Unit 3: Options

Options

An Option is a financial derivative contract that gives the buyer the right (but not the obligation) to buy or sell an asset at a specific price (called strike price) on or before a specific date.

Types of Options

Type	Right Given	Used When You Expect
Call Option	Right to buy the asset	Price will rise
Put Option	Right to sell the asset	Price will fall

Key Terms

Term	Meaning
Strike Price	Pre-agreed price to buy/sell the asset
Premium	Cost paid by the option buyer to the seller
Expiry Date	Date when the option contract ends
ITM/ATM/OTM	In-The-Money, At-The-Money, Out-of-The-Money (describes profitability)

Hedging with Currency Options

Currency options help protect against currency risk in international trade.

How Hedging Works

• Importer’s Risk: USD may rise vs INR
  → Buy Call Option on USD-INR
  → Protects against paying more later.

• Exporter’s Risk: USD may fall vs INR
  → Buy Put Option on USD-INR
  → Protects earnings from dropping.

Example: An Indian exporter expects $50,000 in 1 month. He fears USD will weaken. He buys a USD-INR put option at strike ₹83. If USD falls to ₹80, the option gives him ₹83 — he is hedged.

Speculation with Options

Speculators use options to earn profits from price movements in currencies, stocks, or indices with limited risk (premium paid).

Examples:

Expectation	Action	Why
USD will rise	Buy Call Option	Profit if price goes above strike
USD will fall	Buy Put Option	Profit if price falls below strike

👉 Maximum loss = Premium paid; Unlimited potential gain.

Arbitrage with Options

Arbitrage involves risk-free profits from price discrepancies between the spot, futures, and options markets.

Example: Put-Call Parity Arbitrage

If:

Call + PV(Strike) ≠ Put + Spot Price

Then there’s a mispricing. Arbitrageurs can:

• Buy undervalued instrument
• Sell overvalued instrument
• Lock in profit with no risk

Example Scenario

• Buy a call and sell a put (same strike/expiry)
• Borrow money and buy currency
• Deliver as per the more favorable contract

Result: Profit if prices are misaligned.

Summary Table

Concept	Purpose	Who Uses It?
Hedging	Reduce currency risk	Importers, exporters, investors
Speculation	Earn profits on market movement	Traders, investors
Arbitrage	Risk-free profit from mispricing	Professional arbitrageurs

Pricing of Options

Option pricing means determining the fair value or premium of an option contract.

The value of an option depends on several factors, such as:

Factors Affecting Option Price	Impact
Spot price of the underlying asset	Higher spot increases call value, reduces put value
Strike price	Higher strike lowers call value, increases put value
Time to expiry	More time = higher value (for both calls and puts)
Volatility of the asset	More volatility = higher premium (due to higher potential movement)
Interest rates	Higher rates increase call value, decrease put value
Dividends	Expected dividends reduce call value and increase put value

General Principles of Option Pricing

A. Call Option Pricing

A Call Option becomes more valuable when:

• The underlying price increases
• Time to expiry is long
• Volatility is high

B. Put Option Pricing

A Put Option becomes more valuable when:

• The underlying price decreases
• Time to expiry is long
• Volatility is high

C. Intrinsic Value & Time Value

Component	Explanation
Intrinsic Value	Profit if the option were exercised today 👉 Call: Max(0, S – K) 👉 Put: Max(0, K – S)
Time Value	Extra value due to time till expiry and potential price movement

Option Premium = Intrinsic Value + Time Value

Black-Scholes Option Pricing Model (BSOPM)

The Black-Scholes Model is the most famous model to calculate the theoretical price of European call and put options on non-dividend-paying stocks.

Assumptions of the Black-Scholes Model:

• Stock price follows log-normal distribution
• No dividends during the option life
• No transaction costs or taxes
• Risk-free interest rate is constant
• Markets are efficient (no arbitrage)
• European option (can only be exercised at expiry)

Black-Scholes Formula (for Call Option):

C = S × N(d₁) – K × e^(–rt) × N(d₂)

Where:

• C = Call option price
• S = Current stock/spot price
• K = Strike price
• t = Time to maturity
• r = Risk-free interest rate
• N(d) = Cumulative standard normal distribution function
• 
  
• d₁ = [ln(S/K) + (r + σ² / 2) × t] / (σ × √t)
• d₂ = d₁ – σ × √t

(σ = volatility)

Put Option Price (using Put-Call Parity):

P = K × e^(–rt) × N(–d₂) – S × N(–d₁)

Example

Assume:

• Spot Price (S) = ₹100
• Strike Price (K) = ₹95
• Time (t) = 0.5 years
• Volatility (σ) = 20%
• Risk-free rate (r) = 5%

Using Black-Scholes formulas, you can calculate Call and Put Option Prices. (Can be solved using Excel, calculator, or software tools.)

Summary Table

Component	Call Option	Put Option
Value Increases When	Spot ↑, Time ↑, Volatility ↑	Spot ↓, Time ↑, Volatility ↑
Intrinsic Value	Max(0, S – K)	Max(0, K – S)
Time Value	Always ≥ 0	Always ≥ 0
Pricing Model	Black-Scholes Model (for European)	Use BSM or Put-Call Parity

Index Options

Index Options are derivative contracts where the underlying asset is a stock market index, like Nifty 50, Sensex, Bank Nifty, or S&P 500.

