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Derivatives

Interactive derivatives pricing and hedging tools. From Black-Scholes fundamentals to exotic structures, with full Greeks analysis.

10 Tools Interactive

5 Chapters Source

15 Exercises BUILD

BLACK-SCHOLES-MERTON

C = S₀N(d₁) - Ke^-rTN(d₂)
d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T)

The foundational formula for European option pricing. Basis for delta hedging, volatility trading, and structured products.

Delta

Price sensitivity

Gamma

Delta sensitivity

Theta

Time decay

Vega

Volatility sensitivity

Rho

Rate sensitivity

Interactive Tools

Option Pricer

Price European and American options using BSM, binomial trees, and Monte Carlo.

Multiple pricing models
Early exercise premium
Dividend handling

Greeks Dashboard

Interactive visualization of all Greeks across strike and time dimensions.

3D surface plots
Portfolio-level Greeks
Hedging ratios

Volatility Surface

Build and analyze implied volatility surfaces from market option prices.

Smile/skew visualization
Term structure
Surface interpolation

Strategy Builder

Construct multi-leg option strategies with payoff diagrams.

Spreads and combos
Break-even analysis
Greeks aggregation

Delta Hedger

Simulate dynamic delta hedging with rebalancing costs.

Continuous vs discrete
Transaction cost impact
Hedge error analysis

Exotic Pricer

Price barrier, Asian, lookback, and other exotic options.

Monte Carlo methods
PDE solvers
Variance reduction

BUILD Exercises

BUILD 1

Black-Scholes Implementation

Implement BSM formula with all Greeks from first principles

FOUNDATIONAL

BUILD 2

Binomial Tree Pricer

Build CRR binomial tree for American options

FOUNDATIONAL

BUILD 3

Implied Volatility Solver

Extract implied vol from market prices using Newton-Raphson

INTERMEDIATE

BUILD 4

Delta Hedging Simulator

Simulate continuous hedging with transaction costs

INTERMEDIATE

BUILD 5

Monte Carlo Option Pricer

Price path-dependent options with variance reduction

ADVANCED