Assume: binomial process; current annualized spot rate on riskfree bond with maturity of one year of \(S_{0}=5 \%\); up and down parameters for period equal in length to one year of \(u=1.1\) and \(d\) \(=1 /1.1\); length of binomial period equal to one year; probability of the spot rate increasing in one period of \(q=0.5\).

a. Generate a two-period binomial tree of spot rates.

b. Using the binomial tree, calculate the values at each node of a risk-free bond with a \(\$ 100\) face value, \(5 \%\) annual coupon, and maturity of three years.

c. Using the binomial tree, determine the value of a European call option with an exercise price of 100 and expiration of two years.

d. Using the binomial tree, determine the value of an American call option with an exercise price of 100 and expiration of two years.

e. Using the binomial tree, determine the value of a European put option with an exercise price of 100 and expiration of two years.

f. Using the binomial tree, determine the value of an American put option with an exercise price of 100 and expiration of two years.