Understanding Put-Call Parity and Derivatives Markets
Put–Call Parity
This model states that for a given call price, the corresponding put price for the same exercise price and tenure can be determined. This is known as the Put–Call Parity rule.
Consider two portfolios:
- First Portfolio: Stock + Put
- Second Portfolio: Call + Present Value of Strike Price
At expiry, the value of both portfolios will be equal under all conditions.
Analysis at Expiry
Case 1: Stock Price < Exercise Price (e.g., 80 < 100)
- Portfolio A (Stock + Put): Stock price at end + (Exercise Price – Stock Price) = Exercise Price
- Portfolio B (Call + Bonds): 0 + Exercise Price = Exercise Price
Case 2: Stock Price > Exercise Price
- Portfolio A (Stock + Put): Stock price at end + 0 = Stock price at end
- Portfolio B (Call + Bonds): (Stock price at end – Exercise Price) + Exercise Price = Stock price at end
Formula and Conclusion
The formula is: C + PV(K) = P + S
The value of both portfolios is equal in all situations. Therefore, Put–Call Parity establishes a relationship between call price, put price, stock price, and strike price: Stock + Put = Call + Cash.
Margining System
The margining system is a mechanism in derivatives markets where traders deposit money as security to ensure they fulfill contractual obligations, reducing default risk.
Types of Margin
- Initial Margin: The amount deposited at the beginning to enter a position.
- Maintenance Margin: The minimum balance required in the account.
- Variation Margin: The daily adjustment of profit and loss, also known as Mark-to-Market (MTM).
Margin Calls
When the account balance falls below the maintenance margin, the trader must deposit additional funds. Failure to do so may result in the exchange closing the position.
Comparison of Derivatives Contracts
| Basis | Forward Contract | Futures Contract | Options Contract |
|---|---|---|---|
| Meaning | Private agreement to buy/sell at a future date. | Standardized exchange-traded agreement. | Right, but not obligation, to buy/sell. |
| Nature | Customized | Standardized | Standardized |
| Trading | Over-the-counter (OTC) | Organized exchanges | Exchanges |
| Obligation | Both parties | Both parties | Buyer has right, seller has obligation |
| Risk | High (default risk) | Lower (clearing house) | Limited for buyer, high for seller |
| Margin | Generally none | Required | Required (mainly seller) |
| Settlement | At maturity | Daily (MTM) | At or before expiry |
Functions of Derivatives
- Hedging: Reducing or eliminating price fluctuation risks.
- Speculation: Earning profits by predicting future price movements.
- Arbitrage: Exploiting price differences between markets for risk-free profit.
- Price Discovery: Determining expected future asset prices.
- Portfolio Management: Adjusting risk exposure.
- Cost Efficiency: Using leverage via margin requirements.
- Liquidity: Ensuring smooth trading and market efficiency.