Markets: A Rigorous Course

9A.1 Reading an NSE option chain

Foundation about 10 min

Motivation

The option chain is the first screen most Indian traders open. It packs prices, volatility, positions and flows for every strike of one expiry into one table. Each column is a precise quantity with a known bias. Misreading one column (a stale last price, a spot used in place of the forward) turns into a wrong implied volatility, a wrong delta and a wrong trade.

9A.1.1The columns of a chain#

Layout A chain shows one underlying and one expiry. Strikes run down the middle; calls are on the left and puts on the right. For each option the usual columns are:

Column Definition What to watch
LTP last traded price can be minutes old for illiquid strikes; never use it for IV without checking the time
Bid / ask (and quantities) best displayed buy and sell limit prices the mid (b+a)/2(b+a)/2 is the right input for IV; the spread a−ba-b is your cost
Change LTP minus previous close mixes the effect of spot, time and volatility (9A.3)
IV the implied volatility that reproduces the price (M08 · 8.10) depends on the price used (LTP, mid), the forward and the time convention
OI contracts outstanding, shown in contracts or units a stock of positions, each with a long and a short (M07 · 7.5)
Change in OI OI today minus OI at the previous close a net flow: opening minus closing trades
Volume contracts traded today a gross flow; always at least ∣ΔOI∣\lvert\Delta\text{OI}\rvert in the same unit

Every displayed number is also an estimate of something unobservable. The LTP estimates the current value; the IV column estimates the market's volatility input under a model; the OI column counts positions but says nothing about which side initiated them.

9A.1.2The forward from parity#

The forward, not spot Put–call parity for European options on a forward (M08 · 8.2) is C−P=e−rτ(F−K)C-P=e^{-r\tau}(F-K) at every strike. So the market's own forward is

F=K+erτ (C−P).(9A.1)F = K + e^{r\tau}\,(C-P). \tag{9A.1}

Use the strike where ∣C−P∣|C-P| is smallest; there the bid–ask noise in C−PC-P is smallest relative to the prices. Two reasons to prefer (9A.1) to spot: index options are priced off the future, which includes carry and expected dividends (M07 · 7.1); and the option prices and the index level are often taken at different moments.

9A.1.3A chain one day before expiry#

Worked example 9A.1one day before the October 2026 monthly expiry

The NSE F&O bhavcopy for 26 Oct 2026 has these rows for Nifty options expiring 27 Oct 2026 (closing prices in index points; OI and change in OI in units; one lot = 65 units). The Nifty closed at 22,753.20, up from 22,600.00 on the previous trading day (23 Oct).

Call close Call OI Call ΔOI Strike Put close Put OI Put ΔOI
206.35 55,27,405 −1,07,965 22,600 38.35 1,43,64,935 +81,09,335
133.90 84,13,795 −15,06,440 22,700 65.35 1,06,07,545 +54,93,085
103.55 40,41,895 +6,00,470 22,750 84.95 44,37,615 +29,77,325
77.55 97,08,660 −3,96,890 22,800 108.75 52,09,490 +8,70,740
39.90 89,42,570 +14,18,365 22,900 170.70 28,58,375 +455
20.05 1,75,81,200 −8,18,870 23,000 249.75 26,14,560 −15,18,985

At the 22,750 strike, (9A.1) with r=5.5%r=5.5\% and τ=1/365\tau=1/365 gives F=22,750+(103.55−84.95)×1.00015=22,768.60F=22{,}750+(103.55-84.95)\times1.00015=22{,}768.60: 15.4 points above the index close, against one day's carry of about 22,753×0.055/365≈3.422{,}753\times0.055/365\approx3.4 points. The difference is not carry. It says that the option closing prices and the index close describe slightly different moments or methods, and that the option market's forward is the consistent input. The 22,700 and 22,800 strikes give 22,768.56 and 22,768.80, so the inference is stable.

The consequence for IV is large at one day to expiry. With spot as the forward, the 22,750 call and put imply 21.5% and 18.2%, a 3.3-point gap that no arbitrage-free market can sustain. With F=22,768.6F=22{,}768.6 both imply 19.8%. Across strikes, using the parity forward and OTM options, IV falls from 23.3% at 22,500 to 19.1% at 22,900: the downward skew of M09 · 9.5, compressed into a one-day chain.

Practitioner notes

  • The IV column on a broker's chain uses the broker's choice of forward, rate and time convention. Two screens can disagree by several vol points for short-dated options. Recompute it yourself when the decision matters.
  • Read OI in lots: 40,41,895 units at the 22,750 call is 62,183 contracts. Read change in OI against volume in the same unit. The 22,750 put added 29,77,325 units of OI (45,805 contracts) on a volume of 20,05,776 contracts. Volume in the bhavcopy is in contracts while OI is in units (9A.2); compared naively, ΔOI looks larger than volume, which the accounting identity of M07 · 7.5 forbids.

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