On Wednesday 10 Jun 2026 the Nifty 23,350 call with 48 days to its 28 Jul expiry cost Rs 493.00 a unit. The rate in the chain, a government T-bill yield, was 5.15%. The model's rho for the call was minus Rs 0.65 a unit for each percentage point the rate rises. A call that loses when rates rise sounds wrong, because textbooks say calls gain. Both are right. The sign depends on what you hold still, and for Nifty options that choice matters more than the size of the number. Below: which choice is which, and why the size, once everything is added up, is small next to vega.
3By the end you can
- Say why Black 76 rho is negative for a Nifty call and the textbook rho is positive.
- Add the discounting and carry effects to get the total rate effect.
- Compare a rate move with a volatility move in rupees.
The idea, plainly
Rho is the change in an option's price for a one point change in the interest rate. The rate touches an option in two places. The first is discounting: the payoff arrives at expiry, so a higher rate makes it worth a little less today. The second is carry: a future is priced as the index grown at the rate less dividends, so a higher rate lifts the future, which lifts a call and lowers a put (module F08 builds the future's fair value).
What Black 76 sees
The model used on these pages, Black 76, prices from the future and holds it fixed. It sees only discounting, so its rho is negative for calls and puts alike:
Rho = -T * Price
/ 100
What the textbook sees, and the total
The textbook model, Black Scholes on the spot index, holds spot fixed and lets the future move, so it sees carry too and shows a positive rho for a call. Neither is wrong. For a Nifty option, where the future is an observed price, the honest rate effect is the sum:
Carry = Delta * F * T
/ 100
Total = Carry + Rho
T is the years to expiry and F the future. Because T is in every term, rho grows with time left. A weekly option has almost none.
The term this section turns on: Rho
Rho in the calculator
The Greeks calculator linked below shows both conventions: Black 76 on the future gives the discounting number, and Black Scholes Merton on the spot gives a rho that includes carry. The calculator backs the dividend yield out of the future, so the second lands on the total in the worked example below. That is no accident: the total equals the strike times T times the discount factor times N(d2), the textbook rho, reached by a different route.
Where the rate comes from
The chains on these pages take the rate from government T-bill yields for the example date, matched to the days left: 5.17% for the 6 day option, 5.11% for 20 days and 5.15% for 48 days. It is a curve, one number per expiry. The RBI's Monetary Policy Committee announces policy rate decisions on scheduled dates, and a T-bill yield moves with those expectations every day. A model needs only one rate for one horizon, and a small error in it costs little, which is the same message as the numbers below.
How rho scales with time
The chart shows the Black 76 part, the discounting effect, for three expiries of the same call.
Black 76 rho is below zero for a call, and it deepens with the days left
Worked example: three expiries, 10 Jun 2026
Three at the money calls on one date: nearest the future for the monthly expiries and nearest the parity forward for the weekly. Rho, the discounting effect, is Black 76 at each strike's own volatility. The rho, carry and total columns are rupees for one lot of 65 units, for a one point rise in the rate. The last column converts a quarter point rate move to the number of volatility points that move for the same rupees, using each option's vega.
| Days left | Rho | Carry | Total | Quarter point |
|---|---|---|---|---|
| 48 | −Rs 42 | Rs 1,009 | Rs 967 | 0.11 vol points |
| 20 | −Rs 11 | Rs 415 | Rs 403 | 0.07 vol points |
| 6 | −Rs 2 | Rs 120 | Rs 118 | 0.04 vol points |
Reading the table
Read the second and third columns together. Carry is about 24 times the discounting effect for the 48 day call, so the rate does lift the call once the future follows. A put runs the other way: for the 48 day put the total is −Rs 1,016 a lot. Now read the last column. A move of a quarter point in the rate is about 0.11 of one volatility point for the longest option and less than that for the others. Implied volatility moves by more than that on an ordinary day.
Against a volatility point
Look at the middle row of the grid, where the index does not move. Two points of implied volatility are worth Rs 4,360 a lot, which is about 4.5 times the effect of a full point of the rate. That is the scale that matters.
One point of volatility moves a lot of this call by about Rs 2,180, against Rs 967 for a whole point of the rate
| Index move | Same moment, rupees per lot | ||
|---|---|---|---|
| IV −2 | IV same | IV +2 | |
| −1% | −11,361 | −7,114 | −2,846 |
| 0% | −4,364 | −4 | +4,355 |
| +1% | +3,926 | +8,225 | +12,543 |
Green is profit and red is loss; deeper colour means a larger amount. The outlined cell is the starting point.
Dividends, the other half of carry
The index pays dividends, and the future is priced net of them, so a dividend surprise moves the future against the rate. On 10 Jun 2026 the carry at the T-bill rate for the 20 day future came to 65.0 points, and the future's premium over the index was 25.1. Part of the gap is expected dividends, and an end of day file cannot separate the rest. Rho has no separate input for it. The chains here back the dividend out of the future, so the option sees one forward price and only the sum of rate and dividend matters.
Two terms to hold on to from 14.13
Spreads and parity
Rate effects fade in combinations. A bull call spread buys one call and sells another, and the two rho terms nearly cancel, so the position has almost none. A calendar spread, which trades two expiries, keeps a rate exposure because the two legs have different times left (module I22). For the weekly expiries, which have no future of their own, the forward is read off a call and a put at one strike by put call parity, and that arithmetic uses the rate too (module I05).
The future's premium
The rate also shows up in the future's premium over the index. The chart is the next month premium, annualised, for each close of the series. It is a mix of the rate, expected dividends and demand, and an end of day file cannot separate them, but a large part of it is carry.
The future's annualised premium is the rate and more, and it moves a lot more than the T-bill yield did
The common mistake
The claim: Rho is the Greek to watch before an RBI policy day.
The direct rate effect is small. A quarter point on the 48 day call was about 0.11 of a volatility point. The 24 Feb monthly at the money implied volatility fell 1.9 points, from 15.0% to 13.1%, between 1 and 2 Feb 2026, the Budget weekend. That is about 17 times as large. Around a policy day the index moves prices through delta and implied volatility moves them through vega (module I10). The rate gets in through them and through the future, not as a number of its own. Rho still matters for the longest dated options and for large positions held for months, such as a hedger who rolls long dated puts (module I26). The short answer to Does rho matter in India? has its own page.
Key takeaways
- Rho is the price change for a one point change in the interest rate.
- Black 76 holds the future fixed, so its rho is negative for calls and puts.
- Carry lifts a call and lowers a put, and it is larger than discounting.
- Rate effects grow with time left, so weekly options have almost none.
- A quarter point of rate equals about 0.11 of a volatility point.
- Around policy days, index and volatility move prices more than the rate term.
Where this section sits in module 14.13
Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study