50 MCQS ON OPTION VALUATION FOR IBBI VALUATION EXAMINATION PRACTICE
WITH A FOCUS ON 1 MARK
General Overview of SFA in Insolvency
1. General Principles of Option Valuation
- What is the key principle in option valuation?
a) Arbitrage pricing theory
b) Time decay
c) Risk-neutral valuation
d) Geometric Brownian motion
Answer: c) Risk-neutral valuation - Which of the following is NOT a characteristic of an option?
a) It provides the right, not the obligation, to buy or sell.
b) It always leads to a profit.
c) It has an expiration date.
d) It has an underlying asset.
Answer: b) It always leads to a profit. - In the Black-Scholes model, the underlying asset is assumed to follow which type of process?
a) Poisson process
b) Brownian motion
c) Linear regression
d) Geometric Brownian motion
Answer: d) Geometric Brownian motion - Which of the following factors does NOT directly affect the value of a call option?
a) Volatility of the underlying asset
b) Time to expiration
c) Risk-free interest rate
d) Dividend yield of the underlying asset
Answer: d) Dividend yield of the underlying asset - In the context of option pricing, what does the “Greeks” refer to?
a) The underlying asset’s volatility
b) The various sensitivities of option prices to parameters like stock price, time, and volatility
c) The historical performance of options
d) The fundamental factors influencing the stock market
Answer: b) The various sensitivities of option prices to parameters like stock price, time, and volatility
2. Black-Scholes Model
- The Black-Scholes formula is used for pricing which type of option?
a) European call and put options
b) American call and put options
c) Exotic options
d) Forward contracts
Answer: a) European call and put options - Which of the following is a key assumption of the Black-Scholes model?
a) The market is inefficient.
b) The stock pays dividends at a fixed rate.
c) The stock price follows a random walk with a constant volatility.
d) The option can be exercised at any time before expiration.
Answer: c) The stock price follows a random walk with a constant volatility. - What does the “d1” term represent in the Black-Scholes formula?
a) The difference between the strike price and the current stock price
b) The volatility of the underlying asset
c) The standardized measure of the probability of option finishing in the money
d) The risk-free interest rate
Answer: c) The standardized measure of the probability of option finishing in the money - If the risk-free interest rate increases, what happens to the value of a call option in the Black-Scholes model?
a) The value of the call option decreases
b) The value of the call option increases
c) The value of the call option stays the same
d) The value of the call option becomes negative
Answer: b) The value of the call option increases - In the Black-Scholes model, if the time to expiration of an option is zero, what is the option’s value?
a) The intrinsic value
b) Zero
c) The strike price
d) The sum of time value and intrinsic value
Answer: a) The intrinsic value
3. Black-Scholes-Merton Model
- The Black-Scholes-Merton model is an extension of the Black-Scholes model that includes which of the following?
a) Dividend payments
b) Risk-free interest rates
c) Multiple assets
d) Uncertainty in volatility
Answer: a) Dividend payments - In the Black-Scholes-Merton model, if a stock pays a continuous dividend yield, what is the modification made to the formula?
a) Decrease the strike price
b) Add the dividend yield to the volatility term
c) Subtract the dividend yield from the stock price
d) Increase the risk-free rate
Answer: c) Subtract the dividend yield from the stock price - Which of the following does the Black-Scholes-Merton model assume about dividends?
a) Dividends are paid in a lump sum at expiration.
b) Dividends are assumed to be constant and paid continuously.
c) Dividends are volatile and unpredictable.
d) No dividends are paid during the life of the option.
Answer: b) Dividends are assumed to be constant and paid continuously. - Which assumption in the Black-Scholes-Merton model allows for the inclusion of dividends?
a) The assumption of a perfectly competitive market
b) The assumption that the underlying asset follows a geometric Brownian motion
c) The assumption that there is no transaction cost or taxes
d) The assumption of continuous trading
Answer: b) The assumption that the underlying asset follows a geometric Brownian motion
4. Binomial Tree Method
- Which method uses a discrete-time model to approximate the value of options?
a) Monte Carlo simulation
b) Binomial tree method
c) Black-Scholes model
d) Brownian motion model
Answer: b) Binomial tree method - In a binomial tree model, what does each “step” represent?
a) A change in the underlying asset’s price based on volatility
b) A change in the interest rate
c) A random walk over time
d) A fixed increase in the strike price
Answer: a) A change in the underlying asset’s price based on volatility - What is the key advantage of the binomial tree method over the Black-Scholes model?
a) It is easier to use.
b) It can model American options that can be exercised early.
c) It provides an exact solution for all options.
d) It doesn’t require assumptions about the volatility of the underlying asset.
