Black, Scholes and Merton Model Flashcards
What major breakthrough did BSM achieve in the early 1970s?
It provided a revolutionary model for pricing European stock options.
Why is the BSM model significant?
It has had a massive influence on financial engineering and options pricing.
What does the binomial model assume about stock price movements?
Stock prices move up or down in discrete time steps.
What happens to the binomial distribution as the number of periods approaches infinity?
It approaches a normal distribution.
In the binomial model, how often does the option price change?
Every t/N units of time until maturity.
What are the main assumptions of the Black-Scholes Model?
- Stock prices follow a random walk.
- No transaction costs or taxes.
- No dividends during the option’s life.
- No riskless arbitrage opportunities.
- Continuous trading & perfectly divisible securities.
- Investors can borrow/lend at the risk-free rate.
- The risk-free interest rate is constant over time.
Why does expected return not appear in the Black-Scholes formula?
Because the real-world probabilities of stock price movements are not used.
What is the Put-Call Parity Theorem?
It states that the value of a European call and put option are related as:
C - P = S - Ke^{-rT}
Why is Put-Call Parity important?
It ensures no arbitrage opportunities exist between puts and calls.
What is a major limitation of the Black-Scholes model?
It assumes constant return volatility, which is not true in reality.
How has financial market behavior contradicted this assumption?
Market events, such as financial crises, show that volatility changes over time.
What is implied volatility?
It is volatility estimated from option prices rather than historical data.
What is the VIX Index commonly known as?
The “Fear Gauge” because it measures investor sentiment and risk appetite.
Why does a longer time to maturity increase option premiums?
More time allows for potential price fluctuations, increasing both call and put premiums.
What happens to a call option premium when the underlying stock price rises?
It rises.
