Implied volatility, worked in pounds

Implied volatility is a price, written as a percentage

An option quote in pence or points hides one number the market never states directly: the volatility that makes a pricing model return that quote. That number is the implied volatility (IV). This page works through what it measures, how broker screens rank it, how it varies by strike and by expiry, and what it has and has not told UK investors about future movement, with every figure in pounds.

Put formally, IV is the volatility input that makes the model price match the market price. Everything else in the pricing model is observable on the day: the share price, the strike, the days to expiry, Bank Rate and any dividend expected before expiry. Only the future volatility is unknown, so the market's price for the option is, in effect, its price for volatility. Two options on the same share can then be compared on one scale even when their premiums differ by a factor of ten.

The BP October 530 call at five volatilities

Model inputs. BP at 530p (a model level; BP closed at 519.6p on 17 August 2026), Monday 17 August 2026 to Friday 16 October 2026 (60 days), strike 530p, Bank Rate 3.75%, no dividend (the next ex-date, 12 November 2026, falls after expiry), ICE standard contract of 1,000 shares (£10 per 1p of premium). An American call with no ex-date in its life is priced with Black-Scholes-Merton. BP is used as a model underlying; this is not a view on BP.

At the model sheet's 26% the call is worth 23.88p, or £238.77 a contract. Change nothing but the volatility and the value moves almost in a straight line:

The slope of that line is vega: 0.85p per volatility point here, which is £8.52 a contract. Running the model backwards is how a screen gets its IV column. On the 0.25p tick nearest the model value, 24.00p, the solver returns 26.14%. If the mid-price were 28.00p instead, the IV that reproduces it is 30.84%: the extra 4.12p is roughly 4.8 points of vega. A quote is a volatility, and a volatility is a quote.

The pound figures scale with the contract. ICE lists a 100-share mini option on 22 large UK names (BP is not one of them), where every pound figure above would be one tenth as large, so vega of 0.85p would be £0.85 a contract; a mini is listed on ICE, but whether a broker offers it and quotes a two-way price has to be checked. Contract sizes are set out on the basics page, and the Greeks themselves, with their units, on the Greeks page.

Historical volatility from ten closing prices

Historical (or realised) volatility is the backward-looking cousin: the annualised standard deviation of daily log returns, ln(P_t/P_t−1), using the sample formula (dividing by n − 1) and multiplying by the square root of 252 trading days. Take the eleven closes 100, 101, 99.5, 102, 101.5, 103, 102.2, 104, 103.1, 105 and 104.4. The ten daily returns run from −1.50% to +2.48%; their sample standard deviation annualises to 22.45%. The last five returns alone give 22.04%.

Two measures of "volatility" can therefore disagree for honest reasons. Historical volatility describes a window that has closed, and it depends heavily on the window: BP's 20-day realised volatility ranged from 14.9% to 57.5% in the twelve months to 17 August 2026 (price data: Yahoo Finance). Implied volatility is a price set now for the life of one option. The section on the volatility risk premium compares the two over 26 years of FTSE 100 data.

IV rank and IV percentile: one reading, two very different numbers

A level such as 26% means little on its own: it can be high for one underlying and low for another. Broker screens that show IV therefore often set today's reading against that underlying's own past year, in one of two ways:

• IV rank = (IV now − lowest IV) ÷ (highest IV − lowest IV) × 100. It measures position within the range.
• IV percentile = the share of past readings strictly below IV now × 100. It measures how often IV has been lower. This page excludes ties, as the site engine does; platforms differ on ties and on how many days they look back, so two screens can print different figures for the same option.

With a smooth history the two numbers move together. Take the ten readings 18, 20, 22, 25, 30, 35, 28, 24, 21 and 19. At a reading of 24 the rank is 35.29% and the percentile 50%; at 34, the rank is 94.12% and the percentile 90%.

