A Valid and Efficient Trinomial Tree for General Local-Volatility Models

The 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-vol...

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Bibliographic Details
Published in:Computational economics 2022-10, Vol.60 (3), p.817-832
Main Authors: Lok, U Hou, Lyuu, Yuh-Dauh
Format: Article
Language:English
Subjects:
Arbitrage
Assets
Behavioral/Experimental Economics
Computer Appl. in Social and Behavioral Sciences
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Interest rates
Math Applications in Computer Science
Mathematical models
Numerical analysis
Numerical methods
Operations Research/Decision Theory
Prices
Securities prices
Simplicity
Transition probabilities
Trees
Volatility
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Summary:The 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.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-021-10166-x