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You can solve the following problems manually, but you are encouraged to use Python, MATLAB, Excel or any other programming languages. 4. Consider pricing a 6m-maturity call and put option on one unit of the 1yr-maturity zero-coupon bond for the strike price of $975 under the Ho-Lee model rt=t+tB, with t=0.5,=0.0,=0.01 and r0=r^(21)=0.0525. Here, B takes \pm 1 with equal probabilities of 50%. In addition, the one-year zero-coupon rate (for semiannual compounding) is r^(1)=0.055. 4.1. (4) Calculate the risk neutral probabilities (q,1q). 4.2. (4) Calculate the call option price and hedge ratio. 4.3. (4) Calculate the put option price and hedge ratio