The spike case: rank 9.52%, percentile 80%

One extreme day breaks the link. In the series 18, 18, 19, 19, 20, 20, 21, 21, 22 and 60, a reading of 22 has an IV rank of (22 − 18) ÷ (60 − 18) = 9.52%, yet eight of the ten readings are below it, an IV percentile of 80%. By rank, IV looks near its floor; by percentile, it is higher than on most days in the window. Neither is wrong. The rank is dominated by the single 60 reading, and when that day leaves a 12-month lookback, the same 22 becomes a rank of 100% (with a percentile of 88.89% on the nine readings left) without IV moving at all.

Chart: the ten readings as a histogram, with dashed markers at the low (18%) and the high (60%). The marker for today's 22% sits about a tenth of the way from the low marker to the high marker (its rank), while eight of the ten readings stand to its left (its percentile). If every reading in a window is the same, the range is zero and the rank cannot be calculated: the formula would divide by zero, so a calculator reports "range is zero" rather than a number.

BP on the model sheet: rank 25%, and what 38% would have paid

Every BP example in this library uses one assumed 12-month range for at-the-money IV, from 20% to 44% (a model assumption, not market data). The model sheet's 26% therefore sits at an IV rank of (26 − 20) ÷ (44 − 20) = 25%. The rank matters only through what it does to premiums, so here it is in pounds, on a BP October 500 put (60 days, American, priced on a 200/201-step binomial tree):

A writer of that put would have collected about twice the premium at rank 75% as at rank 25%, and a buyer would have paid twice as much, for the same strike and date. What the table cannot say is which price was the better one: the higher premium is compensation for a market that expects larger moves, and it is paid for exactly the outcomes that make a 500 put expensive to have written.

The IV rank and historical volatility lab

The lab below takes a pasted list of daily IV readings (or a typed 52-week high and low) and, optionally, a list of closing prices. It returns the rank and the percentile side by side, historical volatility over 10, 20 and 60 days where the data allows, and the gap between IV and historical volatility. It starts with a synthetic series, labelled as such, so the spike lesson works before any data is entered. Nothing typed leaves the page.

What the library's IV bands are, and what the evidence says

Strategy pages in this library say where each worked example sat in its 12-month range, for instance "IV rank 25% on the model sheet's range", and what a different IV would have paid, in pounds. They do not set IV-rank thresholds for opening or avoiding a trade. The teaching bands that appear in US retail options education (selling premium only above a set rank, buying below another) are recorded on the methods page with their origin, as conventions.

Their evidence status is thin. The spike case shows how much the rank depends on the lookback window and on one day. The measure also depends on which IV is ranked (a 30-day constant-maturity figure or the front month's at-the-money option), and a results date inside the front month inflates it for reasons that disappear the next morning. We could not find a public, independently tested study showing that a fixed IV-rank threshold, on its own, produces a profit after costs (checked 27 September 2026). What public data does show, in the FTSE 100 record below, is that implied volatility has averaged more than realised volatility over long periods, which is a statement about averages, not a rule for any single trade.

How big a move the price already assumes

IV converts into a range of prices. Under the lognormal model the site uses, a one-standard-deviation band for expiry is S × e^±σ√T, where σ is the IV and T the years to expiry. The band never goes below zero, unlike the simpler S ± Sσ√T, and it is skewed slightly upwards in points because returns compound. It is a description of the price, not a forecast: the model probability (lognormal, zero drift) of finishing inside a one-standard-deviation band is about 68%, and of finishing outside it about 32%.

FTSE 100: the one-standard-deviation band for 16 October

Model inputs. FTSE 100 at 10,750 (a model level; the index closed between about 10,600 and 10,900 in August and September 2026), Monday 17 August 2026 to Friday 16 October 2026 (60 days), at-the-money IV 14.0% from the model surface, Bank Rate 3.75%, dividend yield 3.05% (FTSE Russell factsheet, 28 August 2026), ICE FTSE 100 index option (ESX) at £10 a point, European, cash-settled.

