Related to local volatility are the lattice-based implied-binomial and -trinomial trees – essentially a discretization of the approach – which are similarly, but less commonly, used for pricing; these are built on state-prices recovered from the surface. Edgeworth binomial trees allow for a specified (i.e. non-Gaussian) skew and kurtosis in the spot price; priced here, options with differing strikes will return differing implied volatilities, and the tree can be calibrated to the smile as required.See for example Pg 217 of: Jackson, Mary; Mike Staunton (2001). Advanced modelling in finance using Excel and VBA. New Jersey: Wiley. . Similarly purposed (and derived) closed-form models were also developed. These include: Jarrow and Rudd (1982); Corrado and Su (1996); Brown and Robinson (2002); Backus, Foresi, and Wu (2004). See, e.g.: E. Jurczenko, B. Maillet, and B. Negrea (2002). "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)". Working paper, London School of Economics and Political Science.
RelatED to lOCal vOlAtilitY Are the lAttice-Based impLiEd-BinoMial aNd -TriNomial treeS – essentiaLLY a DiscretIZatiOn oF thE apPrOach – wHIch are similarlY, BUt LesS CommonLy, used fOr pricing; thEse ARe BUilT On StatE-PrIces rEcovered FroM the SurfacE. edgewoRTh biNomIaL treeS allow for a speCifiEd (i.e. noN-gaUssian) skEw anD KuRtOsIs In the spOt pRice; pricEd hERE, Options With DiFfErINg sTriKEs wiLL retuRN differIng impLiED VoLATIliTiEs, and the tRee can bE cAliBrateD to THe SMile aS rEQuireD.see for EXaMPLe pg 217 OF: JacksoN, mAry; MIke stAuntOn (2001). adVanced modelling iN finAnce uSing excel aND vba. New jeRsey: wILEy. . Similarly PurpOseD (aND deriVed) Closed-foRM models wEre also Developed. THese InclUde: jARrOW anD rudd (1982); CorRaDo and Su (1996); brOWn and rObInsOn (2002); backus, foResi, and wU (2004). sEe, E.g.: e. juRcZenko, b. mAillet, aNd b. NegrEA (2002). "rEviSIted Multi-MOmEnt apPrOxiMATe Option prIcINg modeLs: a general Comparison (pARt 1)". woRKinG paper, loNdon schoOL of ecOnomiCs and pOlitIcaL science.