Derivatives and Hedging: Mock Exam Questions

Posted on Mar 21, 2025 in Finance

Mock Exam (Theory)

Hedging and Risk Management

Hedging is used to:

  • (a) Reduce risk.
  • (b) Speculation.
  • (c) Increase exposure to price movements.

Futures vs. Forwards

What is the difference between Futures and Forwards?

  • (a) Futures are traded on an organized exchange, and forwards are traded OTC (Over-the-Counter).
  • (b) Forwards are traded on an organized exchange, and futures are traded OTC.
  • (c) Forwards have daily settlement, and futures settlement at the end of the period.

Bear Spread Payoff

A bear spread:

  • (a) cannot be replicated under a binomial model.
  • (b) has a bounded payoff.
  • (c) is always very risky in comparison with a short put.

Forward Contract Pricing

A forward contract on a non-dividend-paying stock started some time ago at a price of 100. If today’s price of the stock is 100 euros, time to maturity is 1 year, and the interest rate is 5% (continuously compounded), what is (today) the price of the long forward contract?

  • (a) -4.877.
  • (b) 4.877.
  • (c) 0, because it is a forward contract.

Bull Spread Strategy

You should use a Bull Spread if:

  • (a) You expect the corresponding asset price to increase.
  • (b) You expect the corresponding asset price to decrease.
  • (c) You expect the corresponding asset price to remain constant.

Monte Carlo Method for Lookback Options

We want to estimate a lookback option price by using a Monte Carlo method. Then:

  • Simulating n = 106 paths will be always optimal.
  • We should construct a confidence interval to check the accuracy of our estimation.
  • Lookback options cannot be priced using a Monte Carlo method.

Black-Scholes Model: Greeks (Vega)

Choose the correct one. Under the Black-Scholes model:

  • The Delta of a call is negative, and the Delta of a put is positive.
  • Vega is positive.
  • Gamma is the second derivative of the Delta with respect to the stock price.

Black-Scholes Model: Greeks (Gamma)

Choose the correct one. Under the Black-Scholes model:

  • The most relevant Greek is Rho.
  • Theta is always positive.
  • Gamma is the derivative of the Delta with respect to the stock price.

Black-Scholes Model: Replication

Choose the correct one. Under the Black-Scholes model:

  • A call option can be perfectly replicated using static hedging.
  • To do a perfect replication, we would need to continuously rebalance our replicating portfolio.
  • The number of assets in the replicating portfolio is given by the Theta.

Portfolio Replication

We want to construct a portfolio to replicate a stock price S in some time interval. That is, we want to construct a portfolio that has, at every time moment, the same value as the stock price. Which one of the following combinations can be useful for this purpose?

  • A long call, a short put, and a risk-free investment.
  • A short call and a short put.
  • A future.

Black-Scholes Model: Stock Price Distribution

Consider a Black-Scholes model. Then we can say that:

  • The exponential of the stock price is a log-normal random variable.
  • The exponential of the stock price is a normal random variable.
  • The stock price is the exponential of a normal random variable.

Implied Volatility

The implied volatility:

  • Is a synonym of ‘historical volatility’, commonly used by traders.
  • Can be computed from the prices of the assets in the market.
  • Is computed from the prices of options in the market.

Option Strategy Costs

Which one of the following strategies (with the same parameters) is, in general, more expensive?

  • A put option.
  • A bear spread.
  • A long future.