Expiry-Day Short Straddle on a Physically Settled Stock
Expiry Thursday, 15:10. The client is short 20 lots of a stock-option straddle on PQR (lot size 500, so 10,000 shares) at the 620 strike, having collected ₹7.50 on the call and ₹6.00 on the put - ₹1.35 lakh in total. PQR has jumped from ₹610 to ₹620.40 in the last hour on a block-deal report; 20 minutes of trading remain. The client holds no PQR shares, has ₹6 lakh of free cash, and his SPAN-plus-exposure requirement is ₹4.2 lakh, so utilisation is under 60%. Stock F&O is physically settled and the settlement price is the closing price of the underlying. The broker's risk system squares off positions above 80% utilisation at the 15:20 peak-margin snapshot. The client's instruction: 'Let it expire - if it pins at 620 both legs are worthless and I keep the whole premium.'
1. Quantify the two realistic expiry branches (settlement at 620.60 and at 619.40) and the cash consequence of each. Why is the premium a misleading measure of the risk?
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Settlement price = PQR's closing price on expiry day. Any in-the-money stock option is automatically exercised; there is no election to let it lapse.
Branch A - settles at 620.60: the 620 call is in the money by ₹0.60; the put expires worthless.
- The call is assigned: he must deliver 10,000 shares at 620, receiving ₹62,00,000.
- He has no shares, so he buys 10,000 at 620.60 = ₹62,06,000 → delivery loss −₹6,000.
- Premium kept +₹1,35,000 → net +₹1,29,000. Cash needed: ₹62.06 lakh.
Branch B - settles at 619.40: the 620 put is in the money by ₹0.60; the call expires worthless.
- The put is assigned: he must buy 10,000 shares at 620 = ₹62,00,000, immediately worth ₹61,94,000 → −₹6,000.
- Same net result: +₹1,29,000, same ₹62 lakh outlay.
Branch C - exactly 620.00: both legs expire worthless, he keeps ₹1,35,000 and needs no cash. That is the only branch that avoids funding, and it is the least likely of the three.
Why the premium misleads: ₹1.35 lakh collected against a ₹62 lakh delivery obligation is roughly 46 times leverage, and the obligation is triggered by a one-paisa difference in the settlement price. The P&L per branch is trivial (₹6,000); the balance-sheet event is enormous. Risk here is not the option's theta or gamma, it is settlement mechanics.
2. Explain why the SPAN margin number (₹4.2 lakh, under 60% utilisation) understates the actual risk on expiry afternoon, and list the margin and settlement events the client is about to meet.
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SPAN answers a portfolio question - worst-case mark-to-market loss over a set of price and volatility scenarios. With 20 minutes to expiry the straddle's remaining time value is a rupee or two, so the scenario loss is genuinely small. The number is correct for mark-to-market and wrong for settlement.
What the SPAN number omits:
- A binary delivery obligation. After the close the position stops being an option and becomes a stock trade with a T+1 payin of roughly ₹62 lakh, irrespective of how small the option premium was.
- Delivery margin. Physically settled stock derivatives attract VaR + ELM on the full notional at expiry, with no SPAN offsetting benefit; that is an order of magnitude above ₹4.2 lakh.
- The 15:20 peak-margin snapshot. Utilisation can jump from 60% to well above 100% between 15:10 and 15:20 as delivery margin is applied; the broker's own rule then auto-squares off at the worst possible moment.
- Pin risk. The settlement price is the day's closing price, not the last traded price and not where the straddle is quoted. He can be right about the market and wrong about which leg is assigned - the choice flips on a fraction of a rupee.
- Consequences of failure. A short delivery goes to auction/close-out; the client bears the auction price difference, the exchange penalty and the broker's charges. A ₹1.29 lakh expected gain can turn into a six-figure realised loss.
The correct framing: for a physically settled short option near the strike on expiry day, the risk metric is required funding, not SPAN margin.
3. What should the desk do at 15:10 and why? Compare with an identical short Nifty straddle, and state the operating rule for expiry-day short-premium trades.
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Action: buy back both legs now. At 620.40 with 20 minutes left and volatility collapsing, the straddle marks at roughly ₹1.50-2.00, so closing costs about ₹15,000-20,000. Set against a ₹62 lakh funding obligation, an auction penalty and the risk of a 15:20 auto-square-off at an unknown price, this is not a close call - the cost of certainty is under 15% of the premium collected.
If he wants to keep a view: there is no safe residual. Keeping only the call (the in-the-money leg) leaves the assignment obligation; keeping only the put leaves the opposite obligation. The only zero-delivery position is zero lots. He could, if he genuinely wants the stock, keep the short put and fund ₹62 lakh - but he cannot, so that is not on the table.
Identical position in Nifty: cash-settled and European. Expiring at 620.40 equivalent, the debit is intrinsic × 75 - a few thousand rupees, already inside the SPAN margin. There is no delivery, no auction, no funding call, and letting a short index straddle expire worthless is a legitimate, standard strategy. The same trade in a single stock is a different instrument with different settlement risk.
Operating rules:
- Square off short physically settled stock options by early afternoon on expiry day; do not carry them into the closing-price settlement.
- Size the position against the delivery notional, not the premium: ₹62 lakh of stock needs ₹62 lakh of cash or an equivalent holding, regardless of a ₹1.35 lakh premium.
- Charge delivery margin in the pre-trade check from expiry morning, not SPAN.
- Never assume the other leg 'offsets' - a pin near the strike is exactly when one leg is assigned and the offsetting one is not.