Exchange Traded Interest Rate Options

Exchange Traded Interest Rate Options (Part 1)

• Definition: An option is a contract between two parties giving the buyer of an option the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date.
• Key Components:
  • Call Option: The right to buy the asset.
  • Put Option: The right to sell the asset.
  • Strike Price: The pre-specified price at which the underlying asset may be purchased or sold by the option holder.
  • Expiration Date: The date at which the option contract will expire or cease to exist.
  • Time to Maturity: The difference between the date of entering into the contract and the expiration date.
  • Option Buyer: The party that buys the rights but not obligation and pays premium for buying the right.
  • Option Seller/Writer: The party that sells the right and receives premium for assuming such obligation.
  • Option Price/Premium: The price which option buyer pays to option seller to acquire the right.
  • Underlying Asset: The asset which is bought or sold.
• Option Styles:
  • European Options: Can be exercised by the buyer of the option only on the expiration date.
  • American Options: Can be exercised by the buyer any time on or before the expiration date.
  • Bermuda Options: Can be exercised on specific days before expiration.
• Moneyness of an Option:
  • In-the-Money (ITM): An option is said to be in the money if on exercising it, the option buyer gets a positive cash flow.
  • Out-of-the-Money (OTM): An option is said to be out of the money if on exercising it, the option buyer gets a negative cash flow.
  • At-the-Money (ATM): An option is said to be at the money if spot price is equal to the strike price.
• Option Pricing:
  • Intrinsic Value: The amount by which option is in the money.
  • Time Value: The difference between option premium and intrinsic value.
  • Option Premium: The total value of the option, consisting of intrinsic value and time value.

Exchange Traded Interest Rate Options (Part 2)

• Time Value: The time value reflects the probability that the option will gain in intrinsic value or become profitable to exercise before its maturity.
• Option Pricing Fundamentals: The value of an option is determined by various parameters, including:
  • Spot Price of the Underlying Asset: The option premium is affected by the price movements in the underlying instrument.
  • Strike Price: If all other factors remain constant, an increase in strike price decreases the intrinsic value of a call option and increases the intrinsic value of a put option.
  • Volatility of the Underlying Asset’s Price: Higher volatility increases the premium because there is a greater possibility that the option will move in-the-money during the life of the contract.
  • Time to Expiration: Longer maturity of the option increases uncertainty and hence the premium.
  • Interest Rates: High interest rates increase the value of a call option and decrease the value of a put option.

Option Pricing Parameters

The following table summarizes the relationship between different factors and the value of call/put options: | Factor | Change in Factor | Call Premium | Put Premium | | --- | --- | --- | --- | | Spot Price | Increase | ↑ | ↓ | | Spot Price | Decrease | ↓ | ↑ | | Strike Price | Increase | ↓ | ↑ | | Strike Price | Decrease | ↑ | ↓ | | Volatility | Increase | ↑ | ↑ | | Volatility | Decrease | ↓ | ↓ | | Time to Expiry | Longer | ↑ | ↑ | | Time to Expiry | Shorter | ↓ | ↓ | | Interest Rates | Increase | ↑ | ↓ | | Interest Rates | Decrease | ↓ | ↑ |

Option Greeks

• Delta (Δ): Measures the sensitivity of the option value to a given small change in the price of the underlying asset.
• Gamma (γ): Measures the change in delta with respect to change in price of the underlying asset.
• Theta (θ): Measures an option’s sensitivity to time decay.
• Vega (ν): Measures the sensitivity of an option price to changes in market volatility.
• Rho: Measures the sensitivity of an option price to changes in interest rates.

These Option Greeks help traders and investors understand the risks and potential rewards associated with options trading.

Exchange Traded Interest Rate Options (Part 3)

• Rho (ρ): Rho is the change in option price given a one percentage point change in the risk-free interest rate. Rho measures the change in an option’s price per unit increase in the cost of funding the underlying.
• Rho Formula: Rho = Change in an option premium / Change in cost of funding of the underlying
• Call and Put Options: Call options generally rise in price as interest rates increase and put options generally decrease in price as interest rates increase. Thus, call options have positive rho, while put options have negative rho.

