Questions from Business Statistics

Q: How is the market price of risk defined for a variable that

How is the market price of risk defined for a variable that is not the price of an investment asset?

Q: Prove the result in Section 28.5 that when
and

Prove the result in Section 28.5 that when
and
with the dzi uncorrelated, f/g is a martingale for
(Hint: Start by using equation (14A.11) to get the processes for ln f and ln g.)

Q: Show that when w = h/g and h and

Show that when w = h/g and h and g are each dependent on n Wiener processes, the ith component of the volatility of w is the ith component of the volatility of h minus the ith component of the volati...

Q: Consider two securities both of which are dependent on the same market

Consider two securities both of which are dependent on the same market variable. The expected returns from the securities are 8% and 12%. The volatility of the first security is 15%. The instantaneous...

Q: A new European-style floating lookback call option on a stock

A new European-style floating lookback call option on a stock index has a maturity of 9 months. The current level of the index is 400, the risk-free rate is 6% per annum, the dividend yield on the ind...

Q: Suppose that an interest rate x follows the process
where a

Suppose that an interest rate x follows the process
where a, x0, and c are positive constants. Suppose further that the market price of risk for x is
. What is the process for x in the traditional r...

Q: A company caps 3-month LIBOR at 2% per annum

A company caps 3-month LIBOR at 2% per annum. The principal amount is $20 million. On a reset date, 3-month LIBOR is 4% per annum. What payment would this lead to under the cap? When would the payment...

Q: When a bond’s price is lognormal can the bond’s yield be negative

When a bond’s price is lognormal can the bond’s yield be negative? Explain your answer.

Q: Suppose that the yield R on a zero-coupon bond follows

Suppose that the yield R on a zero-coupon bond follows the process
where and are functions of R and t, and dz is a Wiener process. Use Itoˆ ’s lemma to show that the volatility of the zero-coupon b...

Q: Use the Black’s model to value a 1-year European put

Use the Black’s model to value a 1-year European put option on a 10-year bond. Assume that the current cash price of the bond is $125, the strike price is $110, the 1-year risk-free interest rate is 1...