For the HiTech bond of Example 17.4, suppose that default is recognized only at maturity and that no restitution is made, that is, the default is ignored. What is the value of that bond?

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- Example 17.4 (HiTech 2) Consider the HiTech bond of Example 17.1. The firm value follows geometric Brownian motion with V (0) = $1,000,000, p = .15, = .25, r = .05. The bond is described by T = 5, K = $800,000. According to the method of lattice construction of Section 13.9, the parameters of a corresponding lat- tice with At = 1 (not using the small At approximation) are u = 1.3188, d= 1/u, p = .7145, R = 1.05127. Also, q= (R-d)/(u-d)= .5227. Of course, a lat- tice with At = 1 is a rather rough approximation to the continuous-time model, but it illustrates the approach. The value of the bond can be found by straightforward backward evaluation using the risk-neutral probability q and risk-free return R. Figure 17.3 displays the lattices for firm value and for prices of the defaultable bond. The top lattice uses the values of u and d to forecast the possible firm values, beginning with $1,000 (in thousands). The last column of the second lattice shows the