Put-Call Parity

• Definition: Put-call parity shows the relationship that has to exist between European put and call options that have the same underlying asset, expiration, and strike prices.
• Formula: C + PV(x) = P + S
• Variables:
  • C: price of the call option
  • PV(x): present value of x (the strike price)
  • P: price of the put
  • S: spot price (current market value) the underlying asset

Option Pricing Methodology

• Binomial Pricing Model: The binomial option pricing model represents the price evolution of the option’s underlying asset as the binomial tree of all possible prices at equally-spaced time steps from today under the assumption that at each step, the price can only move up and down at fixed rates and with respective simulated probabilities.
• Black & Scholes Model: The Black & Scholes model is used to calculate a theoretical call price (ignoring the dividends paid during the life of the option) using the five key determinants of an option’s price: stock price, strike price, volatility, time to expiration, and short-term (risk free) interest rate.
• Black & Scholes Formula:
  • C = SN(d1) – Xe-rtN(d2)
  • P = Xe-rtN(-d2) - SN(-d1)
  • Variables:
    • S: stock price
    • X: strike price
    • t: time remaining until expiration, expressed in years
    • r: current continuously compounded risk-free interest rate
    • v: annual volatility of stock price
    • In: natural logarithm
    • N(x): standard normal cumulative distribution function
    • e: the exponential function

Black (1976) Model

• Definition: The Black (1976) model is used for the valuation of futures options.
• Formula:
  • C = Fe-rtN(d1) – Xe-rtN(d2)
  • P = e-rt [XN(-d2)-FN(-d1)]
• Variables:
  • F: future price
  • X: strike price
  • t: time remaining until expiration, expressed in years
  • r: current continuously compounded risk-free interest rate
  • σ: volatility
  • In: natural logarithm
  • N(x): standard normal cumulative distribution function
  • e: the exponential function

Implied Volatility (IV)

• Definition: Implied volatility represents the market participant’s expectation on volatility.
• Types of Volatility:
  • Historical Volatility
  • Forecasted Volatility
  • Implied Volatility
• Implied Volatility Formula: Implied volatility can be derived from the cost of the option using mathematical option pricing models.

Payoff Diagrams for Options

• Long on Option: Buyer of an option is said to be “long on option”. The potential loss is limited to the premium amount paid for buying the option.
• Short on Option: Seller of an option is said to be “short on option”. The seller has an obligation but no right with regard to selling/buying the underlying asset in the contract.

Exchange Traded Interest Rate Options (Part 4)

When you are short (i.e., the writer of) an option contract:

• Your maximum profit is the premium received.
• You can be assigned to deliver if the option is exercised by the buyer. All option writers should be aware that assignment is a distinct possibility.
• Your potential loss is theoretically unlimited.

Note that long/short on option and long/short position are different. A long call option has a long position on the underlying, while a long put option has a short position on the underlying asset.

Key Concepts

• Long Call: Gives the buyer the right, but not the obligation to buy the underlying at the strike price.
• Short Call: Gives the seller the obligation to sell the underlying at the strike price if the option is exercised.
• Long Put: Gives the buyer the right, but not the obligation to sell the underlying at the strike price.
• Short Put: Gives the seller the obligation to buy the underlying at the strike price if the option is exercised.

Break-Even Point (BEP)

• For call options: Strike Price + Premium (X + P)
• For put options: Strike Price - Premium (X - P)

Payoff Diagrams

• Long Call: Maximum loss is equal to the premium paid, while maximum gain is unlimited.
• Short Call: Maximum gain is equal to the premium received, while maximum loss is unlimited.
• Long Put: Maximum loss is equal to the premium paid, while maximum gain is unlimited.
• Short Put: Maximum gain is equal to the premium received, while maximum loss is unlimited.

Example

• Long Call: Buy a call option with a strike price of Rs. 98.50 at a premium of Rs. 0.20.
  • If the underlying price is above Rs. 98.50 at expiry, exercise the option and buy the underlying at Rs. 98.50.
  • If the underlying price is below Rs. 98.50 at expiry, let the option expire and lose the premium paid.
• Long Put: Buy a put option with a strike price of Rs. 98.50 at a premium of Rs. 0.30.
  • If the underlying price is below Rs. 98.50 at expiry, exercise the option and sell the underlying at Rs. 98.50.
  • If the underlying price is above Rs. 98.50 at expiry, let the option expire and lose the premium paid.

