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Efficient trinomial trees for local‐volatility models in pricing double‐barrier options

U Hou Lok and Yuh‐Dauh Lyuu

Journal of Futures Markets, 2020, vol. 40, issue 4, 556-574

Abstract: A local‐volatility (LV) model captures the volatility smile while retaining the preference freedom of the Black–Scholes model. Past attempts to construct a smile‐consistent tree for the LV surface do not guarantee validity. This paper presents an efficient and valid smile‐consistent tree for the LV model. The only assumption is that the LV surface be upper‐ and lower‐bounded. With this tree, double‐barrier options can be priced with fast convergence even in the presence of volatility smile. This is confirmed numerically. An implied tree is also presented. It recovers the LV surface reasonably well.

Date: 2020
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