Online Access Free 8002 Practice Test

Consider the linear regression model for the returns of stock A and the returns of stock B.
Stock A is 50% more volatile than stock B.
Which of the following statements is TRUE?

• A.Beta must be greater in absolute value than the correlation of the stocks ( )
• B.The stocks must be positively correlated ( )
• C.Beta must be positive ( )
• D.Alpha must be positive ( )

Maximum likelihood estimation is a method for:

• A.Estimating the implied volatility of a simple European option
• B.Finding parameter estimates of a given density function
• C.Solving a portfolio optimization problem
• D.Estimating the solution of a partial differential equation

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is
7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

• A.5.03
• B.6.49
• C.4.54
• D.4.59

When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

• A.100
• B.25
• C.5
• D.10

Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

• A.f(x)G(x) - F(x)g'(x)dx
• B.F(x)g(x) - F(x)g'(x)dx
• C.F(x)G(x)
• D.F(x)g(x) + f(x)G(x)