Covered Call and Cash Secured Put Income Calculator

Purpose and model boundary

This calculator works out the income and the risk of selling one option for its premium: a covered call, where you own the shares and sell a call on them, or a cash-secured put, where you hold enough cash to buy the shares at the strike and sell a put. You enter the strategy, the share price today, the strike, the premium per share, the days to expiry and the shares covered, and, for the chances, the implied volatility, the risk-free rate and the shares' dividend yield. The main result is the premium you receive. The page also shows the best-case return and the return if the price does not move, both made yearly, the chance the option ends in the money, your break-even share price and your best case at expiry, with your profit or loss for every share price at expiry and the chance the price ends in each range.

Every figure on this page is computed by the spreadsheet; the page adds nothing to it. The option's model value, d1 and d2 use the same Black-Scholes formulas, term for term, as the Option Pricing Binomial Black Scholes Greeks Calculator, which also gives the Greeks; for the income a dividend stock pays over the years, use the Dividend Growth Yield on Cost Calculator.

The chances are the risk-neutral odds that the option's price implies, not a forecast of where the shares will go. The model is educational. It is not financial, investment, tax or legal advice.

Inputs and units

• Strategy: Covered call or Cash-secured put.
• Share price today, strike price and premium received per share, in dollars with at most four decimal places. The share price and the strike run from 0.01 to 1,000,000 and the premium from 0 to 1,000,000. The premium must be less than the share price for a covered call, or less than the strike for a cash-secured put.
• Days to expiry, a whole number of calendar days from 1 to 730.
• Shares covered, a whole number from 100 to 10,000,000; one option contract usually covers 100 shares.
• Implied volatility, from 1% to 300% a year: the volatility the option's market price implies.
• Risk-free rate and dividend yield of the shares, each from 0% to 20% a year, continuously compounded. They enter only the chances and the model value of the option, not your profit or loss.

Every input is required. Money is in US dollars; volatility, rates and yields are yearly percentages.

Governing relationships

Write S for the share price today, K for the strike, p for the premium per share, n for the shares covered, D for the days to expiry, σ for the implied volatility, r for the risk-free rate and q for the dividend yield, with T = D / 365 years.

• The premium you receive is p × n.
• Your profit or loss at expiry, per share, when the price then is x: for a covered call, min(x, K) − S + p; for a cash-secured put, p − max(K − x, 0). The page multiplies by the shares covered.
• The break-even is S − p for a covered call and K − p for a cash-secured put. The best case is (K − S + p) × n for a covered call, being called away at the strike, and p × n for a put that expires. The worst case, if the shares go to zero, is minus the break-even times the shares.
• The money committed is the shares at today's price for a covered call, or the strike in cash for a put. Each return is the profit or loss divided by the money committed, made yearly by multiplying by 365 / D without compounding: the best-case return, and the return if the price at expiry equals today's.

The chances are Black-Scholes risk-neutral probabilities. The chance the price at expiry is above X is

P(above X) = N((ln(S / X) + (r − q − σ² / 2) T) / (σ √T))

where N is the standard normal distribution. With d1 = (ln(S / K) + (r − q + σ² / 2) T) / (σ √T) and d2 = d1 − σ √T, the chance a call ends in the money is N(d2) and a put's N(−d2). The chance of any profit is the chance the price ends above the break-even, or 0 when even the best case is not a profit. The model value of the option you sold is the Black-Scholes value: S e^(−qT) N(d1) − K e^(−rT) N(d2) for a call, and K e^(−rT) N(−d2) − S e^(−qT) N(−d1) for a put.

Calculation sequence

The spreadsheet first checks every input. It then computes T, d1, d2 and the model values of the call and the put; the break-even, the money committed, the best and worst cases and the two returns; and the chances. It builds the profit-or-loss table from 41 evenly spaced prices at expiry around today's price, widened to three standard deviations or past the strike and the break-even, plus the strike, the break-even and today's price, sorted; and the four price ranges between the break-even, today's price and the strike, in order, with the chance of each. A block of consistency checks, put-call parity among them, confirms the arithmetic before the status is returned.

