Assume:

- Binomial process

- Current annualized spot rate on risk-free bond with maturity of 0.25 years of \(S_{0}=4 \%\)

- Up and down parameters for period equal in length to 0.5 years of \(u=1.1, d=1 / 1.1\)

- Length of binomial period 0.5 years (six-month steps)

- Probability of the spot rate increase in one period of \(q=0.5\)

Generate a three-period binomial tree of spot rates. Using the binomial tree, determine the values of an interest rate call option and interest rate put options, each with exercise rates of \(4 \%\), spot rates as reference rates, times periods of 0.25 years, and notional principal of 100.