14.15 A mixed Indian book: rupee Greeks, stress table and margin utilisation

Motivation

A realistic personal book after M01–M13 holds index futures, a short-option position, MCX commodities and delivery equities in one account. This section aggregates it into rupee exposures, stresses it, and tracks how much of the account is consumed by margin before and after the stress.

The book (prices as of 5 Nov 2026) Account equity ₹1,00,00,000.

Position	Quantity	Price used	Source
Nifty Nov-26 future (expiry 23 Nov 2026)	long 2 lots × 65	24,588.0	NSE F&O UDiFF bhavcopy, 5 Nov 2026 (settlement)
Nifty 23-Nov 24000 put	short 3 lots × 65	105.00	same
Nifty 23-Nov 25000 call	short 3 lots × 65	126.75	same
Reliance Industries, delivery	1,000 shares	1,313.39	same file, underlying price
HDFC Bank, delivery	1,300 shares	759.99	same
Infosys, delivery	800 shares	1,167.11	same
MCX GOLDM Dec-26 future	long 1 lot (100 g = 10 × 10 g)	₹1,38,839 per 10 g	MCX GOLD Dec-26 on 2 Nov 2026 (secondary news reports; M10 · 10.5.3); GOLDM assumed at the same price
MCX CRUDEOIL Nov-26 future	short 1 lot (100 bbl)	₹8,370 per bbl	illustrative: WTI $88.6 × USDINR 94.47 (4–5 Nov 2026 levels); not an MCX quote

Lot sizes: Nifty 65 (the bhavcopy's NewBrdLotQty, 5 Nov 2026). If the equities were held as single-stock futures instead, the same bhavcopy gives lots of 500 (Reliance), 650 (HDFC Bank) and 400 (Infosys). MCX lots (GOLDM 100 g, CRUDEOIL 100 bbl) are from secondary sources as of October 2026 (M10 · 10.10); verify on mcxindia.com. Betas to the Nifty are assumed for the illustration: 1.0, 0.9 and 0.8.

Implied volatilities Black-76 (M08 · 8.8) on the Nov future, $r = 5.5\%$ , 18 calendar days to expiry. The two short options' settlement prices imply 14.68% (24000 put) and 13.08% (25000 call): the put is richer, which is the skew.

Step 1: rupee Greeks Per 1% move in the underlying, per volatility point, per day.

Position	₹ delta per 1%	₹ gamma per 1%	₹ vega per vol pt	₹ theta per day
Nifty future × 2	31,964	0	0	0
Short 24000 put × 3	10,713	−4,387	−3,177	+1,301
Short 25000 call × 3	−13,799	−5,622	−3,626	+1,327
Reliance (β 1.0)	13,134	0	0	0
HDFC Bank (β 0.9)	8,892	0	0	0
Infosys (β 0.8)	7,470	0	0	0
Nifty factor total	58,374	−10,009	−6,804	+2,628
GOLDM × 1 (per 1% in gold)	13,884	0	0	0
CRUDEOIL × −1 (per 1% in crude)	−8,370	0	0	0

How to read it: the book is long the Nifty by about ₹58 lakh of beta-adjusted exposure (₹58,374 per 1%), short gamma (each 1% move lowers ₹ delta by ₹10,009 if the move is up, raises it if down: the book gets longer as the market falls), short vega and collecting ₹2,628 a day of theta. The strangle has turned a long-equity book into one that is longer still in a crash. The commodity legs are separate factors.

Step 2: scenarios One-day horizon; all three stocks move by beta times the Nifty move; option implied volatilities shift in parallel; the futures basis stays constant in percentage terms.

Scenario	Nifty	Vol (pts)	Gold	Crude	Full revaluation (₹)	Greek expansion (₹)	Error (₹)
S1 oil shock	−8%	+6	+2%	+12%	−7,96,576	−8,98,140	−1,01,564
S2 crash with liquidation	−12%	+12	−3%	−10%	−11,13,732	−14,58,091	−3,44,360
S3 relief rally	+5%	−4	−2%	−8%	+2,30,634	+2,35,790	+5,156
S4 moderate sell-off	−3%	+3	0	0	−2,32,182	−2,37,944	−5,761
S5 short squeeze	+8%	+2	0	0	+2,32,252	+1,35,724	−96,528

The Greek expansion is (14.14) with the totals of Step 1; full revaluation reprices each option with Black-76 at the shocked future, shocked volatility and one day less to expiry. Small moves (S3, S4) agree within ₹6,000. Large moves do not: in S2 the quadratic overstates the loss by ₹3.4 lakh because both short options have moved far from their strikes and their gamma has fallen. In S5 it overstates the loss on the short call by ₹97,000 for the same reason. Proposition 14.23 says this sign is not guaranteed; a book whose short strikes lie just beyond the shock would show the opposite error.

