Chapter 3: Commodity Options (Part Two — Valuation, Greeks, and Settlement Mechanisms)

1. Determinants of Option Premiums

The premium (or market price) of a commodity option is not static; it fluctuates continuously based on multiple market variables. An option's premium is mathematically composed of two elements: Intrinsic Value and Time Value. While intrinsic value represents the actual amount by which an option is in-the-money, time value reflects the probability of favorable price movements before the contract expires.

To trade options effectively or prepare for the NISM Series XVI exam, you must understand how the following five key determinants impact call and put options differently:

1.1 Price of the Underlying Asset

The current market price of the underlying commodity is the most direct driver of option premiums:

• Call Options: As the price of the underlying asset rises, the value of a call option increases. Conversely, if the underlying asset price falls, the call option premium decreases.
• Put Options: Put options exhibit the opposite relationship. When the price of the underlying asset falls, the value of the put option increases. When the underlying asset price rises, the put option premium decreases.

1.2 Strike Price

The strike price (or exercise price) represents the contractually fixed price of the option. Its relationship with the premium is as follows:

• Call Options: If all other factors remain constant, an increase in the strike price decreases the intrinsic value of a call option, which subsequently reduces its total market premium.
• Put Options: Conversely, an increase in the strike price increases the intrinsic value of a put option, thereby driving its market premium higher.

1.3 Volatility of the Underlying Asset

Volatility represents the magnitude of price movements (either upward or downward) in the underlying commodity.

• Symmetrical Impact: Volatility affects both call and put options in the exact same manner.
• The Volatility Premium: A higher volatility in the underlying commodity results in a higher premium for both calls and puts. This occurs because greater price fluctuations increase the mathematical probability that the option will move deep in-the-money (ITM) during the life of the contract.

1.4 Time to Expiration

The remaining lifespan of an option contract directly dictates its uncertainty and risk profile.

• Symmetrical Impact: Similar to volatility, the time remaining until expiration affects both call and put options in the same way.
• Time Decay Principle: Generally, a longer maturity or more time to expiration results in greater market uncertainty, which translates to a higher option premium. As the expiration day approaches, this uncertainty dissolves, and the time value of the option decays systematically until it reaches zero on the final day of trading.

1.5 Risk-Free Interest Rates

Short-term interest rates also play a role in option pricing models by reflecting the cost of capital:

• Call Options: High interest rates result in an increase in the value of a call option.
• Put Options: High interest rates result in a decrease in the value of a put option.

Key Summary: Option Premium Determinants Matrix

The table below illustrates the directional impact on option premiums when each individual pricing variable increases (assuming all other variables remain strictly constant):

2. Option Pricing Models

Option pricing models are mathematical frameworks used to calculate the "fair" or theoretical value of an option contract. The two most prominent models in derivatives markets are:

2.1 The Binomial Pricing Model

The Binomial Option Pricing Model was developed by William Sharpe in 1978. Over time, it has proven to be the most flexible, intuitive, and popular iterative approach to option pricing.

• How it Works: The binomial model represents the price evolution of the option’s underlying asset as a "binomial tree" of all possible prices at equally-spaced time steps from today into the future.
• Core Assumption: At each discrete step or node in the tree, the price of the underlying asset can only move in one of two directions: up or down, at fixed rates and with respective simulated probabilities.

2.2 The Black-Scholes Model

The Black-Scholes Model was published in 1973 by Fisher Black and Myron Scholes. It is widely celebrated as one of the most popular, simple, and computationally rapid modes of option valuation.

• Analytical Approach: Unlike the binomial model, the Black-Scholes model is a closed-form analytical formula that does not rely on iterative calculations.
• Key Inputs: It calculates the theoretical price of an option using five key determinants:
  1. Current price of the underlying asset
  2. Strike price
  3. Volatility
  4. Time to expiration
  5. Short-term, risk-free interest rate

2.3 The Black-76 Variant

• Application: A specialized variant of the original Black-Scholes option pricing model, known as the "Black-76 model", is utilized to calculate the theoretical price of options contracts where the underlying asset is itself a futures contract rather than a physical commodity.

3. Option Greeks: Sensitivity Measures

Option Greeks are mathematical values that measure the sensitivity of an option’s price to changes in its underlying parameters. They are indispensable tools for risk management, hedging, and portfolio adjustments.

