A lattice-based approach to option and bond valuation under mean-reverting regime-switching diffusion processes

Ahmadi, Z.; Hosseini, Seyed Mohammad; Bastani, Ali Foroush

doi:10.1016/j.cam.2019.06.002

Cited by 4 publications

(3 citation statements)

References 60 publications

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“…In [32], barrier option prices in stochastic volatility models are evaluated using a willow tree. In [33], a lattice-based approach is developed to price barrier options under mean-reverting regime-switching models. In [34], the bino-trinomial tree is used to price implied barriers and moving-barrier options.…”

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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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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“…It can easily deal with American-style features like early redemption and early exercise that are found in many option contracts. It is also exible, since only nominal changes are needed to price complex, nonstandard options, which do not have simple closed-form solutions [3] (Indeed, the exibility of the lattice method makes it widely adopted in recent literature, such as the evaluation of American stock options [6], variable annuity products [7,8], catastrophe equity puts [9], employee stock options [10], swing options [11], or corporate bonds [12][13][14][15]). Technically speaking, a lattice divides the option life into n discrete equal-length time steps and simulates stock price movements discretely at each time step.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Dai

et al. 2022

Mathematical Problems in Engineering

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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 n 2 ), and a large n is required to obtain accurate option values. Although O n -time combinatorial pricing algorithms have been developed for the classical binomial lattice, significantly oscillating convergence behavior makes them impractical. The flexibility of trinomial lattices can be leveraged to reduce the oscillation, but there are as yet no linear-time algorithms on trinomial lattices. We develop O n -time combinatorial pricing algorithms for polynomial options that cannot be analytically priced. The commonly traded plain vanilla and power options are degenerated cases of polynomial options. Barrier options that cannot be stably priced by the binomial lattice can be stably priced by our O n -time algorithm on a trinomial lattice. Numerical experiments demonstrate the efficiency and accuracy of our O n -time trinomial lattice algorithms.

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“…The optimality equations are not analytically solvable in general. Many numerical methods have therefore been proposed from both deterministic 38‐40 and statistical viewpoints 41‐44 …”

Section: Introductionmentioning

confidence: 99%

A hybrid stochastic river environmental restoration modeling with discrete and costly observations

Yoshioka

Tsujimura

Hamagami

et al. 2020

Optim Control Appl Methods

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Summary A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This setting harmonizes with real problems because continuously obtaining environmental and ecological information is difficult, and is often costly. The main problem is to decide when and how much of the sediment should be supplied into a river environment to effectively suppress bloom of benthic algae. The interventions are allowed only at observation times. Finding the optimal river restoration policy ultimately reduces to solving an optimality equation in an unconventional form due to the observation cost and discrete observations. We show its unique solvability and present a connection with degenerate parabolic partial differential equations, with which we can construct an effective algorithm for its approximation. An uncertainty‐averse optimization problem is also considered as an advanced problem. Coefficients and parameter values are identified from experimental and observation results to numerically compute the optimal restoration policy of an existing river environment with and without uncertainty.

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A lattice-based approach to option and bond valuation under mean-reverting regime-switching diffusion processes

Cited by 4 publications

References 60 publications

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

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

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

A hybrid stochastic river environmental restoration modeling with discrete and costly observations

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