Calibrating a Ho-Lee model to market data. We look at a market consisting of ZCBs with maturities m=1,2,3 years. Suppose with the ZCB market prices at time 0 (today), the yields of the bonds are y0,1=2.00%,y0,2=2.19%, y0,3=2.51%. We suppose that interest rates will be non-decreasing over the next three years. a) Compute today's market prices B0,m,m=1,2,3 of the ZCBs (round to 4 significant digits). We want to describe this market by a 3-period Ho-Lee binomial model with independent coin tosses and time-dependent risk-neutral probabilities. That is, the distribution of (Y1,Y2) under P~ is given by P~[Y1=1,Y2=1]P~[Y1=0,Y2=1]P~[Y1=1,Y2=0]P~[Y1=0,Y2=0]=p~1p~2,=(1p~1)p~2,=p~1(1p~2),=(1p~1)(1p~2) for probabilities p~1,p~2(0,1), and the interest rate process R0,R1,R2 is then defined as in the Ho-Lee model Rn=an+bn(Y1++Yn). We assume that a0=a1=a2=0.02 and b1=b2=0.01. b) Compute the time-zero prices B0,m(p~1,p~2)(m=1,2,3) in this model as a function of the risk-neutral probabilities p~1,p~2. c) Find the values p~1,p~2 for which the time-zero model prices B0,m(p~1,p~2) computed in b) are equal to the time-zero market prices in a) for all m= 1,2,3 (round p~1,p~2 to 2 significant digits)