Options planner: the expected move, the real yield and the size in pounds

Expected move and the probability of a level

Implied volatility is an annualised standard deviation of returns. Over T years it scales with √T, and under the lognormal model the site uses, a one-standard-deviation band for the price at expiry runs from S × e^−σ√T to S × e^+σ√T. The band cannot go below zero, and in pence it reaches slightly further above the price than below it, because returns compound. The calculator also accepts an at-the-money straddle price in place of an IV, because a straddle is what a broker screen shows, and it has a panel for the one-day move priced around a results date.

BP at 530p over 60 days: the band, and what two in three means

Model inputs. BP at an illustrative 530p, Monday 17 August to Friday 16 October 2026 (60 days), IV 26%, Bank Rate 3.75%, no dividend (BP's next ex-date, 12 November, falls after this expiry), ICE standard contract of 1,000 shares. These are the calculator's starting values.

σ√T is 0.26 × √(60 ÷ 365) = 10.54%. The one-standard-deviation band runs from 476.97p to 588.92p: 53.03p below the price and 58.92p above it. On one standard contract that is −£530.26 at the lower edge and +£589.21 at the upper edge. The model probability of finishing inside the band is 68.27% (risk-neutral, lognormal, IV 26%), about two times in three; the two-standard-deviation band, 429.25p to 654.39p, holds 95.45%. The daily one-standard-deviation move is 8.68p on 252 trading days a year.

The simpler normal band, S ± Sσ√T, gives 474.13p to 585.87p here, close because σ√T is small. It breaks when σ√T is large. At an IV of 150% over a year it puts the lower edge at −265p, a negative share price, where the lognormal band runs from 118.26p to 2,375.30p; and the normal band would contain the price with a model probability of 91.32% (zero drift, lognormal), not two in three. The calculator shows the normal figure only for comparison, and says when it has gone below zero.

Finishing beyond a level is not the same as touching it

A written 500 put loses at expiry only if BP finishes below 500p, but the price can pass through 500p on the way and recover. That matters to anyone who closes a position when a level is breached, and to a margin account, where the requirement rises as a short put moves into the money. With the inputs above, the model probability of finishing below 500p is 28.82% (about 3 in 10), and of touching 500p at some point before expiry 57.86%. For 580p the figures are 19.78% for finishing above and 39.44% for touching (all risk-neutral, lognormal, IV 26%).

The rule of thumb that touching is about twice as likely as finishing beyond comes from the reflection principle: every path that ends beyond a level must have crossed it, and a path that has just reached the level is roughly as likely to end on either side. Doubling the finishing figures gives 57.65% and 39.56%, close to the exact first-passage values because 60 days of drift at 3.75% is small. The zero-drift setting removes the drift altogether. Delta is a different quantity again, and is not a probability of either kind; the Greeks page shows the gap.

Reading the move off a straddle quote

A screen that shows option prices but no IV still shows the expected move. An at-the-money straddle is worth roughly the average size of the move, and for a normal distribution the average absolute move is √(2/π), about 0.80, of the standard deviation; so one standard deviation is about 1.25 times the straddle. On the model inputs the BP 530 call is worth 23.88p and the put 20.62p, a straddle of 44.50p, or £444.96 for one standard contract of each. 1.25 × 44.50p is 55.62p, against the exact S × σ√T of 55.87p. Typing 44.50 into the straddle field recovers the 26% IV, because the calculator solves Black-Scholes for the volatility rather than applying the rule of thumb. The solve treats both options as European; on an American put the early-exercise value adds a little. The implied volatility page works the same reading on the FTSE 100.

Results day: the move priced into one session

An expiry that spans a results announcement carries extra variance for that day. If σ_f is the IV of that expiry with T_f years left and σ_x the IV the stock usually trades on, the implied one-day event move is √(σ_f² × T_f − σ_x² × (T_f − 1/252)). BP reports third-quarter results on Friday 30 October 2026. Suppose that on Monday 26 October the 20 November expiry, 25 days away, traded at an IV of 30% while the ex-event level was 26%; these are illustrative inputs, not quotes, and they are the panel's starting values. The formula gives a one-day move of ±4.25% (one standard deviation), about ±22.50p, or £225.02 on a standard contract. If the front IV is not high enough for its variance to exceed the ex-event IV's over the same days, there is no event premium to back out, and the panel says so rather than taking the square root of a negative number. The earnings page covers the event premium from the buyer's side and the writer's.

