Complete guide to Derivatives Exam math covering option intrinsic value, break-even calculations, spread profit/loss, Beta hedging formula, and futures pricing calculations.
Derivatives Exam Math & Calculations
The Derivatives Exam requires strong mathematical skills. This guide covers all essential formulas and calculations you need to master.
Option Premium Components
Premium Formula
Option Premium = Intrinsic Value + Time Value
Call Option Intrinsic Value
Intrinsic Value = Stock Price - Strike Price (if positive, otherwise 0)
Example: Stock at $55, Strike at $50 → IV = $55 - $50 = $5
Put Option Intrinsic Value
Intrinsic Value = Strike Price - Stock Price (if positive, otherwise 0)
Example: Stock at $45, Strike at $50 → IV = $50 - $45 = $5
Break-Even Calculations
Long Call Break-Even
Break-Even = Strike Price + Premium Paid
Example: Strike $50, Premium $3 → BE = $50 + $3 = $53
Long Put Break-Even
Break-Even = Strike Price - Premium Paid
Example: Strike $50, Premium $2 → BE = $50 - $2 = $48
Short Call Break-Even
Break-Even = Strike Price + Premium Received
Short Put Break-Even
Break-Even = Strike Price - Premium Received
Profit/Loss Calculations
Long Call P/L
P/L = (Stock Price at Expiry - Strike Price) - Premium Paid
Max Loss = Premium Paid
Max Profit = Unlimited
Long Put P/L
P/L = (Strike Price - Stock Price at Expiry) - Premium Paid
Max Loss = Premium Paid
Max Profit = Strike Price - Premium (stock goes to zero)
Spread Calculations
Bull Call Spread
Buy lower strike call, Sell higher strike call
- Net Premium: Premium Paid - Premium Received
- Max Profit: (Higher Strike - Lower Strike) - Net Premium
- Max Loss: Net Premium Paid
Bear Put Spread
Buy higher strike put, Sell lower strike put
- Net Premium: Premium Paid - Premium Received
- Max Profit: (Higher Strike - Lower Strike) - Net Premium
- Max Loss: Net Premium Paid
Straddle Calculations
Long Straddle
Buy Call + Buy Put at same strike
- Total Cost: Call Premium + Put Premium
- Upper Break-Even: Strike + Total Premium
- Lower Break-Even: Strike - Total Premium
- Max Loss: Total Premium (stock stays exactly at strike)
Futures Pricing
Cost of Carry Model
Futures Price = Spot Price + Carrying Costs - Carrying Benefits
With Interest Rate
F = S × (1 + r × t)
Where: F = Futures Price, S = Spot Price, r = Risk-free rate, t = Time to expiry (in years)
Beta Hedging Formula
Number of futures contracts needed to hedge a portfolio:
Contracts = (Portfolio Value / Futures Contract Value) × Portfolio Beta
Example: Portfolio = $1,000,000, Beta = 1.2, Futures = $250,000
Contracts = ($1,000,000 / $250,000) × 1.2 = 4 × 1.2 = 4.8 ≈ 5 contracts
The Greeks Interpretations
Delta
If Delta = 0.60, option price increases by $0.60 for every $1 increase in stock price.
Gamma
If Gamma = 0.05, Delta changes by 0.05 for every $1 move in stock.
Theta
If Theta = -0.03, option loses $0.03 per day from time decay.
Vega
If Vega = 0.10, option price changes by $0.10 for each 1% change in implied volatility.
Margin Calculations
Margin Call Trigger
Margin call occurs when account equity falls below maintenance margin requirement.
Variation Margin
Daily cash flow = (Today's Settlement Price - Yesterday's Settlement Price) × Contract Size × Number of Contracts
Key Exam Tips for Math
- Always check if intrinsic value is positive (can't be negative)
- Time Value = Premium - Intrinsic Value
- Long positions: subtract premium from profit calculation
- Short positions: add premium to profit calculation
- Beta hedging: round to nearest whole contract
- Contango = F > S; Backwardation = F < S
- Practice calculating break-evens quickly