• Delta (δ or ∆): Measures the sensitivity of the option's value to a given small change in the price of the underlying asset. It represents the expected change in option premium for a one-unit change in the commodity's spot or futures price.
• Gamma (γ): Measures the rate of change in Delta with respect to a change in the price of the underlying asset. It indicates how stable or volatile the option's Delta is as the underlying price moves.
• Theta (θ): Measures an option's sensitivity to time decay. It quantifies the daily loss in the option's premium as the time to expiration decreases, assuming all other factors remain constant.
• Vega (ν): Measures the sensitivity of an option's premium to changes in the market volatility of the underlying asset. It shows how much the option price will fluctuate per percentage point change in implied volatility.
• Rho (ρ): Measures the change in the option's price given a percentage change in the risk-free interest rate.

4. The Put-Call Parity Theorem

The Put-Call Parity Theorem establishes a rigid, non-arbitrage relationship between the prices of European call and put options that share the same underlying asset, strike price, and expiration date.

4.1 Put-Call Parity Formula

In accordance with the simple line-format requirement, the theorem is mathematically expressed as:

C - P = S - K / (1 + r)^t

Where:

• C = Call Option Premium
• P = Put Option Premium
• S = Current Price of the Underlying Commodity
• K = Strike Price of the Options
• r = Risk-Free Interest Rate
• t = Time to Expiration

Note: If the market prices of calls, puts, and the underlying commodity deviate from this equilibrium, arbitrage opportunities arise, allowing traders to lock in riskless profits until the parity is restored.

5. Options on Commodity Futures vs. Options on Goods

In the Indian commodity derivatives market regulated by SEBI, options are traded under two distinct structures: Options on Commodity Futures and Options on Goods. Understanding the differences in their settlement and delivery mechanics is critical.

5.1 Options on Commodity Futures

Options on Commodity Futures do not settle directly into physical commodities. Instead, they settle by "devolving" into active positions in the underlying futures contract.

• The Underlying: The underlying asset for an Option on Futures is a standardized commodity futures contract of a specified month traded on the exchange.
• Devolution Mechanism on Exercise: When an Option on Futures is exercised, the option positions devolve into corresponding futures positions as follows:
  • Long Call devolves into a Long position in the underlying futures contract.
  • Long Put devolves into a Short position in the underlying futures contract.
  • Short Call devolves into a Short position in the underlying futures contract.
  • Short Put devolves into a Long position in the underlying futures contract.

5.2 Options on Goods

Options on Goods are direct options on the physical commodity itself.

• Devolution Mechanism on Exercise: Instead of settling into futures contracts, Options on Goods devolve directly into physical delivery obligations on expiry. The call option buyer has the right to receive physical delivery of the goods, and the put option buyer has the right to deliver physical goods.
• Key Advantage: Because futures contracts are heavily utilized for speculative trading, they can occasionally experience highly volatile or inconsistent price movements. Options on Goods bypass this futures-related speculation, offering direct exposure to physical commodity spot values.
• Delivery Awareness: Traders in Options on Futures are aware that they do not face immediate physical delivery obligations upon exercise (as they first receive a futures position). Conversely, Options on Goods lead directly to physical delivery processes.
• Closing Options on Goods: Just like Options on Futures, there are three methods to exit an Options on Goods contract: Offset, Exercise, and Expiration. The most common and liquid method of exit is by Offset (entering an opposite trade before expiry).

5.3 SEBI Exercise and Settlement Mechanics (Options on Futures)

SEBI's regulatory guidelines mandate a highly structured exercise system upon the expiry of commodity option contracts:

1. In-the-Money (ITM) Options: All ITM option contracts are exercised automatically upon expiration. The only exception is if the long position holder actively submits a "contrary instruction" to the exchange stating they do not wish to exercise.
2. Close-to-the-Money (CTM) Options: CTM options (which include ATM options and adjacent strikes) are excluded from this automatic exercise mechanism. Their exercise is handled via specific instructions.
3. Out-of-the-Money (OTM) Options: All OTM option contracts (except those designated within the CTM series) are deemed worthless and expire automatically without value.

6. Important Terms & Exam-Relevant Highlights

• Black-76: The specific mathematical model used when the underlying of an option contract is a commodity futures contract.
• Theta Decay: Time decay is a non-linear process that accelerates as the option contract approaches its expiration date.
• Automatic Exercise: ITM option contracts automatically devolve into futures unless contrary instructions are given.
• Offset: The most common method of closing out an option position before maturity on the exchange.

Key Formulas (Line Format)

• Put-Call Parity Relationship: C - P = S - K / (1 + r)^t
• Option Premium Composition: Option Premium = Intrinsic Value + Time Value