CMA Final SFM Derivatives Practical Learning Tool
Derivatives Practical Learning Tool
Master SFM Concepts for CMAknowledge.in
How to use this tool
- Study the Theory & Tricks: Read the explanations and our special Normal Calculator Tricks designed for CMA exams.
- Calculate & View Steps: Enter your scenario figures, click compute, and click "Show Steps" to see the mathematical breakdown.
- Visualize: Click the dedicated "Payoff Graphs" tab to analyze the profit/loss zones of 6 different derivative strategies.
Cost of Carry Model
The Cost of Carry Model is used to determine the theoretical price of a futures contract. It asserts that the futures price should equal the spot price plus the cost of carrying (holding) the underlying asset until expiration.
Normal Calculator Trick for ex
To calculate Continuous Compounding factor e(r × T) on a standard calculator:
- Type the value of (r × T)
- Divide by 8192 and Add 1
- Press [×] [=] consecutively 13 times.
Calculate Futures
Final Result:
Options Payoffs
Options have asymmetric payoffs. Maximum loss for a buyer is limited to the premium paid, while the potential gain is unlimited (Call) or substantial (Put).
Put = Max(0, K - ST) - Premium
Calculate Payoff
Final Result:
Put-Call Parity
Defines the relationship between European put and call prices with the same strike and expiration. It prevents arbitrage by ensuring a fiduciary call (Call + PV of Strike) equals a protective put (Put + Asset).
Normal Calculator Trick for PV
To find Present Value of Strike PV(K) = K × e-rT:
- Use the 13-times trick to find erT (positive power).
- Press [÷] [=] to find the reciprocal (which equals e-rT).
- Multiply the result by the Strike Price (K).
Calculate Parity
Final Result:
Black-Scholes Model
The foundational mathematical model used for pricing European options. It considers current stock price, strike price, risk-free rate, time to expiration, and expected volatility.
Normal Calculator Trick for Ln(x)
To calculate the Natural Logarithm ln(S/K) for d1:
- Divide Stock by Strike (S ÷ K)
- Press [√] (Square Root) exactly 13 times.
- Subtract 1.
- Multiply by 3558.
d1 =
d2 = d1 - σ√T
Option Pricing
Pricing Results:
Currency Forward Rate
Calculates the theoretical forward exchange rate based on Interest Rate Parity (IRP). It adjusts the spot rate by the interest rate differential between two countries.
Calculate Forward
Final Result:
Option Greeks (Theory)
The "Greeks" measure the sensitivity of an option's price to various quantifiable factors. They are essential for risk management and hedging in SFM.
-
Delta (Δ): Measures sensitivity to the underlying asset's price.
If Call Delta is 0.60, a ₹1 increase in stock price increases the option price by ₹0.60. -
Gamma (Γ): Measures the rate of change of Delta.
Shows how much Delta will change for a ₹1 move in the underlying asset. Highest for at-the-money options. -
Theta (Θ): Measures time decay.
The daily loss in option value as expiration approaches, assuming all else remains constant. Always negative for long options. -
Vega (ν): Measures sensitivity to volatility.
The amount option price changes for a 1% change in implied volatility. Higher volatility increases both call and put values.
Interactive Payoff Graphs
Select a derivative position below to dynamically visualize its profit and loss zones at expiration. The Break-Even Point (BEP) and Strike Price (K) are clearly marked.
