... computational domain is [l, M ], for a large value M. Boundary conditions atx = l,M become F doc (t, x = l) = 0 and F doc (t, x = M) = M − Ke−r(T −t),respectively. A down-and-in call option is activated ... theBlack–Scholes equation, we have B2−AC = 0, so that (4.3) is a parabolic equationon {x>0}. In quantitative finance, we usually come across parabolic equations:∂yF (y, x) +A∂xxF (y, x) +D∂xF ... Grüne and Semm-ler (2004) and references therein. The use of trees has been extensively adopted in quantitative finance since Cox, Ross and Rubinstein (1979). Self-contained introduc-tions to lattice...