Questions from Business Statistics

Q: Explain the exponentially weighted moving average (EWMA) model for estimating

Explain the exponentially weighted moving average (EWMA) model for estimating volatility from historical data.

Q: Consider an instrument that will pay off S dollars in 2 years

Consider an instrument that will pay off S dollars in 2 years, where S is the value of the Nikkei index. The index is currently 20,000. The yen/dollar exchange rate is 100 (yen per dollar). The correl...

Q: Calculate the price of a 2-year zero-coupon bond

Calculate the price of a 2-year zero-coupon bond from the tree in Figure 32.7 and verify that it agrees with the initial term structure.

Q: Calculate the price of an 18-month zero-coupon bond

Calculate the price of an 18-month zero-coupon bond from the tree in Figure 32.8 and verify that it agrees with the initial term structure.

Q: Repeat Problem 32.3 valuing a European put option with a

Repeat Problem 32.3 valuing a European put option with a strike of $87. What is the put–call parity relationship between the prices of European call and put options? Show that the pu...

Q: Suppose that a =0:05, b =0:

Suppose that a =0:05, b =0:08, and
in Vasicek’s model with the initial shortterm interest rate being 6%. Calculate the price of a 2.1-year European call option on a bond that will mature in 3 years....

Q: Suppose that a = 0:05 and
in the Hull

Suppose that a = 0:05 and
in the Hull–White model with the initial term structure being flat at 6% with semiannual compounding. Calculate the price of a2.1-year European call option on a bond that wi...

Q: Suppose a = 0:05,
, and the term structure

Suppose a = 0:05,
, and the term structure is flat at 10%. Construct a trinomial tree for the Hull–White model where there are two-time steps, each 1 year in length.

Q: ‘‘An option adjusted spread is analogous to the yield on a

‘‘An option adjusted spread is analogous to the yield on a bond.’’ Explain this statement.

Q: ‘‘When the forward rate volatility
in HJM is constant,

‘‘When the forward rate volatility
in HJM is constant, the Ho–Lee model results.’’ Verify that this is true by showing that HJM gives a process for bond prices that is consistent with the Ho–Lee mode...