S1 and S2 differ in the commodity legs. In S1 (an oil shock in the pattern of March 2026, M10 · 10.11) gold and the crude short both lose: the "hedges" add to the loss. In S2 gold falls with equities, as it did in March 2020 and March 2026 when leveraged holders sold what they could. Neither commodity position hedges the Nifty factor in the scenarios that matter; 14.6's lesson about crisis correlation applies to cross-asset books.

Step 3: margin utilisation Define

u = \frac{\text{margin required on derivatives}}{\text{cash available for margin}}, \tag{14.16}

where cash available excludes money already spent on delivery equities (here ₹67.65 lakh; pledging the equities, 14.16, would add their post-haircut value). The book is in trouble well before $u$ reaches 1: brokers square off positions when $u$ crosses 1 intraday, and margins are raised in exactly the conditions in which equity falls.

Exchange margins are not reproduced here. The illustration uses a toy margin model, stated so you can replicate it, not NSE's or MCX's parameters: for the Nifty legs, the worst full-revaluation loss over price moves of $0, \pm\tfrac13, \pm\tfrac23, \pm1$ times a 6% scan range combined with ±4 volatility points, plus 2% of notional on futures and short options as exposure margin; for MCX, 10% of notional on GOLDM and 20% on CRUDEOIL. Actual figures come from NSE Clearing's daily SPAN files, MCX Clearing's margin files, or a broker's margin calculator, and are typically different.

State	Derivative P&L (₹)	Cash available (₹)	Margin required (₹)	Utilisation $u$
Before	0	67,64,935	9,01,156	13.3%
After S1	−5,60,613	62,04,322	9,96,564	16.1%
After S2	−7,59,788	60,05,147	9,28,319	15.5%

Derivative P&L is settled in cash daily (futures and option MTM), so cash falls by the derivative loss while the equity loss sits in the demat account. Utilisation rises because the numerator rises (higher volatility widens the scan loss on short options) while the denominator falls. In this account the book survives both scenarios. Scale every derivative position by four (P&L and margin scale exactly, since both are linear in quantity) and utilisation starts at 53.3% and ends S2 at 99.7%: cash ₹37,25,783 against margin ₹37,13,276, with no change in the equity sleeve. One more adverse tick and the broker closes positions. That is the mechanism of forced liquidation at the low (M03 on ruin, 14.16 on margin calls).

Practitioner notes

Report risk in four numbers per factor: ₹ delta per 1%, ₹ gamma per 1%, ₹ vega per point, ₹ theta per day. Add a full-revaluation scenario table and a utilisation figure. That is a complete morning risk report for a personal book.
Set the stress limit on full revaluation, for example "loss in S2 ≤ 15% of equity", and the ES limit (14.13) on the conditional distribution. Whichever binds governs size.
The theta line is what attracts traders to short options; the S2 line is what it pays for. Here the options alone lose ₹4.18 lakh in one S2 day, about 160 days of the book's theta (₹2,628 a day), and far more than the ₹45,191 of premium collected on the six short lots.

Facts used in 14.13–14.15#

Fact	Value	As of	Source
Nifty lot size	65	5 Nov 2026	NSE F&O UDiFF bhavcopy (`NewBrdLotQty`), https://nsearchives.nseindia.com/content/fo/BhavCopy_NSE_FO_0_0_0_20261105_F_0000.csv.zip
Nifty Nov-26 future settlement; spot	24,588.0; 24,536.6	5 Nov 2026	same
Nifty 23-Nov 24000 PE / 25000 CE / 24500 CE / 24500 PE / 25500 CE settlement	105.00 / 126.75 / 334.55 / 259.05 / 40.45	5 Nov 2026	same
Stock futures lots: Reliance, HDFC Bank, Infosys	500, 650, 400	5 Nov 2026	same
MCX GOLD Dec-26 future	₹1,38,839 per 10 g	2 Nov 2026	secondary news reports (MCX's daily bhavcopy is the primary record; M10 · 10.5.3)
MCX GOLDM / CRUDEOIL lot	100 g / 100 bbl	Oct 2026	secondary summary, 25 Oct 2026; verify with the exchange (mcxindia.com)
Basel FRTB market-risk measure	97.5% ES	standing	BCBS, Minimum capital requirements for market risk (2019)