Premium yield: what a written option pays

A premium divided by the capital it ties up looks like a yield, but part of it may be intrinsic value: the writer's own money, handed back on assignment. So the calculator splits the premium first. Its headlines are the time-value yield, after the opening commission, and the maximum return: if a covered call is assigned, or if a cash-secured put expires worthless. The gross premium yield, which counts intrinsic value as income, comes second. Annualised figures are simple (× 365 ÷ days), assume the same trade could be repeated at the same premium, and are withheld for periods under seven days, where multiplying by 365 says little.

Two BP calls with the same 12p of time value

Model inputs. BP at an illustrative 530p, 60 days to Friday 16 October 2026, IV 26%, Bank Rate 3.75%, no dividend in the period, ICE standard contract; premiums are the engine's model values rounded to the 0.25p tick; IBKR UK's tiered commission of £1.40 a contract, charged on the sale and again on a UK assignment (checked 26 September 2026). Bid-ask spread and tax are left out.

Against 1,000 BP shares worth £5,300, the 560 call has a model value of 11.97p, written here at 12.00p for £120.00. All of it is time value, so the time-value yield is 2.24% after the commission, or 13.6% a year on the simple measure. If BP finishes above 560p and the call is assigned, the position makes (560 − 530 + 12) × £10 less two commissions: £417.20, or 7.87%.

The 500 call, 30p in the money, has a model value of 42.03p, written at 42.00p for £420.00: a gross yield of 7.92%, or 48.2% a year. But 30p of it is intrinsic value. Its time value is the same 12.00p as the 560 call's, so its time-value yield is the same 2.24%, and if it is assigned the position makes (500 − 530 + 42) × £10 − £2.80 = £117.20, or 2.21%. The 48.2% is the figure the calculator deliberately puts second: it counts the writer's own 30p as income.

The in-the-money call buys 30p more protection below the price (a breakeven of 488.00p against 518.00p) and gives up 30p more of the upside. Which of those matters more is the writer's judgement; the calculator's job is to stop the protection being counted as income.

The cash-secured put and the cost of assignment

The BP 500 put, American and priced on the binomial tree, has a model value of 9.04p, written at 9.00p for £90.00 against £5,000 of cash held. The time-value yield after commission is 1.77%, which is also the most the put can return, reached if BP finishes above 500p. If it is assigned, 1,000 shares are bought at 500p, or 491.00p a share after the premium. The buyer of UK shares on an exercised option pays 0.5% stamp duty reserve tax on the strike, here £25.00 or 2.50p a share, and IBKR's commission applies to the assignment as well as to the sale, so the effective price is 493.78p. The assignment page explains who pays the SDRT and who does not. The calculator adds both costs for ICE contracts; US shares carry no SDRT, and a FTSE 100 option settles in cash.

Minis: a fixed commission on a small premium

Tesco is one of 22 UK names with a 100-share mini option on ICE; it is listed there, but a reader would need to check that a broker offers it and quotes a two-way price. At a model 450p (Tesco closed at 447.8p on 17 August 2026; price data: Yahoo Finance), IV 22% and 60 days, the 430 put is worth 8.30p on the binomial tree. That includes an assumed 5.08p interim dividend going ex on 15 October: Tesco announces the interim on 8 October 2026, and without the dividend the put would be worth 6.91p. Written at 8.25p, a mini brings in £8.25 and a standard contract £82.50. A £1.70 commission, the model sheet's placeholder for minis because no mini rate is published, is 20.6% of the mini premium; the standard contract's £1.40 is 1.7% of its premium. On the capital tied up, the time-value yield after commission is 1.52% on the mini (£430) against 1.89% on the standard contract (£4,300). The mini makes the position ten times smaller; it does not make it cheaper to run.

Dividends and early assignment

ICE UK stock options are American, so a written call can be exercised on any business day. The holder of a call gains by exercising just before an ex-dividend date when the dividend is larger than the call's remaining time value, and an options intermediary, which has relief from SDRT on the shares, is the holder most likely to act on it. For a covered call the calculator compares the time value in the premium typed with the dividend entered, and flags the case where the dividend is larger: assignment before the ex-date is then likely, and the dividend would go to the exercising holder. For BP, the next ex-date in the model is 12 November 2026 (6.39p assumed; BP sets the amount with its results on 30 October), after the 16 October expiry, so the examples above carry no dividend. The assignment page works the ex-date calculation, including the extra 0.5% a private holder would pay.

