Markov chain approximation of one-dimensional sticky diffusions

Meier, Christian; Li, Lingfei; Zhang, Gongqiu

doi:10.1017/apr.2020.65

Cited by 15 publications

(3 citation statements)

References 42 publications

(5 reference statements)

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“…(2) e Bayesian networks Bayesian Networks (BNs) are topological structures composed of a directed acyclic graph and related probability distribution functions, representing the joint probability distribution of n random variables [15], which is composed of two parts, BNs � ( G, θ). G stands for a directed acyclic graph, whose nodes are random variables X 1 , X 2 , .…”

Section: Eoretical Preparation (1) Bayesian Networkmentioning

confidence: 99%

Building Construction Design Based on Particle Swarm Optimization Algorithm

Song

2022

Journal of Control Science and Engineering

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In order to take a scientific risk control strategy to reduce the safety risk of construction projects, a construction safety risk decision-making method based on particle swarm optimization algorithm was proposed. Through the analysis of prefabricated building construction safety risk factors, the combination of the Markov Chain and Bayesian networks method was used to estimate the probability of risk factors. The relationship between the various risk factors was described by conditional probability, and a safety risk loss-control investment double objective optimization model was built. The corresponding algorithm was designed and the R language programming was used to solve the problem. The experimental results showed that by taking a high degree of control over the risk factors of the investment strategy, when the constraint cost was RMB 200,000, the global optimal risk loss and the global optimal control cost were RMB 1,400,500 and 19,600, respectively. When the constraint cost was 280,000 yuan, the global optimal risk loss and global optimal control cost were 1.046 million yuan and 278.5 million yuan, respectively. When the constraint cost was 320,000 yuan, the global optimal risk loss and global optimal control cost were 910,100 yuan and 317,300, yuan respectively. It was concluded that, considering the risk correlation optimization model, a reasonable allocation strategy was adopted, combined with the actual situation, which performed a promoting function in improving the assembly building construction safety risk decision-making.

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Section: Eoretical Preparation (1) Bayesian Networkmentioning

confidence: 99%

Building Construction Design Based on Particle Swarm Optimization Algorithm

Song

2022

Journal of Control Science and Engineering

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“…(n) t is a birth-and-death process, Li and Zhang (2016) propose an algorithm based on efficient matrix eigendecomposition which reduces the time complexity to O(n 2 y ). Another very efficient algorithm for matrix exponentials can be found in Meier et al (2021).…”

Section: Ctmc Approximation For the First Passage Problemmentioning

confidence: 99%

“…CTMC approximation has become a popular method for solving various option pricing problems under Markov models in recent years. See Mijatović and Pistorius (2013) and Cui and Taylor (2021) for barrier options, Eriksson and Pistorius (2015) for American options, Cai et al (2015), Song et al (2018) and for Asian options, Zhang and Li (2021c) for maximum drawdown options, Zhang et al (2021) for American drawdown options, Zhang and Li (2021b) for Parisian options, and Meier et al (2021) for option pricing under financial models with sticky behavior. In all these papers, the original Markov model is approximated by a CTMC, and then the option price under the CTMC model is derived.…”

Section: Introductionmentioning

confidence: 99%

A General Approach for Lookback Option Pricing under Markov Models

Zhang

2021

Preprint

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We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient numerical quadrature with continuous-time Markov chain approximation for the first passage problem to price lookbacks. Our method is applicable to a variety of models, including one-dimensional timehomogeneous and time-inhomogeneous Markov processes, regime-switching models and stochastic local volatility models. We demonstrate the efficiency of our method through various numerical examples.

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Pricing and hedging autocallable products by Markov chain approximation

Cui,

Li,

Zhang

2024

Rev Deriv Res

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We propose a unified pricing framework based on continuous-time Markov chain (CTMC) approximation for autocallable structured products. Our method is applicable to a variety of asset price models, including one-dimensional Markov jump-diffusions (the coefficients can be time dependent), regime-switching models, and stochastic local volatility (SLV) models. For SLV models, we develop a hybrid Markov chain approximation scheme that significantly improves the existing CTMC approximation method. We test our pricing method under various popular models and show that it is computationally efficient. To hedge autocallable products, we consider a dynamic hedging approach in the presence of transaction costs. To address the problem that the product’s delta can become too large near the barriers, we apply payoff modification and barrier shifting techniques. We determine the optimal size of adjustments that minimize conditional value-at-risk (CVaR) of the hedging loss using stochastic gradient descent. Empirical experiments demonstrate the effectiveness of our approach in reducing CVaR of the hedging loss.

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Markov chain approximation of one-dimensional sticky diffusions

Cited by 15 publications

References 42 publications

Building Construction Design Based on Particle Swarm Optimization Algorithm

Building Construction Design Based on Particle Swarm Optimization Algorithm

A General Approach for Lookback Option Pricing under Markov Models

Pricing and hedging autocallable products by Markov chain approximation

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