Risk for option books: scenarios, stress, VaR, ES and margin shocks

On Wednesday 10 Jun 2026 a sold Nifty strangle on the 30 Jun expiry, a 22,950 put and a 23,550 call, took in Rs 389.60 a unit, which is Rs 25,324 a lot. Its net delta was 0.0 units a lot, so a report that reads only delta would show almost nothing at risk. A one day move of 99% size, 512 index points either way on that day's implied volatility, takes about Rs 7,805 off the position through gamma, while delta explains only Rs 11 of it. That is the whole subject: a book can be flat on one measure and exposed on the next, so a risk report needs several. This module is education about measuring risk. It is not a position, a limit for anyone's account, or a view on any contract.

The idea, plainly

What does a risk report for an option book hold?

Six layers, each answering a different question. None replaces the others, and the order runs from the quick and local to the slow and complete.

• Greeks: how value changes for a small move.
• Scenario grid: how value changes for a big move, with every option repriced.
• Stress: a named event, replayed.
• VaR and ES: how large a bad day is, in probability terms.
• Margin: what the clearing house demands, which is itself a risk number.
• Limits: the numbers that stop trading, written before the position.

Why do Greeks mislead on a big move?

A Greek is a slope at one point. Delta is the slope of value against the index, gamma is how fast that slope changes. A sold strangle starts near delta neutral, so a delta based report shows almost no risk, while gamma is large and negative: every point of movement makes the position more exposed in the same direction.

• Delta of the strangle: 0.0 units a lot. Gamma: −0.060 units of delta a point.
• Vega: −2,627 rupees a lot for each point of implied volatility. Theta: 975 rupees a lot a day, the income side.

The estimate that adds the three slopes, delta times the move plus half gamma times the move squared plus vega times the volatility change, is only good for moves small enough that the slopes hold.

How do Greeks add up across a whole book?

A book is many positions, so each Greek is summed across strikes and expiries, and the sum hides structure. A short near expiry option and a long far expiry option can net to zero vega and still lose when the front of the curve moves alone.

• By expiry: report vega and gamma in buckets, not as one total.
• By strike: a wing and a body can offset in delta and differ in gamma.
• By underlying: a Nifty book and a stock book are different risks, and their moves are only partly linked.

What does the scenario grid show?

The grid reprices every option for a move in the index and a shift in implied volatility, so it needs no slope. One day later, a rise of five points in volatility on top of a fall of three per cent is a cell the Greeks ladder cannot see.

What are VaR and ES?

Value at risk answers a narrow question: what loss is exceeded on only one day in a hundred? Expected shortfall, ES, asks how large the losses are on those worst days, on average. VaR is a threshold, ES is the average beyond it.

• Parametric: assume moves follow a normal curve with a stated volatility. Quick, and thin in the tails.
• Historical: use the past moves themselves. No curve, but only as rich as the sample.
• Simulation: draw moves from a stated model and reprice. Handles options, and is as good as the model.

How few observations sit behind a historical VaR?

The NSE file of Nifty closes holds 299 daily returns, so the worst one per cent is about 3 days. A 99% historical VaR is near the third worst day of that file, and ES the average of the three worst. Both are one lucky or unlucky run from moving. The cone shows another effect: the volatility measured on a short window swings widely, so the window chosen is itself a choice.

What does a stress test add?

A stress test replays a named event, whatever its probability. The question is no longer how likely it is, but whether the position, the margin and the account survive it. India VIX closed at 22.79 on 7 Apr 2025, a stress session, against 15.63 on 10 Jun 2026.

• If every option's implied volatility rose by that gap, 7.16 points, the strangle's vega of 2,627 rupees a point would take about Rs 18,808 a lot off the value.
• The loss arrives before the index moves, and before any exit price is on the screen.
• A scheduled gap, such as a Budget session, is a stress test written in the calendar.

What do margin shocks do?

NSE Clearing's page says its initial margin requirements are based on 99% value at risk over a one day horizon, and that it computes them with SPAN, a portfolio based system. Extreme loss margin is added: 2% of notional for index derivatives. So margin is itself a VaR number, and it moves with volatility. When volatility rises, the loss on a short option and the margin on it rise together.

• On expiry day SEBI's circular of 1 Oct 2024 adds 2% of extreme loss margin on short options expiring that day, from 20 Nov 2024: Rs 31,186 a lot at the index level on 16 Jun 2026.
• From 1 Feb 2025 a calendar spread has no margin benefit on the expiry day of the contract expiring that day.
• Option premium payable is collected upfront from 1 Feb 2025.

The practical reading: a buffer that covers only today's requirement does not survive a volatility spike, so the buffer is sized against the shocked margin.

Where does liquidity belong in the report?

A reprice uses a settlement price, and a settlement price is not a price anyone offered. On a stress day the bid ask spread widens and far strikes may have no bid at all. A report that values a position at settlement and assumes a free exit is optimistic by the cost of leaving.

• Add a haircut scenario: exit each leg at a stated number of rupees worse than settlement.
• Prefer limits that need no exit, such as a smaller size or a bought wing, since a wing caps the worst cell without a trade.
• Look at contracts traded, not only open interest, before assuming a strike can be closed.

How do limits close the loop?

• Scenario limit: the worst cell of the grid is capped at a stated share of capital, before the trade is placed.
• Greek limits: bounds on gamma and vega, not only delta, since delta can be zero while the others are not.
• Margin buffer: spare capital above the requirement, tested against a volatility shock.
• Loss rule: a drawdown that stops new risk, written down before the first position.

Worked example: one strangle through the whole report

The position is one lot of 65 units of the sold 22,950 put and 23,550 call, on the 10 Jun 2026 chain, 20 days to expiry.

1. Credit. Rs 389.60 a unit, Rs 25,324 a lot, before costs.
2. Greeks. Delta 0.0 units, gamma −0.060 a point, vega −2,627 a point, theta 975 a day, all per lot.
3. Parametric VaR on delta. Delta times the 99% move: Rs 11. A report that stops here shows no risk.
4. Delta and gamma. Half gamma times the move squared: Rs 7,805. That is the gamma loss on a 512 point move.
5. Volatility. The vega effect of a rise by the VIX gap of 7 Apr 2025: Rs 18,808.
6. Scenario grid. The corners of the grid above, a move of six per cent with a volatility rise of ten points, are the stress the account must survive, not the average case.
7. Margin. The requirement is a 99% one day VaR plus extreme loss margin of 2% of notional, and it grows if volatility rises.

The estimates agree on direction and disagree on size. Delta says nothing, the delta and gamma estimate says thousands, and the grid says more at the edges. A risk process uses the largest honest number, not the most comfortable.

The common mistake

The claim: My VaR is small, so my loss cannot be large. VaR is a threshold on one day in a hundred. It says nothing about how much worse the worse days are, and for an option book computed from delta it can be near zero while the position loses thousands on a gap. ES asks the next question, and the grid and the stress test ask the one after. SEBI's Aug 2026 study found 87.7% of individual F&O traders lost money in FY26, counted by trader, not by structure, and it does not rate any one position. Start the report with the largest cell, not the average.

Key takeaways

• A flat delta can hide large gamma and vega risk.
• A scenario grid reprices every option, so it holds for big moves.
• VaR is a threshold. Expected shortfall averages the days beyond it.
• A historical VaR at the top one per cent rests on very few observations.
• NSE Clearing margin rests on a one day VaR, so it rises with volatility.
• Write the largest honest loss first, and a buffer above margin.

Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study