CMA Final SFM Derivatives Practical Learning Tool
CMA Final SFM - Derivatives Practical Learning Tool
Interactive calculators and explanations for key derivatives concepts
Futures Pricing (Cost of Carry Model)
Explanation
The Cost of Carry Model is used to determine the theoretical price of a futures contract. It's based on the concept that the futures price should equal the spot price plus the cost of carrying (holding) the underlying asset until the futures expiration.
This model assumes no arbitrage opportunities exist in the market. If the futures price deviates significantly from this theoretical value, arbitrageurs would step in to profit from the discrepancy, bringing the price back in line.
Example
Suppose the spot price of gold is $1,800 per ounce, the risk-free interest rate is 5% per annum, and the time to futures expiration is 6 months (0.5 years). The theoretical futures price would be calculated as:
F = 1800 × e^(0.05 × 0.5) = 1800 × e^0.025 ≈ 1800 × 1.0253 ≈ $1,845.54
How to use the formula:
1. Identify the current spot price (S₀) of the underlying asset
2. Determine the risk-free interest rate (r) for the period until expiration
3. Calculate the time to expiration (T) in years
4. Apply the formula: Futures Price = Spot Price × e^(interest rate × time)
Calculator
Result:
Options Payoffs
Explanation
Options payoffs represent the profit or loss from an options position at expiration. Unlike futures, options have asymmetric payoffs - the maximum loss for a buyer is limited to the premium paid, while the potential gain is unlimited for calls or substantial for puts.
Call options give the holder the right to buy the underlying asset at the strike price. Put options give the holder the right to sell the underlying asset at the strike price.
Example
Suppose you buy a call option with a strike price of $100, paying a premium of $5. If the underlying asset price at expiration is $120:
Payoff = max(0, 120 - 100) - 5 = 20 - 5 = $15 profit
If the price is $90 at expiration:
Payoff = max(0, 90 - 100) - 5 = 0 - 5 = -$5 loss (limited to premium paid)
Put Payoff = max(0, K - Sₜ) - Premium
How to use the formula:
1. Determine the type of option (call or put)
2. Identify the strike price (K) and premium paid
3. Determine the underlying asset price at expiration (Sₜ)
4. Apply the appropriate formula based on option type
Calculator
Result:
Put-Call Parity
Explanation
Put-Call Parity is a fundamental principle that defines the relationship between the prices of European put and call options with the same strike price and expiration date. It shows that a portfolio consisting of a call option and a risk-free bond (present value of strike price) should have the same value as a portfolio consisting of a put option and the underlying asset.
This relationship prevents arbitrage opportunities and ensures pricing consistency between puts and calls.
Example
Suppose a stock is trading at $100, a call option with a $100 strike price costs $10, the risk-free rate is 5%, and the time to expiration is 1 year. According to put-call parity:
Put Price = Call Price + PV(Strike) - Stock Price
PV(Strike) = 100 × e^(-0.05×1) ≈ 95.12
Put Price = 10 + 95.12 - 100 = $5.12
Where PV(K) = K × e^(-r×T)
How to use the formula:
1. Identify the current stock price (S₀)
2. Determine the strike price (K) and time to expiration (T)
3. Find the risk-free interest rate (r)
4. If you know the call price (C), you can calculate the put price (P), or vice versa
Calculator
Result:
Currency Forward Rate
Explanation
The currency forward rate formula calculates the theoretical forward exchange rate based on the spot rate and the interest rate differential between two currencies. This relationship is derived from the concept of covered interest rate parity, which states that the forward rate should reflect the interest rate differential to prevent arbitrage.
If the domestic interest rate is higher than the foreign interest rate, the forward rate will be at a discount to the spot rate, and vice versa.
Example
Suppose the USD/INR spot rate is 75, the US interest rate is 3%, the Indian interest rate is 6%, and the forward period is 1 year. The forward rate would be:
Forward Rate = 75 × (1 + 0.06) / (1 + 0.03) = 75 × 1.06 / 1.03 ≈ 77.18
This means the forward rate is higher than the spot rate, reflecting the higher interest rate in India.
How to use the formula:
1. Identify the current spot exchange rate (S)
2. Determine the domestic interest rate (rd)
3. Determine the foreign interest rate (rf)
4. Apply the formula: Forward Rate = Spot Rate × (1 + domestic rate) / (1 + foreign rate)
Calculator
Result:
Derivative Concept Visualization
This visualization shows how the value of a derivative changes with the underlying asset price.