---
title: "Rho and Interest Rates in Nifty Options, Explained"
description: "Rho on dated NSE Nifty chains: why Black 76 rho is negative for a call, how carry lifts it back, and why the rate effect is small next to vega."
source_url: "https://www.rupeecase.com/learn/path-14/module-14-13-rho"
---

[Path 14 13 of 17](/learn/path-14/)Rho and interest rates in Indian options[Next 14.14](/learn/path-14/module-14-14-position-greeks)

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

1. Say why Black 76 rho is negative for a Nifty call and the textbook rho is positive.
2. Add the discounting and carry effects to get the total rate effect.
3. Compare a rate move with a volatility move in rupees.

Watch in the terminal: why do the hero, key figure and XIRR differ? A short tutorial on sample data.

## 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](/learn/path-13/module-13-2-futures-basis-and-carry) 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

From the module glossary; every term is in the Learn glossary too. Source: Module 14.13, Rho and interest rates in Indian options.

### 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

Black 76 rho of the 23,350 call per lot of 65 units for a one point rise in the rate, at the volatility of the 10 Jun 2026 chain of the 28 Jul expiry. This is the discounting effect only. The carry effect works in the other direction and is larger. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.

## 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.

Watch in the terminal: how bumpy was the ride? A short tutorial on sample data.

### 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.

One lot of the 23,350 call repriced the same day with Black 76. The middle row, an unchanged index, shows vega alone: roughly Rs 2,180 for each volatility point. The rate effect in the table above is Rs 967 for a full percentage point, and a quarter of that for a quarter point. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.

### 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

From the module glossary. Source: Module 14.13, Rho and interest rates in Indian options.

### 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](/learn/path-17/module-17-9-option-calendar-spreads)). 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](/learn/path-14/module-14-10-put-call-parity)).

### 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

Next month Nifty future less the index close, as a simple annualised percentage of the index, at each close from 1 Jul 2025 to 29 Jun 2026. Carry, expected dividends and demand all feed it. The premium is what the rate acts on in an option price. Source: NSE end of day data, computed by RupeeCase. As of 29 Jun 2026.

## 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](/learn/path-14/module-14-12-vega)). 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](/learn/path-17/module-17-13-hedging-with-nifty-puts)). The short answer to [Does rho matter in India?](/learn/questions/does-rho-matter) 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

Sections 1 to 4 of 4; the highlighted one is next. Source: Module 14.13, Rho and interest rates in Indian options.
**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](https://www.sebi.gov.in/reports-and-statistics/research/aug-2026/study-profitability-of-individual-traders-in-the-equity-derivatives-segment-fy25-fy26-_103835.html)

What does Rho and interest rates in Indian options cover?Rho is the rate Greek. On Nifty options the sign depends on what you hold fixed, and the size is small next to vega. It works through The idea, plainly, Worked example: three expiries, 10 Jun 2026, The common mistake, Key takeaways. It is module 14.13 of Path 14, Options and Greeks, about 8 minutes of reading, free.

TTry it

## Greeks calculator, on the same example.
Delta to rho, and vanna to colour in expert mode, from one Black 76 engine. Dated NSE end of day data, nothing live, no orders.

**Greeks calculator**, Nifty, 10 Jun 2026, 28 Jul 2026 expiry.

[Open the greeks calculator](/learn/tools/greeks-calculator?chain=NIFTY_2026-06-10_2026-07-28)

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QQuick check

## 10 questions, 7 to pass.
Each attempt draws 10 of the 15 questions in this module's bank, and a retake draws a fresh set. A pass gives this module's Certificate of Completion. Your result stays on this device and counts towards the Path 14 certificate.

7 of 10 correct passes module 14.13

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CCheck yourself

## Path 14 so far.
Your quick check results on this device, stop by stop.

Stop 13 of 17 on Path 14

Options and Greeks: every live stop, this module ringed. Source: RupeeCase Learn, Path 14.

