Efficient and Robust Combinatorial Option Pricing Algorithms on the Trinomial Lattice for Polynomial and Barrier Options

Wang, Jr‐Yan; Wang, Chuan‐Ju; Dai, Tian‐Shyr; Chen, Tzu‐Chun; Liu, Liang‐Chih; Zhou, Lei

doi:10.1155/2022/5843491

Cited by 2 publications

(2 citation statements)

References 34 publications

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“…It is also known as an asymmetric power option [4]. Lee et al [3] and Wang [8] described a generalization of such options in (9) as polynomial options, given as…”

Section: Mathematical Modelmentioning

confidence: 99%

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

Nwankwo

Dai

2023

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In this research, we propose fourth-order non-uniform Hermitian differencing with a fifth-order adaptive time integration method for pricing system of free boundary exotic power put options consisting of the option value, delta sensitivity, and gamma. The main objective for implementing the above scheme is to carefully account for the irregularity in the locality of the left corner point after fixing the free boundary. Specifically and mainly, we stretch the performance of our proposed method threefold. First, we exploit the non-uniform fourth-order Hermitian scheme to locally concentrate space grid points arbitrarily close to the left boundary. Secondly, we further leverage the adaptive nature of the embedded time integration method, which allows optimal selection of a time step based on the space grid point distribution and regional variation. Thirdly, we introduce a fourth-order combined Hermitian scheme, which requires fewer grid points for computing the near boundary point of the delta sensitivity and gamma. Another novelty is how we approximate the optimal exercise boundary and its derivative using a fifth-order Robin boundary scheme and fourth-order combined Hermitian scheme. Our proposed method consistently achieves reasonable accuracy with very coarse grids and little runtime across the numerical experiments. We further compare the results with existing methods and the ones we obtained from the uniform space grid.

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“…It is also known as an asymmetric power option [4]. Lee et al [3] and Wang [8] described a generalization of such options in (9) as polynomial options, given as…”

Section: Mathematical Modelmentioning

confidence: 99%

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

Nwankwo

Dai

2023

Axioms

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“…See also [19] for a different approach. On the one hand, the computation of these option prices can be made more efficient by employing combinatorial techniques, as shown in [20,21], leveraging Catalan numbers as explored in [22], or using spectral methods, as demonstrated in [23,24]. On the other hand, for barrier options, the convergence speed of option prices is typically of order 1/…”

Section: Introductionmentioning

confidence: 99%

The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing

Leduc

2024

Mathematics

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Oscillations in option price convergence have long been a problematic aspect of tree methods, inhibiting the use of repeated Richardson extrapolation that could otherwise greatly accelerate convergence, a feature integral to some of the most efficient modern methods. These oscillations are typically caused by the fluctuating positions of nodes around the discontinuities in the payoff function or its derivatives. Our paper addresses this crucial gap that typically prohibits the use of lattice methods when high efficiency is needed. Focusing on double barrier options, we develop a trinomial tree in which the positions of the nodes are precisely adjusted to align with these discontinuities throughout the option’s lifespan and across various time steps. This alignment enables the use of repeated extrapolation to achieve high order convergence, including near barriers, a well-known challenge in many tree methods. Maintaining the inherent simplicity and adaptability of tree methods, our approach is easily applicable to other models and option types.

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Efficient and Robust Combinatorial Option Pricing Algorithms on the Trinomial Lattice for Polynomial and Barrier Options

Abstract: Options can be priced by the lattice model, the results of which converge to the theoretical option value as the lattice’s number of time steps n approaches infinity. The time complexity of a common dynamic programming pricing approach on the lattice is slow (at least O … Show more

Cited by 2 publications

References 34 publications

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing

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