C17-18: Extensions of the BSM Model

What are index options?

Options whose underlying asset is a stock market index

How are index options typically settled?

Cash settled rather than physical delivery

What determines contract size for index options?

Typically a multiple of the index level (e.g., 100 × index)

What is a key use of index put options?

Portfolio insurance against market declines

How does portfolio insurance using index puts work?

Buying puts to protect against downside in a portfolio

What role does beta play in portfolio insurance?

It determines the number of index options needed to hedge a portfolio

How does a higher beta affect hedging?

More options are required to hedge higher market sensitivity

What is the key idea in pricing index options?

Treat the index as an asset paying a continuous dividend yield

Why can index options be treated like dividend-paying stocks?

Because index returns include dividends

How are dividends incorporated into index option pricing?

By reducing the effective underlying price

What is the impact of dividend yield on option prices?

It lowers call values and increases put values

What is the adjusted underlying price in index option pricing?

The current index level reduced by expected dividends

What is the lower bound for index call options?

It reflects discounted strike and dividend-adjusted index value

What is the lower bound for index put options?

It reflects discounted strike relative to dividend-adjusted index value

How does put-call parity change for index options?

It includes the dividend-adjusted index price

What is an alternative way to express index option pricing?

Using forward prices instead of spot prices

What are currency options?

Options on exchange rates between two currencies

Where are currency options typically traded?

Primarily in OTC markets with customized terms

Why are currency options customized?

To meet specific hedging needs of firms

How are currencies treated in option pricing?

As assets that provide a yield equal to the foreign interest rate

What does the foreign interest rate represent?

The opportunity cost of holding foreign currency

How does the domestic vs foreign rate affect pricing?

The difference influences forward exchange rates and option values

What is the key adjustment in currency option pricing?

Replace dividend yield with foreign interest rate

What are futures options?

Options whose underlying asset is a futures contract

What is a key feature of futures options?

Exercise results in a futures position rather than the underlying asset

When do futures options typically expire?

At or just before the delivery date of the underlying futures

Why are futures options widely used?

They are often more liquid and easier to trade than spot assets

What happens when a call futures option is exercised?

The holder receives a long futures position and a cash payment

What happens when a put futures option is exercised?

The holder receives a short futures position and a cash payment

How are futures option payoffs determined?

Based on the difference between futures price and strike price

What is a key property of futures contracts in pricing?

They require no initial investment

What does this imply about expected returns?

The expected return on futures is zero in a risk-neutral world

How are futures treated in option pricing models?

Like assets paying a yield equal to the risk-free rate

What is Black’s model?

A pricing model for options on futures

Why is Black’s model used instead of BSM?

It simplifies pricing for futures-based derivatives

What is the key assumption in Black’s model?

Futures prices follow a lognormal process under risk-neutral valuation

What is the advantage of using futures prices in option valuation?

Avoids estimating dividends or convenience yield

What is the relationship between spot and futures options at maturity?

They have identical payoffs when futures price equals spot price

How does put-call parity differ for futures options?

It uses the present value of the futures price instead of spot price

What is the general insight across index, currency, and futures options?

All can be treated as assets with a yield adjustment

What is the unified framework for BSM extensions?

Adjust the underlying asset price or yield depending on the asset type

What are the yield equivalents for different assets?

Index: dividend yield; currency: foreign interest rate; futures: risk-free rate

What is the key takeaway of BSM extensions?

Option pricing remains based on no-arbitrage with adjustments for income or yields