Lok U.HYUH-DAUH LYUU2022-04-252022-04-25202109277099https://www.scopus.com/inward/record.uri?eid=2-s2.0-85112651357&doi=10.1007%2fs10614-021-10166-x&partnerID=40&md5=2599dac1689b4c45e067c38be1368da1https://scholars.lib.ntu.edu.tw/handle/123456789/607501The local-volatility model assumes the instantaneous volatility is a deterministic function of the underlying asset price and time. The model is very popular because it attempts to fit the volatility smile while retaining the preference freedom of the Black–Scholes option pricing model. As local-volatility model does not admit of analytical formulas in general, numerical methods are required. Tree is one such method because of its simplicity and efficiency. However, few trees in the literature guarantee valid transition probabilities and underlying asset prices simultaneously. This paper presents an efficient tree, called the extended waterline tree, that is provably valid for practically all local-volatility models. Numerical results confirm the tree’s excellent performance. ? 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Extended waterline treeLocal-volatility modelTrinomial treeVolatility surface[SDGs]SDG8journal article10.1007/s10614-021-10166-x2-s2.0-85112651357