With σ = 14% and T = 60/365, σ√T is 5.68%. The one-standard-deviation band runs from 10,156.80 to 11,377.84, with a model probability (lognormal, zero drift, IV 14%) inside it of 68.25%; the two-standard-deviation band runs from 9,596.34 to 12,042.35 (95.44%). In round terms the move is S × σ√T = 610.19 points, or £6,101.91 at the ESX contract's £10 a point. The daily equivalent, S × σ ÷ √252, is 94.81 points.

Reading the move off the straddle

A screen that shows prices but no IV still shows the expected move. An at-the-money straddle (a call plus a put at the same strike) is worth about 0.8 × S × σ√T, because √(2/π) ≈ 0.798, so one standard deviation is about 1.25 times the straddle. On the model sheet the October 10,750 call is worth 248.24 points and the put 235.94 points, a straddle of 484.18 points, or £4,841.83 for one call and one put. Multiplying by 1.25 gives 605.23 points against the exact 610.19: the rule of thumb is close, not exact, because interest and dividends move both option values and because 1.25 is a rounded 1.2533. The expected-move calculator on the planner does the same sums on a reader's own numbers.

A dollar example: a $150 US share

Model inputs. A hypothetical US share at $150 (not a real company), 30 days, IV 30%, US rate 3.625% (the model sheet's midpoint of the Federal Reserve's 3.50%-3.75% range in force on 17 August 2026), no dividend, 100-share contract, at an illustrative $1.3559 per £1 on 17 August 2026 (ECB reference-rate cross); use your broker's rate.

US share options are American, so the put is priced on the binomial tree. The at-the-money call is worth $5.36 and the put $4.95, a straddle of $10.31 a share. On 100-share contracts that is $1,031.07, or £760.43 at the illustrative rate. The one-standard-deviation band runs from $137.64 to $163.47; the move of $12.90 a share is $1,290.11 across 100 shares, or £951.48, and 1.25 times the straddle again lands close to it. For a UK holder the pound figure moves with the exchange rate as well as the share. The US options page covers trading in dollars from the UK, and the tax page sets out the rule that converts each leg at its own date's rate.

Skew: why the 10,250 put is priced at 15.9% and the 11,250 call at 12.2%

If the pricing model were a complete description of markets, every strike on one expiry would share one IV. It is not, and they do not. On equity index options such as the FTSE 100, lower strikes usually carry higher IV: the pattern called skew. Every FTSE 100 page in this library uses one fixed model surface, IV(K) = 14.0% − 0.40 × ln(K / 10,750), so that the pages agree with each other. It was fitted to the quotes on the library's own 10,750 pages and rounded; it is a model assumption, not market data.

Chart: the model surface across strikes from 9,750 to 11,750 for the 16 October 2026 expiry, against a flat 14%. The two lines cross at the 10,750 model level.

What skew does to the price of protection, in pounds

The table prices the out-of-the-money option at each strike (puts below 10,750, calls above) on the surface and on a flat 14%, with the model inputs above. The difference is what skew adds to, or takes from, one contract.

Protection below the market costs more than a flat-volatility model says: the 10,250 put is worth 87.29 points (£872.92) on the surface against 64.06 points (£640.55) flat, so skew adds £232.37 to one contract. Upside calls cost less: the 11,250 call is £226.64 cheaper than a flat model would price it. A collar buys its put on the expensive side of the surface and sells its call on the cheap side; a put spread sells a lower strike that carries more IV than the strike it buys. That is why the collar, ratio spread and jade lizard pages price each strike at its own IV rather than at one IV for the whole expiry.

What skew does to the model probabilities

The probabilities in the table are model probabilities (risk-neutral, lognormal, from the skew surface), taken from the slope of the option price across strikes rather than from one flat-volatility formula. Skew moves probability in two directions at once. It adds weight to large falls: the probability of finishing below 10,000 rises from 10.28% flat to 11.18%. It removes weight from small falls and from large rises: the probability of finishing below the 10,750 model level falls from 50.32% to 43.85%, and of finishing above 11,500 from 11.58% to 9.28%. A risk-neutral distribution with put skew has a fatter left tail and more of its weight a little above the current level. That is also why delta is not a probability: the 10,250 put's delta of −0.21 is not the 18.47% the surface gives for finishing below 10,250.