Answer: b) It can model American options that can be exercised early. - In the binomial tree model, what is the role of the risk-neutral probability?
a) It represents the likelihood of the option expiring in the money.
b) It ensures that the option pricing model is arbitrage-free.
c) It determines the dividend payout.
d) It adjusts for the volatility of the underlying asset.
Answer: b) It ensures that the option pricing model is arbitrage-free. - Which of the following is true about the binomial tree method?
a) It is less computationally intensive than the Black-Scholes model.
b) It can handle European and American options.
c) It requires continuous trading assumptions.
d) It cannot be used for options with multiple exercise periods.
Answer: b) It can handle European and American options.
5. Monte Carlo Simulation
- Monte Carlo simulation is best used for which type of option?
a) European call options
b) American put options
c) Exotic options
d) Binary options
Answer: c) Exotic options - Monte Carlo simulation helps to model which of the following in option pricing?
a) The continuous price movements of the underlying asset
b) The deterministic price of the underlying asset
c) The random movements of the option price
d) The time decay of options
Answer: a) The continuous price movements of the underlying asset - Which of the following is true about Monte Carlo simulation in option pricing?
a) It provides exact solutions for all types of options.
b) It uses random sampling to simulate possible outcomes.
c) It is the simplest and fastest method for option pricing.
d) It cannot handle complex pricing structures.
Answer: b) It uses random sampling to simulate possible outcomes. - What is the primary drawback of using Monte Carlo simulation for option valuation?
a) It requires highly sophisticated algorithms.
b) It has a high computational cost.
c) It cannot handle stochastic volatility.
d) It cannot model exotic options.
Answer: b) It has a high computational cost. - How does Monte Carlo simulation handle path-dependent options?
a) It uses a backward induction method.
b) It averages the prices at expiration.
c) It simulates multiple paths of the underlying asset to estimate the payoff.
d) It assumes that the price only depends on the current state.
Answer: c) It simulates multiple paths of the underlying asset to estimate the payoff.
6. Advanced Option Valuation Concepts
- Which option pricing model is best suited for valuing American-style options?
a) Black-Scholes model
b) Black-Scholes-Merton model
c) Binomial tree method
d) Monte Carlo simulation
Answer: c) Binomial tree method - In the Black-Scholes model, which of the following is NOT a factor in calculating the option price?
a) Current price of the asset
b) Strike price of the option
c) Volatility of the asset
d) Future dividend payments
Answer: d) Future dividend payments - What does the “delta” of an option measure?
a) The time decay of the option
b) The change in the option price relative to a change in the price of the underlying asset
c) The option’s probability of finishing in the money
d) The change in option price relative to changes in volatility
Answer: b) The change in the option price relative to a change in the price of the underlying asset - Which of the following statements is correct about the binomial model for American options?
a) The binomial model assumes the option can only be exercised at expiration.
b) The binomial model assumes the option can be exercised any time before expiration.
c) The binomial model provides an exact solution for all European options.
d) The binomial model ignores early exercise possibilities.
Answer: b) The binomial model assumes the option can be exercised any time before expiration. - Which of the following is considered a path-independent option?
a) Asian option
b) Barrier option
c) Vanilla option
d) Lookback option
Answer: c) Vanilla option - Which model allows for modeling stochastic volatility and jumps in asset prices?
a) Black-Scholes model
b) Binomial model
c) Heston model
d) Monte Carlo simulation
Answer: c) Heston model
7. Practical Application of Option Valuation
- If a European call option has a strike price of ₹100, the underlying asset is currently priced at ₹120, and the risk-free rate is 5%, the option’s intrinsic value is:
a) ₹120
b) ₹100
c) ₹20
d) ₹5
Answer: c) ₹20 - A call option’s time value is best described as:
a) The difference between the option’s market price and its intrinsic value
b) The value derived from the current price of the underlying asset
c) The dividend paid out by the underlying asset
d) The amount paid by the holder when exercising the option
Answer: a) The difference between the option’s market price and its intrinsic value - In a risk-neutral world, the expected return of the underlying asset is:
a) Equal to the risk-free rate
b) Equal to the return on the stock
c) Higher than the risk-free rate
d) Zero
Answer: a) Equal to the risk-free rate - If the volatility of an underlying asset increases, what is the effect on the value of a call option according to the Black-Scholes model?
