9A.12 Margins for hedged positions

Motivation

A short strangle and an iron condor have similar expected P&L in normal weeks and very different capital requirements. Margin decides return on capital and, through forced closure, survival. M07 · 7.4.2 described SPAN plus exposure margin; this section computes it for multi-leg option positions.

Position Greeks For legs $j$ with signed quantities $q_j$ , every Greek of the position is the sum

\Delta_P=\sum_jq_j\Delta_j,\quad\Gamma_P=\sum_jq_j\Gamma_j,\quad\mathcal V_P=\sum_jq_j\mathcal V_j,\quad\Theta_P=\sum_jq_j\Theta_j, \tag{9A.16}

because value is additive and differentiation is linear. A future contributes $q$ to delta and nothing else (M09 · 9.7 lists the Greeks of standard structures).

9A.12.1Scenario margin and its properties#

A SPAN-like scenario margin Revalue the position under a set of scenarios $\{(F_k,\sigma_k)\}$ and charge the worst loss:

M_{\text{scen}}(P)=\max\Big(0,\ \max_k w_k\big[V_P(F,\sigma)-V_P(F_k,\sigma_k)\big]\Big), \tag{9A.17}

with $F_k=F(1+m_k\cdot\text{scan})$ , $m_k\in\{0,\pm\frac13,\pm\frac23,\pm1\}$ combined with $\sigma\pm$ a vol shift ( $w_k=1$ ), plus two extreme moves $\pm2\times$ scan at a reduced weight. This is the classic 16-scenario design (M07 · 7.4.2). Real SPAN adds further components (inter-month spread charges, a short-option minimum, a credit for the value of long options), and NSE Clearing's parameters are published daily in its risk-parameter files; the defaults in m09a_margin_greeks (scan 6%, vol shift 4 points, extremes $\pm2\times$ at 35%) are illustrative. Exposure margin (ELM) is then a percentage of the notional of short options and futures; about 2% for index derivatives is the figure usually quoted (M07 · 7.4.2; not re-verified against NSE Clearing for this module).

Proposition 9A.12portfolio margining

(a) $M_{\text{scen}}$ is subadditive: $M_{\text{scen}}(P_1+P_2)\le M_{\text{scen}}(P_1)+M_{\text{scen}}(P_2)$ . (b) For a position whose payoff at expiry is bounded below by $-L$ (a defined-risk spread), if every scenario value satisfies $V_P(F_k,\sigma_k)\ge-L$ and the position's current value is $V_P\le0$ (a credit position), then $M_{\text{scen}}\le L$ .

Proof

(a) Losses are additive across positions in each scenario, $\ell_k(P_1+P_2)=\ell_k(P_1)+\ell_k(P_2)$ , and $\max_k(a_k+b_k)\le\max_ka_k+\max_kb_k$ ; the outer $\max(0,\cdot)$ preserves the inequality. (b) $\ell_k=V_P-V_P(F_k,\sigma_k)\le0+L$ . The hypothesis on scenario values holds automatically for model prices: each scenario value is $e^{-r\tau}\mathbb E^{\mathbb Q}[\text{payoff}]\ge-e^{-r\tau}L\ge-L$ . For a credit vertical spread of width $W$ and quantity $Q$ , or an iron condor with equal wings (only one side can finish in the money), $L=WQ$ . The extreme scenarios carry weight $w_k<1$ , which only lowers their losses.∎

Part (a) is why the exchange margins portfolios rather than legs; part (b) is why a spread needs margin of at most its maximum loss.

9A.12.2Strangle versus condor#

Worked example 9A.6strangle versus condor; illustrative parameters

Nifty forward 24,500, flat IV 13%, $r=6\%$ , 7 days, one lot (65 units). Computed with m09a_margin_greeks:

Position (per lot)	Credit (₹)	Delta	Gamma	Vega per vol pt (₹)	Theta per day (₹)	Scenario margin (₹)	ELM 2% (₹)	Total (₹)
Short 24,000 put	1,777	+8.1	−0.030	−451	+419	61,778	31,850	93,628
Short 24,000/25,000 strangle	3,676	−0.6	−0.062	−924	+858	60,175	63,700	1,23,875
Iron condor, 200-pt wings	2,303	−0.1	−0.028	−425	+395	10,660	63,700	74,360
Put credit spread 24,000/23,800	1,136	+4.6	−0.014	−214	+199	11,827	31,850	43,677

Three observations. The strangle's scenario margin is below the single short put's: the scenario that hurts one side helps the other (subadditivity in action). The wings cut the scenario margin from ₹60,175 to ₹10,660, below the condor's maximum loss of $(200-35.4)\times65=\text{₹}10{,}697$ and well below $200\times65=\text{₹}13{,}000$ , as Proposition 9A.12(b) guarantees. And in this model the ELM on short legs dominates the condor's margin; it does not recognise that the wings cap the loss. Exchange treatment of exposure margin on hedged positions is a detail to check on a margin calculator, not to assume.

9A.12.3Dated Indian margin rules#

Dated Indian rules (from SEBI circular SEBI/HO/MRD/TPD-1/P/CIR/2024/132 of 1 Oct 2024, fetched 6 Nov 2026; M09 · 9.10).

Upfront premium from option buyers, from 1 Feb 2025. A buyer's margin is the premium; it cannot be funded by the premium of a leg sold in the same order.
Extra 2% ELM on short index options on their expiry day, from 20 Nov 2024. In Worked example 9A.6 the strangle's total margin on a Tuesday expiry day rises by $0.02\times24{,}500\times130=\text{₹}63{,}700$ to ₹1,87,575.
Calendar-spread margin benefit removed on expiry day for positions involving the expiring contract, from 1 Feb 2025 (SEBI circular of 1 Oct 2024, para 5.2). A calendar spread whose short leg expires today is margined as if that leg were naked.
Intraday monitoring of position limits from 1 Apr 2025 (1 Oct 2024 circular), tightened into an entity-level intraday framework for index options with at least four random snapshots a day from 1 Oct 2025 (SEBI circular SEBI/HO/MRD/TPD/CIR/P/2025/122 of 1 Sep 2025; institution-sized limits; M09 · 9.10).