Set the global evaluation date to January 3, 2006.
Construct a binomial tree approximating a Black-Scholes process with an initial value of 100, a risk-free rate of 10%, and constant volatility of 40%. Assume that no dividend is paid. Build the tree by subdividing the time period 0..0.6 into 1000 equal time steps.
Consider an American put option with a strike price of 100 that matures in 6 months.
Calculate the price of this option using the tree constructed above. Use the risk-free rate as the discount rate.
The next set of examples will demonstrate how to price American-style swaptions using Hull-White trinomial trees.
Construct an interest rate swap receiving the fixed-rate payments in exchange for the floating-rate payments.
Compute the at-the-money rate for this interest rate swap.
Construct three swaps.
Here are cash flows for the paying leg of our interest rate swap.
Here are cash flows for the receiving leg of our interest rate swap.
These are the days when coupon payments are scheduled to occur.
Price these swaptions using the Hull-White trinomial tree.
Price your swaptions using the tree constructed above.