Options Strategy Builder: P&L, Greeks & Scenarios

About the Options Strategy Builder: P&L, Greeks & Scenarios

Put together any options strategy of up to eight legs — calls, puts and the underlying, bought or sold, in one expiry or several — and see what it does at every price and date: the profit or loss at the first expiry and on any day before it, the breakevens, the maximum profit and loss (or that one of them has no limit), the net premium, the aggregate Greeks in money and per unit, the probability of profit under a lognormal price, and a price × date grid with an implied-volatility shift for what-if questions.

Options on shares and indices are valued with Black–Scholes–Merton and a dividend yield; options on futures with Black-76. Start from one of 24 structures — spreads, straddles, strangles, condors, butterflies, calendars, diagonals, ratios, collars — whose premiums are filled with model values at your volatility (replace them with your broker’s prices), or type your own legs. Save a strategy as a file, load it again later, and put up to three of your own strategies side by side.

It works for any market: the contract multiplier follows your market where an official figure exists (100 shares for standard US, Canadian and Australian equity options), and you type the lot size where exchanges set and revise it, as in India. It uses no market data: every price is one you enter.

Common uses

• See an iron condor’s breakevens and probability of profit before you place it, with your broker’s premiums.
• Check how much of a calendar spread’s value is left a week before the first expiry, and what an IV drop does to it.
• Put a bull call spread, a call and a ratio spread side by side with your own premiums and margin.
• Read the delta, theta and vega of a multi-leg position in money, for your own risk limits.

The formulas

• P&L = Σ side × (value − premium) × lots × units per lot, with side +1 for a leg you buy and −1 for one you sell.
• At expiry a call is worth max(S − K, 0), a put max(K − S, 0) and the underlying S (the payoffs of Hull, Options, Futures, and Other Derivatives, ch. 12).
• Before expiry a share or index option is worth 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, with d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ σ√T and d₂ = d₁ − σ√T (Black and Scholes, Merton); an option on a futures price uses F in place of S e^(−qT) and discounts at r (Black’s model90024-6)).
• Greeks come from the same formulas (Hull, ch. 19): delta per 1.00 move of the underlying, gamma per 1.00, theta per calendar day, vega per volatility point and rho per interest-rate point.
• Probability of profit = Σ over the price zones where the strategy makes money of [N(d₂(lo)) − N(d₂(hi))], with d₂(K) = [ln(S/K) + (μ − σ²/2)T] ÷ σ√T: a lognormal price at the first expiry, with a drift μ of 0 or r − q as you choose.
• Breakevens are exact at a single expiry (the payoff is straight between strikes); with legs in several expiries they are found numerically, as are the maximum and minimum.

Reading the results

• At expiry means the first expiry of the strategy. With a calendar or a diagonal, the later legs are still alive then and are valued with the model at their own volatility.
• No limit means the loss or the profit keeps growing as the price rises: more calls (or more of the underlying) are sold than bought, or the other way round.
• The valuation day shows the P&L before expiry, with the time value left; the IV shift moves every leg’s volatility up or down by the points you choose.
• The probability is what the lognormal model says for the volatility named under it: it is a property of the model and your inputs, not a forecast, and it changes when they change.
• Greeks in money are the change in the strategy’s P&L: theta is what one calendar day costs or earns with the price unchanged.

What it leaves out

Commissions, taxes and the bid–ask spread; early exercise and assignment of American options (a short option can be assigned before expiry, most often just before an ex-dividend date); changes of volatility other than the shift you set, and the smile across strikes beyond the IV you give each leg; dividends paid as cash amounts (use a yield here, or the option pricing calculator for cash dividends); and the margin your broker asks for, which you type. Each of these can make the real result differ from the one shown.

Limitations

• European-style valuation: early exercise of American options is not modelled.
• One underlying per strategy, with one price, rate and dividend yield.
• Premiums must be above 0 and implied volatilities at least 0.1% a year; a leg expiring today counts its value at expiry.
• Margin is not worked out: enter the figure your broker or exchange gives you.
• It calculates from your numbers and uses no market data: it says nothing about where any price is going.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.