They give the right (but not obligation) to buy or sell the index at a predetermined strike price on or before expiry.

These are cash-settled (you don’t get actual stocks) because indices are not tangible assets.

Types of Index Options 

Hedging with Index Options

Index options are widely used for portfolio hedging to protect against overall market movement (systematic risk).

Example: You own a portfolio of large-cap stocks (similar to Nifty 50), and you are worried about a market fall.

Solution

• Buy Index Put Option on Nifty 50
• If the market falls, the put option will gain in value, offsetting your portfolio losses.

Benefits of Index Option Hedging

• Cheaper than selling all stocks
• Protects against downside while retaining upside potential
• Easy to manage, low transaction costs

Speculation with Index Options

Speculators use index options to bet on the direction of the market.

Expectation	Action	Why
Market will rise	Buy Index Call Option	Profit if index moves above strike price
Market will fall	Buy Index Put Option	Profit if index drops below strike price

Risk is limited to the premium paid, but potential profit is high if the market moves sharply.

Example: You expect Nifty to rise from 20,000 to 20,500.

• Buy a 20,000 Call Option
• If Nifty goes to 20,500, you make a profit minus the premium paid

Arbitrage with Index Options

Arbitrage involves risk-free profit using mispricing between the index spot price, futures, and options.

Techniques:

• Put-Call Parity Arbitrage
• Index Future vs. Options Arbitrage

Put-Call Parity Formula:

Call + PV(Strike) = Put + Spot Index

If this equality doesn't hold, arbitrageurs can:

• Buy undervalued side
• Sell overvalued side
• Lock in riskless profit

Summary Table

Concept	Purpose	Who Uses It
Hedging	Protects portfolio from market losses	Long-term investors, fund managers
Speculation	Earn from market moves	Short-term traders
Arbitrage	Risk-free profit from mispricing	Professional arbitrageurs

Popular Index Options in India:

Index	Exchange	Expiry	Lot Size (As of 2024)
Nifty 50	NSE	Weekly & Monthly	50
Bank Nifty	NSE	Weekly & Monthly	15
Sensex	BSE	Monthly	15

Index Options Market in Indian Stock Market

Index options in India are derivatives contracts based on stock market indices like:

• Nifty 50
• Bank Nifty
• Nifty Financial Services
• Sensex

These contracts are cash-settled, and regulated by SEBI, and traded on:

• NSE (National Stock Exchange)
• BSE (Bombay Stock Exchange)

Key Features of Indian Index Options Market:

Parameter	Details
Regulator	SEBI
Exchanges	NSE, BSE
Index Options Available	Nifty 50, Bank Nifty, Sensex, Nifty Financial Services
Settlement Type	Cash-settled
Expiry	Weekly (mostly Thursday), and Monthly
Lot Size (as of 2024)	Nifty 50 (50 units), Bank Nifty (15 units)
Trading Time	9:15 AM to 3:30 PM (Mon-Fri)

Use of Different Option Strategies to Mitigate Risk

Investors and traders use option strategies to manage risk, reduce losses, or lock in profits in volatile markets.

Below are some commonly used Index Option Strategies:

A. Protective Put

Buy a Put Option on the index while holding a portfolio of stocks/index.

• Use: To protect downside risk in falling markets.
• Example: Hold Nifty stocks → Buy Nifty Put at 20,000

B. Covered Call

Sell a Call Option while holding the underlying index (via ETF or futures).

• Use: To earn extra income in a flat or slightly bullish market.
• Example: Long Nifty → Sell Nifty 21,000 Call

C. Bull Call Spread

Buy a Call Option at lower strike, and sell another Call at higher strike.

• Use: To reduce premium cost and profit from moderate bullish movement.
• Example: Buy Nifty 20,000 Call, Sell Nifty 20,500 Call

D. Bear Put Spread

Buy a Put at higher strike, Sell Put at lower strike.

• Use: For moderately bearish outlook.
• Example: Buy 20,000 Put, Sell 19,500 Put

E. Straddle

Buy both a Call and Put at the same strike price.

• Use: When expecting high volatility but unsure of direction.
• Example: Buy Nifty 20,000 Call + Put

F. Iron Condor

Combination of two spreads (Bull Put + Bear Call)

• Use: For low volatility markets, to earn premium.

Example

• Sell 19,500 Put & Buy 19,000 Put
• Sell 20,500 Call & Buy 21,000 Call

Summary Table: Option Strategies to Mitigate Risk

Strategy	Market View	Risk	Reward
Protective Put	Bearish or uncertain	Limited	Unlimited
Covered Call	Neutral to slightly bullish	Limited downside	Limited upside
Bull Call Spread	Moderately bullish	Limited	Limited
Bear Put Spread	Moderately bearish	Limited	Limited
Straddle	Highly volatile	High (premium cost)	Unlimited
Iron Condor	Low volatility	Limited	Limited

Real-Life Application

• Mutual funds and institutional investors hedge large portfolios using Nifty/Bank Nifty options.
• Retail traders speculate or protect their holdings using these strategies.