Questions from Business Statistics

Q: Confirm that Merton’s jump–diffusion model satisfies put–call parity

Confirm that Merton’s jump–diffusion model satisfies put–call parity when the jump size is lognormal.

Q: Consider the case of Merton’s jump–diffusion model where jumps always

Consider the case of Merton’s jump–diffusion model where jumps always reduce the asset price to zero. Assume that the average number of jumps per year is
. Show that the price of a European call opti...

Q: At time 0 the price of a non-dividend-paying

At time 0 the price of a non-dividend-paying stock is S0. Suppose that the time interval between 0 and T is divided into two subintervals of length t1 and t2. During the first subinterval, the risk-fr...

Q: ‘‘The IVF model correctly values any derivative whose payoff depends on

‘‘The IVF model correctly values any derivative whose payoff depends on the value of the underlying asset at only one time.’’ Explain why.

Q: The variable S is an investment asset providing income at rate

The variable S is an investment asset providing income at rate q measured in currency A. It follows the process
in the real world. Defining new variables as necessary, give the process followed by...

Q: Explain the difference between the way a forward interest rate is defined

Explain the difference between the way a forward interest rate is defined and the way the forward values of other variables such as stock prices, commodity prices, and exchange rates are defined.

Q: ‘‘If X is the expected value of a variable, X

‘‘If X is the expected value of a variable, X follows a martingale.’’ Explain this statement.

Q: Suppose that the market price of risk for gold is zero.

Suppose that the market price of risk for gold is zero. If the storage costs are 1% per annum and the risk-free rate of interest is 6% per annum, what is the expected growth rate in the price of gold?...

Q: Suppose that in Problem 23.17 the price of silver at

Suppose that in Problem 23.17 the price of silver at the close of trading yesterday was $16, its volatility was estimated as 1.5% per day, and its correlation with gold was estimated as 0.8. The price...

Q: The spread between the yield on a 3-year corporate bond

The spread between the yield on a 3-year corporate bond and the yield on a similar risk-free bond is 50 basis points. The recovery rate is 30%. Estimate the average hazard rate per year over the 3-yea...