Passa al contenuto

Options Pricing - Heatmap


Click here to try the Web App

If the app is "sleeping," press the "Yes, get this app back up!" button.

Key Features:


Black-Scholes Option Pricing

  • Computes theoretical prices for European call and put options using the closed-form Black-Scholes formula.
  • Supports all standard inputs:
    • Underlying asset price (S)
    • Strike price (K)
    • Time to maturity (T)
    • Implied volatility (σ)
    • Risk-free interest rate (r)

Option Greeks Calculation

  • Calculates first- and second-order sensitivities:
    • Delta (Δ) – Price sensitivity to underlying asset movements.
    • Gamma (Γ) – Rate of change of Delta.
    • Vega (ν) – Sensitivity to volatility changes.
    • Theta (Θ) – Time decay effect.
    • Rho (ρ) – Sensitivity to interest rate changes.

Dynamic Sensitivity Analysis

  • Generates interactive heatmaps to visualize:
    • Price sensitivity across a range of underlying prices (spot range).
    • Impact of volatility changes (σ range) on option premiums.
  • Call and put price surfaces displayed in separate heatmaps for comparative analysis.

Professional Financial Interface

  • Clean, responsive dashboard optimized for financial analytics.
  • Real-time updates on parameter adjustments.
  • Annotated heatmaps with precise numerical values for quantitative analysis.

Customizable Parameter Ranges

  • Adjustable bounds for sensitivity analysis:
    • Minimum/maximum underlying price (S_min, S_max).
    • Minimum/maximum volatility (σ_min, σ_max).
  • Supports both default and user-defined ranges



Usage:


1. Model Configuration

  • Input option parameters in the sidebar:
    • Set Underlying Price (S), Strike Price (K), and Time to Maturity (T).
    • Adjust Volatility (σ) and Risk-Free Rate (r) via sliders or manual entry.

2. Results Interpretation

  • Option Premiums:
    • Call and put prices displayed in structured metric cards.
    • Greeks values presented alongside for risk assessment.
  • Heatmap Analysis:
    • X-axis: Underlying price range (spot sensitivity).
    • Y-axis: Volatility range (volatility sensitivity).
    • Color gradient indicates option price magnitude.

3. Sensitivity Analysis

  • Modify spot and volatility ranges to test different market scenarios.
  • Observe how Delta and Gamma change with moneyness (ITM, ATM, OTM).
  • Assess Theta decay and Vega exposure under varying conditions.

Applications

  • Trading & Risk Management:
    • Estimate fair value for European options.
    • Hedge positions using Greeks (e.g., Delta-neutral strategies).
  • Education & Research:
    • Demonstrate non-linear pricing effects (e.g., volatility smile).
    • Visualize convexity (Gamma) and time decay (Theta) in option pricing.

Technical Notes

  • All calculations update in real-time upon parameter changes.
  • Heatmaps use plasma colormap for optimal contrast in price visualization.
  • Supports both percentage and absolute value inputs for flexibility.



Click here to view the code on GitHub