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%?

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

The natural logarithm of x is:

Which of the following statements about skewness of an empirical probability distribution are correct?

1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns

2. When the mean is significantly less than the median, this is an indication of negative skewness

3. Skewness is a sign of asymmetry in the dispersion of the data

Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X ≤ 0 and Y ≤ 1.96 is approximately

Which of the following can induce a 'multicollinearity' problem in a regression model?

At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…

Consider the following distribution data for a random variable X: What is the mean and variance of X?

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

The Newton-Raphson method

In a multiple linear regression, the significance of R2 can be tested using which distribution?

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

What is the simplest form of this expression: log2(165/2)

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay Duration of the bond?

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

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

The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?