Questions from Business Statistics

Q: Deduce the differential equation for a derivative dependent on the prices of

Deduce the differential equation for a derivative dependent on the prices of two non-dividend-paying traded securities by forming a riskless portfolio consisting of the derivative and the two traded s...

Q: Prove that, when the security f provides income at rate q

Prove that, when the security f provides income at rate q, equation (28.9) becomes
(Hint: Form a new security f that provides no income by assuming that all the income from f is reinvested in f.)...

Q: Show that when f and g provide income at rates
and

Show that when f and g provide income at rates
and
, respectively, equation (28.15) becomes
Hint: Form new securities
and
that provide no income by assuming that all the income from f is reinve...

Q: ‘‘The expected future value of an interest rate in a risk

‘‘The expected future value of an interest rate in a risk-neutral world is greater than it is in the real world.’’ What does this statement imply about the market price of risk for (a) an interest ra...

Q: Derive a put–call parity relationship for European bond options.

Derive a put–call parity relationship for European bond options.

Q: Suppose that the spot price, 6-month futures price,

Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in eq...

Q: Derive a put–call parity relationship for European swap options.

Derive a put–call parity relationship for European swap options.

Q: Explain why there is an arbitrage opportunity if the implied Black (

Explain why there is an arbitrage opportunity if the implied Black (flat) volatility of a cap is different from that of a floor.

Q: What is the value of a European swap option that gives the

What is the value of a European swap option that gives the holder the right to enter into a 3-year annual-pay swap in 4 years where a fixed rate of 5% is paid and LIBOR is received? The swap principal...

Q: Carry out a manual calculation to verify the option prices in Example

Carry out a manual calculation to verify the option prices in Example 29.2.