Using Black–Scholes to Price Options and Plot Portfolio Payoffs
Summary
The document explains how to use a spreadsheet model to price calls and puts with the Black–Scholes formulas and chart the payoff of a portfolio across underlying prices. Users enter each option’s expiry, type, strike, premium, contract count, volatility, and spot price. The model estimates option values and expected profit or loss, aggregates investment and current portfolio value, and plots the combined payoff. It also notes that market option prices can be used in reverse to infer implied volatility.
The pricing framework shown assumes a non-dividend-paying underlying and uses spot, strike, risk-free rate, volatility, and time to expiry. A separate sheet varies spot prices to recalculate option values and total payoff. The spreadsheet supports combinations of calls and puts, with a stated limit unless the macro is edited. The guide is operational rather than an evaluation of trading performance; it gives no evidence that Black–Scholes estimates match market prices or that a plotted payoff predicts realized returns. Expiry dates must also yield positive time to expiry for the calculation to work.
Key ideas
- Black–Scholes estimates call and put prices from spot, strike, risk-free rate, volatility, and time to expiry.
- A spreadsheet can aggregate option premiums and contract counts to estimate portfolio value and profit or loss.
- Varying the underlying price lets users chart the combined option payoff across price scenarios.
- Market option prices can be used to infer implied volatility through reverse pricing.
- The described formulas assume a non-dividend-paying underlying and do not establish realized strategy performance.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.