Interactive European option pricer and Greeks calculator built on the Black-Scholes-Merton model, developed as part of my CFA Level 1 preparation to deepen my understanding of derivatives pricing mechanics.
This tool was built to consolidate my grasp of the Derivatives readings in the CFA Level 1 curriculum (Readings 73-75, plus Book 4 LOS on risk management). The CFA L1 curriculum introduces options qualitatively: payoffs, moneyness, the six factors affecting option value, and the Greeks as directional sensitivities, without going into the Black-Scholes-Merton formula itself, which belongs to Level 2. Implementing BSM end-to-end (from the normal distribution up to the analytical Greeks) is my way of going one step beyond the curriculum to actually see how each L1 concept translates into a live price.
- Real-time pricing of European calls and puts with continuous dividend yield
- Five analytical Greeks (Delta, Gamma, Vega, Theta, Rho) with market-convention scaling
- Three sensitivity charts: price vs underlying, Delta vs underlying, price vs volatility
- Arithmetically exact decomposition: price = intrinsic value + time value
- Correct handling of negative time value for deep-ITM European puts (a subtle CFA point on early exercise impossibility)
- High-precision normal CDF (West 2009 approximation, max error 7.5e-9)
- Clean professional interface, fully responsive
- Toggle between Call and Put in the sidebar
- Adjust underlying price, strike, rates, volatility, dividend yield, and time
- The hero bar shows the option price and moneyness in real time
- Navigate the four tabs: Valuation, Greeks, Sensitivity, Reference
- All values recompute instantly on every input change
- The six factors of option value (CFA L1 Reading 73) stop being abstract once you see them move the price live on screen. The Reference tab maps each factor to its directional effect, and the Sensitivity charts let you verify those effects visually.
- Negative time value for a deep-ITM European put is the kind of subtlety the curriculum mentions in passing but only fully clicks once you've coded it. Early exercise is impossible, so the holder must wait until maturity to receive X. When X·e^(-rT) - S falls below max(X-S, 0), the time value is correctly negative.
- Greeks as partial derivatives. The CFA L1 introduces Delta, Gamma, Vega, Theta, and Rho qualitatively. Coding their closed-form expressions and visualising Delta across the underlying range made the link between the Greeks and the option's behavior tangible.
- The Black-Scholes-Merton model is the continuous-time limit of the binomial model taught at L1. Working through BSM gave me a much stronger intuition for what the risk-neutral pricing approach really achieves.
HTML · Vanilla JS · SVG · No external dependencies · Runs locally via file://
- European exercise only (no early exercise modeled)
- Constant volatility assumed (no volatility surface, smile, or skew)
- Log-normal underlying with continuous trading and frictionless markets
- Time to expiration bounded at T >= 0.08 years (~1 month): Gamma and Theta diverge for ATM options as T approaches 0, which is a display choice and not a model limitation
- Black-Scholes-Merton is beyond the CFA Level 1 curriculum (it is part of Level 2 Derivatives); the formula and analytical Greeks here rely on Hull (2017) for the technical specification
- CFA Institute Curriculum 2025, Derivatives, Readings 73, 74, 75; Risk Management Applications of Option Strategies, Book 4
- Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy.
- Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics.
- Hull, J. C. (2017). Options, Futures, and Other Derivatives (10th ed.). Pearson.
Built by Nieucel Mahe · Educational purpose only