🎯 What Are We Doing?
    We are pricing a European call option using the Black-Scholes formula. This method gives us a fair price based on math, market conditions, and time.
  
  
    📌 Step 1: Inputs Given
    • Stock Price S = 21
    • Strike Price X = 21
    • Risk-Free Rate r = 5% = 0.05
    • Time to Expiry t = 0.36 years (about 4.3 months)
    • Volatility σ = 0.3 (30% annual standard deviation)
  
  
    📈 Step 2: Formula Overview
    C = S × N(d1) − X × e−rt × N(d2)
    Where:
    • d1 = [ln(S/X) + (r + σ²/2)t] / [σ × √t]
    • d2 = d1 − σ × √t
  
  
    🧮 Step 3: Calculate d1 and d2
    1. 
ln(S/X) = ln(21/21) = 0
    2. 
(r + σ²/2)t = (0.05 + 0.3² / 2) × 0.36 = (0.05 + 0.045) × 0.36 = 0.095 × 0.36 = 0.0342
    3. 
σ × √t = 0.3 × √0.36 = 0.3 × 0.6 = 0.18
    4. 
d1 = 0.0342 / 0.18 = 0.19
    5. 
d2 = d1 − 0.18 = 0.19 − 0.18 = 0.01
    So, d1 = 0.19 and d2 = 0.01
   
  
    📊 Step 4: Get N(d1) and N(d2)
    We use the normal distribution table or a calculator:
    • N(d1) = N(0.19) ≈ 0.5753
    • N(d2) = N(0.01) ≈ 0.5040
  
  
    💰 Step 5: Final Call Option Price
    Plug into the formula:
    
C = 21 × 0.5753 − 21 × e−0.05×0.36 × 0.5040
    • First part: 
21 × 0.5753 = 12.0813
    • Discount factor: 
e−0.05×0.36 = e−0.018 ≈ 0.9822
    • Second part: 
21 × 0.9822 × 0.5040 = 10.3943
    • Call price = 
12.0813 − 10.3943 = 1.687
    ✅ Final Answer: The call option is worth approximately $1.687