NISM Series IV: Exchange Traded Interest Rate Options – Basics, Greeks & Pricing Models
This is Part 5 of our NISM Series IV Interest Rate Derivatives study notes. This post covers Chapter 4 — Exchange Traded Interest Rate Options. Options are one of the most important and conceptually rich topics in the NISM derivatives exam. This post will walk you through all the key concepts, from basic option definitions to option Greeks, the Black-Scholes model, and implied volatility.
Why Options? From Futures to Options
A forward/futures contract is a commitment to buy/sell the underlying. It has a linear payoff, meaning unlimited losses and profits are possible. Some market participants desired to ride the upside while restricting losses. This gave rise to options — a financial instrument that restricts losses while allowing unlimited profits on buy/sell of the underlying asset.
What is an Option?
An option is a contract that gives the option buyer the right, but not the obligation, to buy or sell the underlying asset on or before a specified date/day, at a pre-determined price. For acquiring this right, the option buyer pays a certain price/premium to the option seller.
Key Option Terminology Call Option
The right to buy the underlying asset at the strike price.
Put Option
The right to sell the underlying asset at the strike price.
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/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 right but not the obligation and pays the premium for acquiring that right.
Option Seller / Writer
The party that sells the right and receives the premium for assuming the obligation.
Option Premium / Option Price
The price the option buyer pays to the option seller to acquire the right.
To Exercise
In options trading, "to exercise" means to put into effect the right to buy or sell the underlying security specified in the options contract.
European vs American Options
| Feature | European Option | American Option |
|---|---|---|
| Exercise | Only on the expiration date | Any time on or before the expiration date |
| Flexibility | Less flexible | More flexible |
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 when the spot price equals the strike price. On exercise, the buyer gets zero cash flow.
Option Premium Components
The option value (option premium) consists of two parts:
1. Intrinsic Value
The amount by which the option is in the money. An ATM or OTM option has zero intrinsic value.
2. Time Value
The difference between the option premium and the intrinsic value. Time value is directly proportional to the length of time to the expiration date.
- Longer the time to expiration → Higher the time value.
- A 2-month call option at the same strike price will be priced higher than a 1-month call option.
- Time value decreases with the passage of time — this is called time decay.
Option Premium = Intrinsic Value + Time Value
Five Fundamental Parameters That Affect Option Price 1. Spot Price of the Underlying Asset
- If the spot price goes up → Call option value increases; Put option value decreases.
- If the spot price goes down → Call option value decreases; Put option value increases.
2. Strike Price
- If the strike price increases → Call option value decreases; Put option value increases.
3. Volatility
Higher volatility → Higher premium for both call and put options, because there is a greater possibility that the option will move in-the-money during the life of the contract.
4. Time to Expiration
Generally, longer maturity → Greater uncertainty → Higher premium. The time value portion of an option's premium decreases as expiry approaches (time decay).
5. Interest Rates (Risk-Free Rate)
Higher interest rates → Increase in the value of a call option and a decrease in the value of a put option.
Option Greeks — Key Exam Topic for NISM Series IV Delta (δ)
Delta measures the sensitivity of the option value to a given small change in the price of the underlying asset.
- For a call option: Delta is positive (between 0 and 1).
- For a put option: Delta is negative (between -1 and 0).
Gamma (Γ)
Gamma measures the change in Delta with respect to a change in the price of the underlying asset. This is the second derivative of the option price with regard to the price of the underlying asset.
Theta (θ)
Theta is a measure of an option's sensitivity to time decay. It is the change in option price given a one-day decrease in time to expiration. Theta is used to understand how time decay is affecting your option positions.
Vega (ν)
Vega is a measure of the sensitivity of an option price to changes in market volatility. It is the change in an option premium for a given change in the underlying's volatility.
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.
Quick Reference: Effect of Parameters on Option Price
| Parameter Increases | Call Option | Put Option |
|---|---|---|
| Spot Price ↑ | Increases | Decreases |
| Strike Price ↑ | Decreases | Increases |
| Volatility ↑ | Increases | Increases |
| Time to Expiry ↑ | Increases | Increases |
| Interest Rate ↑ | Increases | Decreases |
Put-Call Parity
Put-call parity shows the relationship that must exist between European put and call options that have the same underlying asset, expiration, and strike prices. Put-Call parity holds only for European options.
Formula: C + PV(x) = P + S
Where:
- C = Call option price
- PV(x) = Present value of strike price
- P = Put option price
- S = Current spot price of underlying
Option Pricing Models 1. The Binomial Pricing Model
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. The assumption is that at each step, the price can only move up or down at fixed rates with respective simulated probabilities.
2. The Black & Scholes Model
This is one of the most popular, relatively simple, and fast modes of option pricing calculation. Unlike the binomial model, it does not rely on calculation by iteration. It is used to calculate the theoretical call price (ignoring dividends paid during the life of the option).
Black-Scholes Formulas:
C = S × N(d₁) – X × e^(-rT) × N(d₂)
P = X × e^(-rT) × N(–d₂) – S × N(–d₁)
Where:
- d₁ = [ln(S/X) + (r + v²/2) × t] / (v × √t)
- d₂ = d₁ – v × √t
- S = Stock price
- X = Strike price
- t = Time remaining until expiration (in years)
- r = Current continuously compounded risk-free interest rate
- v = Annual volatility of stock price (standard deviation of short-term returns over one year)
- N(x) = Standard normal cumulative distribution function
Types of Volatility Historical Volatility
Calculated from past closing prices of the stock/index/bonds/currency. Easy to calculate and useful for day-to-day requirements.
Forecasted Volatility
Predicting volatility over a desired time frame using statistical models.
Implied Volatility (IV)
IV represents the market participants' expectation on volatility. It can be thought of as the consensus volatility arrived at by all market participants, with respect to the expected amount of underlying price fluctuation over the remaining life of an option.
Quick Recap for NISM Series IV Exam
- Call = right to buy; Put = right to sell.
- ITM = positive cash flow on exercise; OTM = negative; ATM = zero.
- Option Premium = Intrinsic Value + Time Value.
- 5 factors affecting option price: Spot price, Strike price, Volatility, Time to expiry, Interest rate.
- Option Greeks: Delta, Gamma, Theta, Vega, Rho.
- Put-Call Parity: C + PV(x) = P + S (only for European options).
- Two pricing models: Binomial model and Black-Scholes model.
- Implied volatility = market consensus on expected future volatility.
Next Blog Post: Chapter 5 — Strategies Using Exchange Traded Interest Rate Derivatives. We will cover hedging, option spreads, straddles, strangles, butterfly spreads, covered calls, and protective puts.
Start practicing now with NISM Series IV mock tests at passnism.in.