1. [14.1The call option, told as a storyNot yet](/learn/path-14/module-14-1-call-option-explained)
2. [14.2The put option, told as a storyNot yet](/learn/path-14/module-14-2-put-option-explained)
3. [14.3Buyer or seller: payoffs, margin, win rate and expectancyNot yet](/learn/path-14/module-14-3-option-buyer-vs-seller)
4. [14.4Moneyness, intrinsic value and time valueNot yet](/learn/path-14/module-14-4-moneyness-intrinsic-and-time-value)
5. [14.5Five things that move an option's priceNot yet](/learn/path-14/module-14-5-what-moves-an-option-price)
6. [14.6Expiry and settlement: cash, physical, exercise and STTNot yet](/learn/path-14/module-14-6-expiry-and-settlement)
7. [14.7Delta: speed, hedge ratio and the probability shortcutNot yet](/learn/path-14/module-14-7-delta)
8. [14.8Theta: the time decay curve into expiryNot yet](/learn/path-14/module-14-8-theta-time-decay)
9. [14.9From a binomial tree to Black Scholes and Black 76Not yet](/learn/path-14/module-14-9-binomial-tree-to-black-76)
10. [14.10Put call parity and synthetic positionsNot yet](/learn/path-14/module-14-10-put-call-parity)
11. [14.11Gamma: why it grows so fast near expiryNot yet](/learn/path-14/module-14-11-gamma)
12. [14.12Vega: volatility exposure across weekly and monthly expiriesNot yet](/learn/path-14/module-14-12-vega)
13. [14.13Rho and interest rates in Indian optionsNot yet](/learn/path-14/module-14-13-rho#quiz)
14. [14.14Position Greeks for multi leg strategiesNot yet](/learn/path-14/module-14-14-position-greeks)
15. [14.15Dynamic delta hedging and the P&L identityNot yet](/learn/path-14/module-14-15-delta-hedging)
16. [14.16Gamma scalpingNot yet](/learn/path-14/module-14-16-gamma-scalping)
17. [14.17Second order Greeks: vanna, volga, charm, speed and colourNot yet](/learn/path-14/module-14-17-second-order-greeks)
18. [TPath test, 30 questionsNot yet](/learn/path-14/module-14-17-second-order-greeks#pathTestSection)

Path 14 in reading time: 149 minutes over 17 modules

Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 14.

    Explore next

## Put the module to work.

* [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder)
* [Free module 13.2Why futures trade above spot: basis, carry and convergence8 min read](/learn/path-13/module-13-2-futures-basis-and-carry)
* [Free module 14.7Delta: speed, hedge ratio and the probability shortcut8 min read](/learn/path-14/module-14-7-delta)
* [Free module 14.12Vega: volatility exposure across weekly and monthly expiries9 min read](/learn/path-14/module-14-12-vega)
* [Free module 14.9From a binomial tree to Black Scholes and Black 769 min read](/learn/path-14/module-14-9-binomial-tree-to-black-76)
* [Free module 14.10Put call parity and synthetic positions9 min read](/learn/path-14/module-14-10-put-call-parity)

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SSources

## Go to the source.
7 sources, NSE the most cited

The publisher of each source listed below. Source: Module 14.13 source list.
1. [NSE, equity derivatives contract specifications (European exercise, lot sizes, expiry days)](https://www.nseindia.com/static/products-services/equity-derivatives-contract-specifications) NSE
2. [NSE Clearing, settlement price of futures and options](https://www.nseclearing.in/clearing-settlement/equity-derivatives/settlement-price) NSE
3. [SEBI Investor, Understanding derivatives](https://investor.sebi.gov.in/understanding_derivatives.html) SEBI
4. [NISM, Series VIII Equity Derivatives certification examination: test objectives](https://www.nism.ac.in/revamp-nism/test-objectives-revised-nism-series-viii-equity-derivatives-certification-examination/) NISM
5. [Black, F. (1976), The pricing of commodity contracts, Journal of Financial Economics](https://ideas.repec.org/a/eee/jfinec/v3y1976i1-2p167-179.html) Paper
6. [Black, F. and Scholes, M. (1973), The pricing of options and corporate liabilities, Journal of Political Economy](https://ideas.repec.org/a/ucp/jpolec/v81y1973i3p637-54.html) Paper
7. Hull, J., Options, Futures, and Other Derivatives, Pearson (the Greek letters) Book

GTerms

## 4 terms from this module.
RhoThe change in an option's price for a one point change in the interest rate. Black 76 rho shows only the discounting effect, since it holds the future fixed.
Cost of carryThe amount by which the future exceeds the spot index because of the interest to hold the index, less expected dividends. A higher rate raises it.
DiscountingValuing a payoff that arrives at expiry in today's rupees. A higher rate makes the same payoff worth less today.
Risk free rateThe rate used in the pricing model for the time to expiry. These pages take it from government T-bill yields on the example date.
[All 230 terms in the glossary](/learn/glossary)

[Question people askDoes rho matter in India?A short answer with a dated chart](/learn/questions/does-rho-matter)[Question people askWhat are option Greeks (Greeks kya hai)?A short answer with a dated chart](/learn/questions/what-are-option-greeks)[Related module13.2 Why futures trade above spot: basis, carry and convergence8 min, Beginner](/learn/path-13/module-13-2-futures-basis-and-carry)[Related module14.7 Delta: speed, hedge ratio and the probability shortcut8 min, Beginner](/learn/path-14/module-14-7-delta)[Pillar guideDerivatives and Quant115 modules across paths 12 to 19](/learn/derivatives)

Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.