How the premium is taxed

In a general investment account, writing an option is a disposal: the premium, less the costs of the sale, is a chargeable gain in the tax year of the grant (TCGA 1992 s144(1)), and it stays there if the option lapses. If the writer buys the option back, the cost of the buy-back reduces that gain (s148). If the shares are called away, s144(2)(a) treats the grant and the sale of the shares as one transaction: the premium is added to the sale proceeds on the exercise date, and any tax already charged on the grant is set off or repaid (HMRC CG12317). If a written put is assigned, the premium reduces the cost of the shares bought (s144(2)(b)). So the 560 call's assigned outcome is not a £120 gain in the grant year plus a separate share gain: it is one disposal of the shares, with the premium in the proceeds. Gains are taxed at 18% or 24% in 2026/27 above the £3,000 annual exempt amount, and the tax worked examples page sets out each case. No ISA can hold an option.

Position size in pounds

The calculator turns a loss per contract into a whole number of contracts. The account is always in pounds, so a US position's dollar loss is converted at a stated exchange rate before it is compared with the budget. Commission is added to the loss per contract (legs × rate, doubled when the closing trade is included). A cash-secured put's collateral can also be capped at a share of the account. A short call or short strangle has no maximum loss, so for those the tool uses the loss at a stated stress move and says plainly that the true worst case is larger. When one contract costs more than the budget, the answer is zero, with the reason.

A FTSE 100 put spread at 1% and at 2%

Model inputs. FTSE 100 at the model 10,750, 60 days to Friday 16 October 2026, IVs from the library's FTSE 100 surface (15.32% at 10,400 and 15.52% at 10,350), Bank Rate 3.75%, dividend yield 3.05% (FTSE Russell factsheet, 28 August 2026), ESX contract at £10 a point, IBKR UK's £1.70 index-option commission. These are the calculator's starting values.

Selling the 10,400 put (model value 119.15 points) and buying the 10,350 put (107.52 points) collects 11.63 points, filled at 11.5 on the half-point tick. The most the spread can lose is (50 − 11.5) × £10 = £385.00; two legs, opened and closed, add £6.80, so the loss per contract is £391.80. On a £20,000 account a 1% budget is £200, and the tool returns zero contracts: one contract risks £391.80, more than the £200 budget. At 2% (£400) it returns one contract, using £391.80, or 1.96% of the account, with £8.20 unused. The 1% and 2% bands are the library's own round numbers, recorded with their origin on the methods page; they are teaching conventions, not findings.

Standard or mini: Tesco puts against a 5% collateral line

Take the Tesco 430 put written at 8.25p, on the same £20,000 account, with the budget and the collateral cap both set at 5% (£1,000) and the opening commission only. A standard contract ties up £4,300 of collateral and would lose £4,218.90 if Tesco went to zero, so the tool returns zero contracts. A mini ties up £430 and would lose £423.45, so it returns two, using £860 of collateral and £846.90 of the budget, 4.23% of the account. The stress line shows the loss after an instant 20% fall to 360p: £63.45 a mini, against £618.90 a standard contract. Sizing still uses the loss to zero, because a share can fall further than any scenario.

No maximum loss: a stress figure instead

A short FTSE 100 strangle that sells the 10,000 put (51.11 points on the surface, IV 16.89%) and the 11,500 call (16.75 points, IV 11.30%) collects 67.5 points after each leg is rounded to the tick. There is no maximum loss to size against, so the tool uses a scenario: the index 10% away at expiry, 9,675 or 11,825, where the position loses (325 − 67.5) × £10 = £2,575.00, plus £6.80 of commission: £2,581.80 a contract, against a 2% budget of £400. An instant move of the same size marks a larger loss, because time and volatility are still in the options: on the entry day, with every volatility unchanged, the strangle is marked at −£3,841.62 after a 10% fall and −£3,555.58 after a 10% rise. The tool's figure is a floor for the stress loss, not the stress loss itself. The tool returns zero contracts on the stress figure and adds that the true worst case is larger and that the broker sets the margin. The Level 3 page has the history of one-day gaps and the stress-test method.

US contracts: convert, then size

Take a hypothetical US share at $100 (not a real company), 45 days, IV 30% and the model sheet's US rate of 3.625%. On the binomial tree the 95 put is worth $1.95 and the 90 put $0.77, priced at $1.95 and $0.75 on the $0.05 tick, so the 95/90 put spread collects $1.20. Its maximum loss of $380 a contract is £280.26 at an illustrative $1.3559 per £1 (ECB reference-rate cross, 17 August 2026); IBKR's $1.00 order minimum applies to each leg of a combination order, so on one contract a leg its $0.65 rate becomes $1.00: two legs opened and closed add $4.00, or £2.95. At £283.21 a contract, a 2% budget of £400 allows one contract. At $1.25 per £1 the same spread would cost £307.20 a contract: the budget still holds, but the pound loss moves with the exchange rate even when the dollar loss does not. The US options page covers trading in dollars from the UK.