Why FTSE 100 options carry a put skew

Two forces are usually cited, and the second can be seen in public data. First, demand: holders of UK equity portfolios buy index puts as protection, and the writers of those puts charge for carrying the risk of a crash. Second, volatility tends to rise when the index falls. FTSE Russell's factsheet for its FTSE 100 Implied Volatility Index reports the correlation between the 30-day index and the FTSE 100 level as negative on average in every year shown, at −0.60 on average since 2000 (data as at 30 June 2026; values before the index's launch in February 2013 are back-calculated). A put that pays off in a fall also pays off in the higher-volatility market that tends to come with it. For single UK shares the shape varies by company and around events; we could not find a free public source of skew data for ICE single-stock options (checked 27 September 2026), so the chain on a broker platform is the practical place to look.

Term structure: 30-day against 360-day volatility

IV also varies by expiry. The line joining the at-the-money IVs of successive expiries is the term structure. When longer expiries carry higher IV, the curve slopes upward; when the front month is higher, it is inverted. It matters most to structures that own one expiry and sell another: the calendar, the diagonal and the poor man's covered call, whose results depend partly on the two IVs moving differently.

Five tenors of the FTSE 100 IVI

FTSE Russell publishes the FTSE 100 IVI at five fixed tenors, 30, 60, 90, 180 and 360 days, which makes the UK index's own term structure visible. Its factsheet (data as at 30 June 2026) gives each tenor's average, high and low by calendar year, in volatility points.

On average the curve slopes gently upward: in 2025 from 13.55 at 30 days to 15.68 at 360 days. The highs tell the other half of the story. The 30-day index reached 37.92 in 2025 while the 360-day index peaked at 21.78, and since 2000 the highest 30-day reading, 84.82, is almost twice the highest 360-day reading, 43.84. The highs of different tenors need not fall on the same day, but the arithmetic still says something: on the day the 30-day index reached 84.82, it stood at least 40.98 points above the 360-day index, whose highest reading ever was 43.84. Short-dated IV does most of the moving, and in a sell-off the curve inverts. A calendar spread that is long the back month and short the front month is exposed to exactly that change of shape.

A results date inside one expiry: BP on 30 October

Single shares add a bump for scheduled events. BP reports its third-quarter results on 30 October 2026, which falls inside the November expiry (Friday 20 November, 95 days from 17 August) but not the October one. If, for illustration, the November options were priced at 28% while October stayed at the model sheet's 26%, the extra variance in November would imply a results-day move of √(0.28² × 95/365 − 0.26² × (95/365 − 1/252)) = 5.55%, about 29.41p on 530p. Both IVs in that sum are assumptions chosen to show the arithmetic; the earnings page treats event premium and the fall in IV after results from both sides.

Implied against realised: the volatility risk premium

If implied volatility were an unbiased forecast of realised volatility, the two would average out at about the same level over long periods. In the FTSE 100 record below, the average implied level has been above the average realised level in every period shown. The gap is usually called the volatility (or variance) risk premium, and it is usually read as what option buyers pay, on average, for protection against the periods when realised volatility jumps.

The FTSE 100 record since 2000

FTSE Russell's factsheet for the FTSE 100 IVI (data as at 30 June 2026) sets the average level of the 30-day and 90-day index against the FTSE 100's realised volatility, year by year, in volatility points:

In every period in the factsheet the average 30-day implied figure is above the average realised figure, by 2.88 points since 2000 and 3.84 points in the year to June 2026. Three limits apply. These are averages of daily readings, and an average hides the days when realised volatility overtook implied, which are the days that decide a short-option position. The index figures before February 2013 are back-calculated by FTSE Russell, not observed. And an index of volatility says nothing about the costs, the strikes or the sizing of any trade. The data describe the price of volatility; they do not make selling it a reliable income.

