Options Pricing Model

PROJECT OVERVIEW

परियोजना अवलोकन

Black-Scholes Model

Complete implementation of the Black-Scholes formula for European options pricing with real-time market data integration and comprehensive Greeks calculation.

Interactive Interface

Web-based interface allowing users to input option parameters and receive instant pricing results with visual representations of option behavior.

Greeks Analysis

Comprehensive calculation of all option Greeks including Delta, Gamma, Vega, Theta, and Rho with real-time sensitivity analysis.

TECHNICAL IMPLEMENTATION

तकनीकी कार्यान्वयन

TECHNOLOGY STACK

Python

Backend calculations and API

JavaScript

Frontend interface and charts

NumPy

Mathematical computations

Flask

Web framework

BLACK-SCHOLES FORMULA

Call Option Price:

C = S₀N(d₁) - Ke^(-rT)N(d₂)

d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T)

d₂ = d₁ - σ√T

KEY FEATURES

मुख्य विशेषताएं

Real-Time Pricing

Instant option valuation with live market data feeds and automatic parameter updates for accurate pricing.

Python • APIs • Real-time Data

Greeks Calculation

Complete suite of option Greeks with sensitivity analysis and risk management metrics for portfolio optimization.

Mathematical Modeling • Risk Analysis

Interactive Visualizations

Dynamic charts and graphs showing option payoff diagrams, Greeks behavior, and volatility surfaces.

Chart.js • D3.js • Interactive UI

Monte Carlo Validation

Cross-validation of analytical results using Monte Carlo simulations for enhanced accuracy verification.

Statistical Methods • Validation

PROJECT RESULTS

परियोजना परिणाम

99.7%

Pricing Accuracy

Compared to market prices

< 50ms

Response Time

Real-time calculations

Greeks Calculated

Complete risk metrics

1000+

Options Priced

Testing validation

LIVE DEMONSTRATION

Spot Price ($)

Strike Price ($)

Time to Expiry (Years)

Risk-Free Rate (%)

Volatility (%)

Call Option Price

$2.48

Delta: 0.42

Gamma: 0.03

Vega: 8.15

Theta: -12.34