Outputs and interpretation

The headline is the premium you receive. Beside it are the best-case return and the return if the price does not move, both yearly, the chance the option ends in the money, the break-even share price and the best case at expiry. The tables show the profit or loss at each price at expiry, beside holding the shares alone, and each price range with its chance. The worst case, the money committed, the chance of any profit, the model value of the option, d1, d2 and the workbook's self-check are returned to the API and MCP.

With the default inputs, a covered call on 100 shares at 100 dollars, selling the 105 call for 2.00 a share with 30 days to go, you receive 200 dollars. Your break-even is 98. If the shares are called away at 105 you make 700 dollars, 7% of the 10,000 committed in 30 days, or 85.17% a year; if the price does not move you keep the 200, 24.33% a year. At 25% implied volatility, a 4.5% risk-free rate and a 1.5% dividend yield, the chance the call ends in the money is 24.8%, and the chance of any profit is 61.0%. The model value of the call is about 1.14 a share, so the 2.00 premium is above it. Selling a put at 95 for 1.60 instead brings 160 dollars, a break-even of 93.40 and 20.49% a year whether the price stays or rises.

The first chart draws your profit or loss at expiry for each share price: blue where it is a profit, red where it is a loss, with holding the shares alone as a dashed grey line and dashed vertical guides at the strike and the break-even. The second chart shows the chance of each price range.

Validation and status logic

The workbook evaluates the conditions below from top to bottom and returns the first matching status.

NOT VALID is a refusal, not a numeric answer: every number reads zero and the tables are empty. CHECK accompanies a computed result but calls for the stated review. The self-check is reported separately as arithmetic-integrity evidence; it does not replace this ordered status chain.

Assumptions and limitations

The option is European and held to expiry: early assignment, which can happen to an American call before an ex-dividend date, is not modelled, and neither is rolling, closing the option early or combining several options. The dividends you receive and the interest on a put's cash are not added to your profit or loss; the dividend yield and the risk-free rate enter only the chances and the model value. Commissions and taxes are left out. The chances assume the share price follows the lognormal distribution that the implied volatility describes; real prices jump and their volatility changes, so the chances are the market's risk-neutral odds, not a forecast. Returns are made yearly by simple multiplication, not compounded.

Restrictions and non-computing states

This calculator enforces its numeric and choice limits before it accepts a result. The share price, the strike and the premium must be whole numbers of 0.0001 dollars, so that the sign of the best case is exact; the page's sliders move by 0.01. The premium must be below the share price for a covered call or below the strike for a put, the days to expiry and the shares are whole numbers, and the strategy comes from its list.

Errors and warnings

A request rejected by the page's input limits is not a computed result. A transport or service failure cannot establish a fresh workbook answer. Review the workbook's References and Disclaimer, and check any trade with a qualified professional before using a result for a real decision.

Sources and further reading

The share price, strike, premium, volatility and rates come from the inputs, not market data. The workbook's References sheet identifies the sources below. The links explain the methods the model follows; they do not endorse this calculator.

• The Option Pricing Binomial Black Scholes Greeks Calculator on this site: its workbook's d1, d2 and option-value formulas (sheet Calculations, cells H46, H47 and H50) are reused here term for term, and its shipped example (a 100 share price and strike, one year, 5% rate, 20% volatility) gives the same d1 of 0.35, d2 of 0.15 and call value of about 10.4506 in both workbooks.
• Microsoft Support's NORM.S.DIST documentation describes the standard normal distribution the chances and the model value use.

The profit or loss at expiry is the payoff arithmetic the methodology states; the chances are the Black-Scholes risk-neutral probabilities, not forecasts.

This is an educational estimate, not financial, investment, tax or legal advice. Options can lose money quickly, early assignment and taxes can change the outcome, and the odds shown are not predictions; check any trade with a qualified professional.