The waterline tree for separable local-volatility models

Lok, U Hou; Lyuu, Yuh‐Dauh

doi:10.1016/j.camwa.2016.12.008

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…Indeed, the averages of the absolute relative differences for the up-move, middle-move, and down-move probabilities are 8.8%, 9.3%, and 9.4%, respectively. That the transition probabilities of implied trees can witness significant departures from the LV tree's has been observed by Lok and Lyuu (2017) for the more restrictive separable LV models. To the best of our knowledge, no other paper brings up this issue.…”

Section: Trinomial Implied Tree From Implied Volatility Surfacementioning

confidence: 74%

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

Lok

Lyuu

2019

Journal of Futures Markets

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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.

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Section: Trinomial Implied Tree From Implied Volatility Surfacementioning

confidence: 74%

“…However, the tree may not match the LV surface. Lok and Lyuu's () provably valid binomial tree matches only separable LV surfaces.…”

Section: Introductionmentioning

confidence: 99%

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

Lok

Lyuu

2019

Journal of Futures Markets

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“…Charalambous et al [10] construct an implied non-recombining tree and calibrate the volatility smile by quasi-Newton algorithm. Lok and Lyuu [20] find a potentially fundamental reason why the negative probabilities linger and construct a waterline tree for separable local volatility which combines two kinds of binomial trees by matching the moments of the underlying asset price and logarithmic asset price. Gong and Xu [17] propose an implied non-recombining trinomial tree and calibrate the volatility smile.…”

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confidence: 99%

An alternative tree method for calibration of the local volatility

Gong¹,

Xu²

2022

JIMO

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In this paper, we combine the traditional binomial tree and trinomial tree to construct a new alternative tree pricing model, where the local volatility is a deterministic function of time. We then prove the convergence rates of the alternative tree method. The proposed model can price a wide range of derivatives efficiently and accurately. In addition, we research the optimization approach for the calibration of local volatility. The calibration problem can be transformed into a nonlinear unconstrained optimization problem by exterior penalty method. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. Numerical results confirm the excellent performance of the alternative tree pricing model.

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

Lok

Lyuu

2021

Comput Econ

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The waterline tree for separable local-volatility models

Cited by 4 publications

References 33 publications

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

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

An alternative tree method for calibration of the local volatility

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

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