Questions from Business Statistics

Q: Suppose that a central bank’s policy is to allow an exchange rate

Suppose that a central bank’s policy is to allow an exchange rate to fluctuate between 0.97 and 1.03. What pattern of implied volatilities for options on the exchange rate would you expect to see?

Q: A stock price is currently $50. It is known that

A stock price is currently $50. It is known that at the end of 6 months it will be either $60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum. Calculate the value o...

Q: A stock price is currently $40. Over each of the

A stock price is currently $40. Over each of the next two 3-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. (a)...

Q: Using a ‘‘trial-and-error’’ approach, estimate how

Using a ‘‘trial-and-error’’ approach, estimate how high the strike price has to be in Problem 13.22 for it to be optimal to exercise the option immediately. Data from Problem 13.22: A stock price is c...

Q: A stock price is currently $30. During each 2-

A stock price is currently $30. During each 2-month period for the next 4 months it will increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value...

Q: Repeat Problem 13.25 for an American put option on a

Repeat Problem 13.25 for an American put option on a futures contract. The strike price and the futures price are $50, the risk-free rate is 10%, the time to maturity is 6 months, and the volatility i...

Q: Footnote 1 of this chapter shows that the correct discount rate to

Footnote 1 of this chapter shows that the correct discount rate to use for the real-world expected payoff in the case of the call option considered in Figure 13.1 is 55.96%. Show that if the option is...

Q: A stock index is currently 990, the risk-free rate

A stock index is currently 990, the risk-free rate is 5%, and the dividend yield on the index is 2%. Use a three-step tree to value an 18-month American put option with a strike price of 1,000 when th...

Q: Calculate the value of 9-month American call option to buy

Calculate the value of 9-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is 0.80 (both...

Q: A company’s cash position, measured in millions of dollars, follows

A company’s cash position, measured in millions of dollars, follows a generalized Wiener process with a drift rate of 0.1 per month and a variance rate of 0.16 per month. The initial cash position is...