Price European options using Black-Scholes model with implied volatility solver, Greeks display, and sensitivity surface plots.
This tool evaluates the closed-form Black-Scholes-Merton equation to price a European call or put from spot, strike, time to expiry, risk-free rate, and volatility. Feed it a market price instead of volatility and it inverts the formula numerically to solve for implied volatility, then reports the five Greeks and can plot a price or Greek sensitivity surface across a grid of spot and volatility values. The most common surprise: results assume European exercise and zero dividends unless you set a dividend yield, so American-style equity options near a payout date will be mispriced without that adjustment.
A concrete input and expected output from the current implementation.
Input
S=100, K=100, T=1 year, r=5%, sigma=20%, dividend yield=0, call and put
Expected output
Call = $10.45, Put = $5.57, call delta N(d1) = 0.637
d1=0.35 and d2=0.15 give N(d1)=0.6368 and N(d2)=0.5596; Call = 100(0.6368) - 100e^-0.05(0.5596) = 10.45, and put-call parity (C - P = S - Ke^-rT) confirms Put = 10.45 - 100 + 95.12 = 5.57.
From S, K, T (in years), r and sigma it computes d1 = (ln(S/K) + (r + sigma^2/2)T) / (sigma*sqrt(T)) and d2 = d1 - sigma*sqrt(T), then Call = S*N(d1) - K*e^(-rT)*N(d2) and Put = K*e^(-rT)*N(-d2) - S*N(-d1), using the standard normal CDF N(). An entered dividend yield q discounts S by e^(-qT) throughout.
Given an observed option price instead of sigma, the tool repeatedly reprices the option with a numerical root-finding search and adjusts sigma until the model price matches the input price within a defined convergence tolerance, stopping and reporting non-convergence if that tolerance isn't reached within a fixed number of iterations.
No. It implements Black-Scholes-Merton, which is a European-exercise model. For American options, especially puts or calls on dividend-paying stocks, the early-exercise premium means the true value can exceed what this tool reports; a method that accounts for early exercise - such as a binomial or trinomial tree, a finite-difference scheme, or an analytic American approximation - is needed for that.
Usually the entered option price falls outside the arbitrage-free bounds implied by discounted spot and strike given the other inputs, or the search hit its iteration limit without converging. Check that spot, strike, price, rate, and time are all in consistent units and reflect the same moment.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate gross, operating, and net profit margins from cost and revenue with breakeven analysis.
Convert between annual salary and hourly rate with adjustments for work hours, overtime, and benefits.
Calculate sales tax amounts, tax-inclusive and tax-exclusive prices for any tax rate or jurisdiction.
Calculate return on investment from initial cost and final value with annualized ROI and comparison tables.
Convert between markup and margin percentages, calculate selling price, and compare pricing strategies.
Convert numeric amounts to written words for invoices, checks, and legal documents in multiple currencies.