a 3. Suppose that X x, (ii) Pb(S(6),t) as S(O), and (iii) P(x,c). (b) Let 18 = ln(X/E), and assume that the transformed the boundary conditions for the plain vanilla and IB down-and-out put options are plain vanilla down-and-out t(1,0) = max(e-3(1-1) -e]{1+b)x,0), 2ER, u(3,0) = max(e+(1*) eX(1+2)5,0), 18, (2,T) + 0 as 10, (T)0 as 100, u(0,5) = 1, T>0 u(XB,T)=0, T>0. - Let u(x, t) = u1(x, T)+u2(x, t) be the transformed price of the down-and-out put option. Assume that u1(x,T) is the transformed price of a plain vanilla put and that u2(x, T) = a u1(bx+c,T). Compute the values of a,b,c so that the boundary conditions for the down-and-out put option will be satisfied. The derivation in $9.3.1 for the down-and-out call option may be helpful. (c) Bonus: Using the result of part (b) and following the derivation in 89.3.1, derive the price Pb(S,t) of the down-and-out put option. a 3. Suppose that X x, (ii) Pb(S(6),t) as S(O), and (iii) P(x,c). (b) Let 18 = ln(X/E), and assume that the transformed the boundary conditions for the plain vanilla and IB down-and-out put options are plain vanilla down-and-out t(1,0) = max(e-3(1-1) -e]{1+b)x,0), 2ER, u(3,0) = max(e+(1*) eX(1+2)5,0), 18, (2,T) + 0 as 10, (T)0 as 100, u(0,5) = 1, T>0 u(XB,T)=0, T>0. - Let u(x, t) = u1(x, T)+u2(x, t) be the transformed price of the down-and-out put option. Assume that u1(x,T) is the transformed price of a plain vanilla put and that u2(x, T) = a u1(bx+c,T). Compute the values of a,b,c so that the boundary conditions for the down-and-out put option will be satisfied. The derivation in $9.3.1 for the down-and-out call option may be helpful. (c) Bonus: Using the result of part (b) and following the derivation in 89.3.1, derive the price Pb(S,t) of the down-and-out put option