a) The call option’s value decreases
b) The call option’s value increases
c) The call option’s value remains unchanged
d) The call option becomes worthless
Answer: b) The call option’s value increases - The value of an option with no time left to expiration is:
a) The intrinsic value
b) Zero
c) The strike price
d) The option’s time value
Answer: a) The intrinsic value
8. Final Application Questions
- If an investor is pricing an exotic option using Monte Carlo simulation, which factor will most likely cause the simulation to run more slowly?
a) Increasing the number of simulation paths
b) Decreasing the strike price
c) Increasing volatility
d) Reducing the time to expiration
Answer: a) Increasing the number of simulation paths - Which is an example of an exotic option?
a) European call option
b) American put option
c) Barrier option
d) Vanilla option
Answer: c) Barrier option - Which valuation model is best suited for options where the payoff depends on the path of the underlying asset?
a) Black-Scholes model
b) Binomial tree model
c) Monte Carlo simulation
d) Bachelier model
Answer: c) Monte Carlo simulation - In the binomial tree model, the number of time steps used affects the:
a) Accuracy of the option price estimate
b) Intrinsic value of the option
c) Dividend yield
d) Exercise price
Answer: a) Accuracy of the option price estimate - Which method is most commonly used to model European-style options?
a) Monte Carlo simulation
b) Black-Scholes model
c) Binomial tree method
d) Jump-diffusion model
Answer: b) Black-Scholes model
9. Advanced Topics
- If an American call option is deep in-the-money, what will the value of the option be?
a) Equal to the intrinsic value
b) Zero
c) The sum of intrinsic and time value
d) The strike price
Answer: a) Equal to the intrinsic value - In the context of option pricing, what does the term “vega” represent?
a) The option’s sensitivity to changes in volatility
b) The option’s sensitivity to changes in time decay
c) The option’s sensitivity to changes in stock price
d) The option’s sensitivity to changes in interest rates
Answer: a) The option’s sensitivity to changes in volatility - Which option model uses an assumption of constant volatility throughout the life of the option?
a) Heston model
b) Black-Scholes model
c) Monte Carlo simulation
d) Binomial model
Answer: b) Black-Scholes model - What would happen to a call option’s value if the underlying asset’s price increases?
a) The value of the call option would decrease.
b) The value of the call option would remain the same.
c) The value of the call option would increase.
d) The value of the call option would become zero.
Answer: c) The value of the call option would increase.
10. Practical Valuation Techniques
- In a Monte Carlo simulation, which random process is commonly used to model the underlying asset price?
a) Poisson process
b) Geometric Brownian motion
c) Exponential process
d) Jump-diffusion process
Answer: b) Geometric Brownian motion - Which method would be best for pricing an option with complex payoffs that cannot be easily expressed in a closed-form solution?
a) Black-Scholes model
b) Binomial model
c) Monte Carlo simulation
d) Heston model
Answer: c) Monte Carlo simulation - A European call option is exercised at expiration. Its value at expiration is determined by:
a) The strike price and interest rate
b) The stock price and volatility
c) The intrinsic value of the option
d) The time value of the option
Answer: c) The intrinsic value of the option
Conclusion
- The option pricing model that accounts for early exercise and dividends is:
a) Binomial model
b) Black-Scholes model
c) Monte Carlo simulation
d) Heston model
Answer: a) Binomial model - Which option model is least likely to use historical volatility in its calculation?
a) Black-Scholes model
b) Monte Carlo simulation
c) Binomial model
d) Heston model
Answer: a) Black-Scholes model - The concept of “implied volatility” refers to:
a) The volatility assumed in the option pricing model
b) The historical volatility of the underlying asset
c) The expected future volatility of the underlying asset
d) The volatility derived from the market price of the option
Answer: d) The volatility derived from the market price of the option
These questions cover a broad spectrum of concepts related to option valuation models, including Black-Scholes, Black-Scholes-Merton, Binomial Trees, and Monte Carlo simulation, as well as practical applications and advanced option pricing techniques. They should help in preparing for the IBBI Valuation Examination.