Exchange Traded Interest Rate Options (Part 5)

• Definition: Exchange Traded Interest Rate Options are a type of financial derivative that allows investors to hedge against interest rate risks or speculate on interest rate movements.
• Details: These options are traded on exchanges, providing a standardized and transparent platform for buyers and sellers to interact.

Key Concepts

• Long Put Position: A long put position gives the buyer the right, but not the obligation, to sell an underlying asset at a predetermined price (strike price) before a certain date (expiry date).
• Short Put Position: A short put position obligates the seller to buy the underlying asset at the strike price if the buyer exercises the option.
• Pay-off Chart: A pay-off chart illustrates the potential profits and losses of an option position at expiry, given different prices of the underlying asset.
• Maximum Loss: The maximum loss for a long put position is limited to the premium paid, while the maximum loss for a short put position can be substantial if the underlying asset price falls significantly.
• Break-Even Point (BEP): The BEP for a short put position is equal to the strike price minus the premium received.

Square-off Option Positions

• Definition: Square-off refers to the process of closing an open option position before expiry.
• Example: A dealer buys a put option and later sells it before expiry, realizing a profit or loss based on the difference between the purchase and sale prices.

Contract Specification of Exchange Traded Interest Rate Options

• Underlying Asset: Government of India (GOI) dated securities, such as bonds.
• Unit of Trading: 1 lot = notional bonds of face value INR 2 lakhs (2000 bonds).
• Quotation: Premium for options contracts quoted in Indian Rupees.
• Contract Value: Trade price * 2000.
• Tick Size: Rs. 0.0025.

Comparison of Exchange Traded IRO and OTC IRO

• Operational Mechanism: Exchange traded IRO involve contracts between two parties through a centralized trading platform, while OTC IRO are mainly bilateral over-the-counter transactions.
• Terms of Contracts: Exchange traded IRO have standardized contracts, while OTC IRO have non-standardized, custom-designed contracts.
• Available Products: Exchange traded IRO mainly offer European Interest Rate Options, while OTC IRO offer a broader range of products, including caps, floors, collars, and swaptions.
• Price Discovery: Exchange traded IRO provide price discovery through free interaction of buyers and sellers on a centralized trading platform, while OTC IRO rely on negotiation, which may not be as efficient.

Exchange Traded Interest Rate Options (Part 6)

• Definition: Exchange Traded Interest Rate Options are standardized contracts that are traded on an exchange, providing a guarantee of settlement by a clearing corporation.
• Details: These contracts are standardized, liquid, and provide price transparency, eliminating counterparty credit risk.

Key Characteristics

• Liquidation Profile: High, as contracts are standardized exchange-traded contracts.
• Market Maker: Currently not applicable, but Scheduled Banks, PDs, AIFIs are eligible to act as market makers.
• Settlement: Clearing & Settlement through a clearing corporation with guaranteed settlement.
• Quality of Information and Dissemination: Traded nationwide, with information available online on trading platforms and websites.

Advantages and Limitations

• Advantages:
  • Price Transparency: Provides price transparency.
  • Elimination of Counterparty Credit Risk: Settlement is guaranteed by a clearing corporation.
  • Customized Product: Can provide a perfect hedge.
• Limitations:
  • Imperfect Hedge: May lead to an imperfect hedge as settlement is standardized.
  • Liquidity Risk: Lower liquidity risk compared to OTC, but still present.
  • Counterparty Risk: Not applicable due to guaranteed settlement.

Comparison with OTC IRO

• Parameters:
  • Exchange Traded IRO: Guarantee by clearing corporation, access to all types of market participants, credit agnostic, lower liquidity risk.
  • OTC IRO: Customized product, but liquidity risk, counterparty risk, and not accessible to all kinds of market participants.

Market Indicators

• Open Interest: Total number of options or futures contracts that are not closed in a particular trading cycle, key indicator of market participation and liquidity.
• Put Call Ratio (PCR): An indicator to measure market sentiment, high PCR indicates bearishness, and low PCR indicates bullishness.

Put Call Ratio (PCR) Interpretation

• General Interpretation: A PCR above 1 indicates bearish sentiment, while a PCR below 1 indicates bullish sentiment.
• Contrarian Indicator: PCR is often used as a contrarian indicator, signaling potential reversals when it reaches extreme levels.
• Limitation of PCR: Must be used in addition to other indicators, and investors must know how to read the put-call ratio chart correctly.