The gap in pounds per day: a delta-hedged BP call

For an option whose delta is hedged with shares, the day's profit or loss depends on how realised variance compares with implied variance. Ignoring the interest terms, it is approximately ½ × Γ × S² × (σ_realised² − σ_implied²) × (1/365) for the holder, and the same with the sign reversed for the writer. On the BP 530 call above (gamma 0.00710 per share per 1p, which is 71 share-equivalents of delta per 10p on one contract; implied 26%), one contract of 1,000 shares gives:

When realised equals implied, the gains from re-hedging (gamma) pay for the time decay (theta), and the position stands still. The same formula gives the theta itself as ½ × Γ × S² × σ² ÷ 365, or −£1.85 a day here, against the full model theta of −£2.12 once interest is included. Because the formula works in variance (volatility squared), a rise in realised volatility counts for more than an equal fall: 6 points below implied costs the holder £0.75 a day, while 6 points above, at 32%, earns £0.95 (and 9 points above, at 35%, £1.50), and realised volatility has no upper limit. This is the mechanism behind the averages in the table above, and the reason a short-volatility position can give back months of small gains in a few days.

When the FTSE falls 250 points, what happens to each strike's IV?

A skew describes one day. When the index moves, the model has to say how the surface moves with it, and two simple rules bracket the answer.

• Sticky strike: each strike keeps its own IV. After a fall, the 10,500 put still carries the 14.94% it had at 10,750.
• Sticky moneyness (close to what is often called sticky delta): IV follows the distance from the current level. After a fall to 10,500, the 10,500 put is at the money and takes the at-the-money 14.0%.

This library prices every FTSE page on sticky strike, and where a stress row needs volatility to rise it adds a stated parallel shift to every strike. That keeps the pages consistent with one another (the ratio spread and backspread pages, mirror images priced on the same 10,750 surface, both use it), and it is explained once, here.

Three answers for the 10,500 put

The October 10,500 put, 60 days, model inputs as in the expected-move example, is worth 145.82 points (£1,458.19) at entry on the surface. Now let the index fall instantly to 10,500:

The rule chosen is worth £158.86 on one contract, the gap between the sticky-strike and sticky-moneyness rows, and a writer of the put would feel every pound of it. Neither rule is how markets behave in a fall. The negative correlation in the FTSE Russell data means implied volatility, as the IVI measures it, has tended to rise as the index drops, which neither sticky rule captures on its own; that is why the stress tables on the Level 3 page and on the short-volatility strategy pages add an explicit IV rise, and why the library's stress rows look like the last row of this table.

The FTSE 100 IVI, the VIX and where a UK reader finds IV

A volatility index turns a whole chain of option prices into one number for a fixed horizon. Neither index below uses a single at-the-money option; both combine out-of-the-money puts and calls across many strikes from the two expiries either side of the target horizon, so the skew contributes to the result.

An index level of 14 means 14% annualised volatility, so the IVI and the IV of a FTSE option can be compared directly, with one caution: the 30-day IVI is a blend across strikes, while an at-the-money option's IV is one point on the skew. Neither index can be bought. The VIX has listed futures (from March 2004) and options (from February 2006) on Cboe markets; we could not find a listed derivative on the FTSE 100 IVI (checked 27 September 2026). The name VFTSE also appears on data sites: Euronext lists an index called FTSE 100 Volatility (symbol VFTSE) on its Amsterdam index pages, but we could not confirm its methodology or that it is still calculated (checked 27 September 2026). The FTSE 100 IVI is the UK index with a published rulebook.

For a single ICE option, the practical source is the chain on a broker platform that offers the contract. Platforms compute IV with their own models, rate and dividend inputs and prices (bid, ask, mid or last), so two platforms can show different IVs for the same quote, and the same platform can differ from the solver on this site. We could not find a free public source of implied volatility for ICE UK single-stock options or for individual FTSE 100 options, beyond FTSE Russell's IVI factsheet (checked 27 September 2026).

Pages that put these ideas to work

Each of these pages applies one part of this page to a specific structure, with its own numbers:

How these numbers are calculated

Self-check: ten questions with the working

Not scored. Each answer uses only this page's model inputs.