9A.13 Position management and adjustments

Motivation

Short-premium positions get "tested": the index moves toward a short strike. Indian options culture has a rich vocabulary of adjustments: rolling, converting to a condor, delta-neutralising, "rolling the untested side". Each is a trade. Its effect is a change of Greeks, and its cost is explicit.

9A.13.1Adjustments as new trades#

Proposition 9A.13an adjustment is a new trade

Let $P$ be the current position and $A$ the set of trades in an adjustment. Then the adjusted position's value, Greeks and P&L from now on are those of $P$ plus those of $A$ , and

\mathbb E[\text{P\&L}(P+A)]=\mathbb E[\text{P\&L}(P)]+\mathbb E[\text{P\&L}(A)]-c(A), \tag{9A.18}

with $c(A)$ the transaction costs of $A$ . Under the pricing measure $\mathbb E^{\mathbb Q}[\text{P\&L}(A)]=0$ for trades at fair prices, so an adjustment changes the expected discounted P&L only through costs and through its exposure to whatever premium (variance premium, a directional view) makes $\mathbb P$ differ from $\mathbb Q$ . The loss already incurred on $P$ does not enter.

Proof

Linearity of value (9A.16) and of expectation. Losses to date are $\mathcal F_t$ -measurable and appear in both the adjusted and unadjusted totals.∎

The practical rule follows: adjust only if you would open $A$ as a fresh trade at today's prices, given its Greeks and costs. "Adjusting to get back to break-even" is the sunk-cost and disposition pattern of M14 · 14.9.2.

9A.13.2A tested strangle#

Worked example 9A.7a tested strangle; illustrative

The 24,000/25,000 strangle of Worked example 9A.6 (7 days, 13%) is opened at 24,500. The forward rallies to 24,800 with the same IV and time (to isolate the price effect). Per lot:

	Delta	Gamma	Vega per vol pt (₹)	Theta per day (₹)
Strangle after the rally	−19.3	−0.064	−975	+904
(a) Buy 19.3 units of futures	0.0	−0.064	−975	+904
(b) Roll the put from 24,000 up to 24,400	−9.7	−0.091	−1,395	+1,294
(c) Add 200-point wings (condor)	see 9A.6	less negative	less negative	lower

(a) Removes delta and nothing else: gamma, vega and theta are unchanged. But the future trades in lots of 65 units; the hedge needs 19.3 units, 0.30 lot. The nearest feasible hedges are 0 or 1 lot. For small accounts, delta-neutral hedging with futures is coarse; option legs give finer delta.
(b) Buys back the 24,000 put at 5.93 and sells the 24,400 put at 44.16: a credit of 38.23 points (₹2,485 per lot). It halves the delta, but raises short gamma by 43% and short vega by 43%. It is a larger short-volatility position, now with strikes 600 points apart instead of 1,000. If the rally continues, the call side loses as before; if the index reverses, the put is now much closer. It feels like collecting more premium; in Greeks it is adding risk.
(c) Pays for the wings (₹1,374 per lot at the original spot) to cap the loss and cut margin by about ₹50,000; it lowers theta and reduces short gamma and vega.

9A.13.3Rolling and its costs#

Rolling out in time Rolling the original strangle from 7 to 14 days (same strikes, at 24,500) collects 92.6 more points per unit, keeps gamma about the same ( $-0.062\to-0.060$ per lot) and nearly doubles short vega ( $-924\to-1{,}800$ per vol point). A roll is a calendar trade: it is a bet on the term structure and on time, not a repair.

Costs Each leg traded pays brokerage, exchange charges (0.03553% of premium at NSE) and STT of 0.15% of premium on sales (from 1 Apr 2026; NSE circular NSE/FATAX/73524, fetched 6 Nov 2026), plus half a bid–ask spread. A roll is four trades (close two, open two); a wing conversion two. In m09a_margin_greeks.adjustment_cost with a half-spread of 0.5 point and ₹20 per order, the roll costs ₹210 per lot and the conversion ₹105, before STT; against a weekly theta of a few thousand rupees, frequent adjustment is a material drag.