Portfolio heat

Heat is the total that open positions could lose if each reached its maximum loss, or its stress loss, at the same time, as a share of the account. Entering the open risk already carried gives the heat after the new trade. It is a blunt measure: it treats every position as losing at once, which overstates the risk of unrelated positions, and it understates a correlated book whose stress losses were set too low. The position-sizing page discusses limits on heat and on exposure to one underlying.

Strategy page finder

The finder lists the strategy pages whose descriptions match seven inputs: outlook, objective, where implied volatility sits in its own past year, the course level reached, assignment, horizon and capital style. It scores 25 of the library's 26 strategy pages; the uncovered short call is never listed. The output is a reading list, the closest strategy pages to read, ranked by how closely each page's description fits the inputs. It matches descriptions, not suitability, and knows nothing about an account, its owner's experience or aims beyond the seven answers.

How the description score is built

Each page carries a short description of the conditions its structure is built for. The finder compares the seven inputs with those descriptions and adds up points out of 21. The table is the whole rubric.

Four rules sit on top of the points. Pages above the level chosen are not listed, and the uncovered short call is never listed. A page whose structure is built for the opposite direction is left out, so a bullish search does not return a bearish credit spread. Only pages that list the objective are shown, with a count when fewer than three do and a note of how many more sit at a higher level; if no page at the chosen level lists it, the finder shows the nearest descriptions on the other inputs and labels them as such. Ties go to the higher outlook score, then the lower level, then the page name. For a hedge, the outlook describes the shares being protected, so it is not used to rule pages out, and only pages that describe a hedge are listed.

Three searches, and why they return what they do

Bullish, collecting premium, IV high, Level 2, closed before assignment, two to eight weeks, capital-efficient. The bull put spread scores 19 of 21 (it loses two outlook points because its description is mildly bullish to neutral), then the poor man's covered call and the diagonal spread at 16. The bear call spread is not listed: it is built for a neutral to mildly bearish view.

Protecting shares already held, at Level 2, with the other inputs at their starting values. The bear put spread scores 21 of 21, the long put 19 and the collar 17, whatever the outlook: the long put and the collar are Level 1 pages, so each takes one level point of three, and the collar's full-collateral description takes no capital points against a capital-efficient answer. With the capital style set to full collateral, the collar and the bear put spread score 19 and the long put 17. Pages that add exposure, such as the cash-secured put, are not listed. At Level 1 only the long put and the collar appear, with a note that one more hedge page, the bear put spread, sits at Level 2.

Volatility, split in two. "Large move either way" lists the long straddle and long strangle, and at Level 3 the backspread too unless the outlook is bullish, because the library's backspread example is built for a fall. "Price stays in a range" draws on the iron condor, the iron and long butterflies and the calendar spread, and at Level 3 also on the broken wing butterfly, short straddle, short strangle and jade lizard; as in every search, only the three closest descriptions are shown. The IV input follows the usual pairing: the large-move pages score for the low and middle parts of the range, and the credit structures among the range pages for the middle and high parts, while the calendar spread and long butterfly, both bought for a debit, score for the lower part. Where the example pages sit in their own 12-month range is explained on the implied volatility page.

Levels, broker permissions and the uncovered short call

The level input filters. Level 1 holds the five structures whose worst case is fixed by the premium or covered by shares or cash; Level 2 adds the defined-risk multi-leg structures and the time spreads; Level 3 adds structures with uncovered or asymmetric risk. The level pages frame each step as a self-check, not a requirement. Brokers run their own permission ladders, which do not line up one for one with the course's levels: at Interactive Brokers, uncovered calls and short straddles and strangles sit at the top options level, and portfolio margin is a separate, optional account type rather than the permission itself (IBKR guides, checked 26 September 2026). The Level 1 page maps the two.

The uncovered short call is taught last in the curriculum and, by design, the finder never lists it. The short straddle and short strangle, which also carry an uncapped loss if the price rises, appear only when Level 3 is chosen, under a warning. The uncovered call's own page explains the mechanics for readers who arrive there deliberately.