be much less attractive once both legs are filled at real prices.

Because the people who need them are not very price-sensitive. A fund holding a large basket of Indian shares has a duty to limit its losses. When it buys index puts for protection, it is buying insurance, and buyers of insurance accept a price above the fair value. That is what insurance means. There is no matching steady demand for far out-of-the-money calls, so the two sides of the chain are not equal in who wants them.

The result is a different implied volatility at different strikes for the same expiry. Downside strikes usually carry a higher implied volatility than at-the-money strikes on an equity index. Drawn across the chain, this gives a downward-sloping curve called the skew. The model assumes one flat volatility for the expiry, so against the model the puts look expensive and stay that way. It is not a temporary error waiting to correct itself.

There is a second reason, and it is the more honest one. The smooth-price assumption in the model treats a violent gap down as nearly impossible. Indian market history says otherwise. The extra price on downside strikes is the market paying for a risk that the formula leaves out. Someone who sells that premium because it looks rich against the model is collecting a real payment for a real risk.

On single-stock contracts, a dividend inside the life of the option matters. The share price drops on the ex-date by about the amount paid, and this fall is known in advance. Option prices do not ignore it. Call prices on that share already allow for the drop, and so do put prices. If you value the call with a model that has not been told about the dividend, the call will look strangely cheap and the put strangely dear, and nothing is actually mispriced.

Index options are cleaner on this point, because an index absorbs the ex-dates of its many shares gradually and not all at once. This is one of several reasons why Nifty and Bank Nifty chains behave more like the textbook than single-stock chains do, and one reason why much small-trader activity gathers there.

The interest-rate input matters far less than beginners expect on short-dated contracts. Over a two-week Nifty option, changing the rate by half a percentage point changes the price by only a small amount, often less than the spread you just paid. It grows with time to expiry, so it can matter for long-dated positions and almost never for weekly ones. Rho, the Greek that measures it, is the one desks check last.

The check takes about fifteen seconds and comes 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 old on a quiet strike and tells you nothing about what you can trade at now. Work out the spread as a share of the ask. Then look at the quantity showing on each side and ask whether it covers your size.

The second half of the check is about leaving, where most damage happens. A strike you can enter easily at 11:00 may have no bid at all at 3:15 pm on expiry day. Ask whether the position you are opening will still have a market when you want to close it. If the honest answer is no, the plan must be to hold to expiry and accept whatever it brings.

None of this replaces having a view. It only stops a correct view from being turned into a loss by the mechanics of getting in and out. The simplest way to control all the costs in this article is to use near-the-money strikes in the nearest expiry, in a size the market can absorb, with limit orders. But do not read this as a rule that such trades will be profitable. It only reduces the cost of trading, not the risk of being wrong.

It is a reference point, not a target. Knowing the model value tells you roughly where the middle of the market should be, so you can judge whether a quote is reasonable or whether the strike is simply unloved. It tells you how the price should react to a move in the index, to a day passing and to a change in expected volatility. Those reactions are the Greeks, and they stay 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 prices, because those depend on distance and time. They compare implied volatilities, which is the model run backwards. Without the model, there is no common unit in which a 24,500 call and a 25,600 call can be compared at all.

What it is not is an entitlement. A model value of ₹15 against a market price of ₹22 does not mean you are owed ₹7. It means that either the market is charging for something the model leaves out, or the strike is so unloved that no honest price exists there. Both readings lead to the same action, which is to trade where the market is working properly.