Options Pricing Model - Rutvik Babar

Market Parameters

Spot Price (S)

Strike Price (K)

Time to Expiry (Years)

Risk-Free Rate (%)

Volatility (%)

Python Implementation

Python Black-Scholes Greeks

Real-time calculations using Black-Scholes formula (no dividend yield):

Call: C = S₀N(d₁) - Ke⁻ʳᵀN(d₂)

Put: P = Ke⁻ʳᵀN(-d₂) - S₀N(-d₁)

Option Prices

Call Option

$2.4847

Intrinsic: $0.0000

Time Value: $2.4847

Put Option

$6.1738

Intrinsic: $5.0000

Time Value: $1.1738

Option Greeks

Delta (Δ)

Call: 0.377 Put: -0.623

Price sensitivity to underlying

Gamma (Γ)

Both: 0.038

Delta sensitivity to underlying

Theta (Θ)

Call: -0.026 Put: -0.011

Time decay per day

Vega (ν)

Both: 0.190

Volatility sensitivity

Rho (ρ)

Call: 0.088 Put: -0.171

Interest rate sensitivity

Sensitivity Analysis

Real-time Parameter Impact

Current: S=$100, K=$105, T=0.25yr, r=5%, σ=20%

Scenario Call Price Put Price Call Delta

S +10% $7.35 $1.04 0.741

S -10% $0.47 $15.11 0.096

σ +5% $3.48 $7.17 0.412

σ -5% $1.68 $5.37 0.337

Live Analysis:

Higher spot price increases call value, decreases put value
Higher volatility increases both call and put values
Delta shows price sensitivity to underlying moves
Time decay affects out-of-money options more