A Markov chain approximation scheme for option pricing under skew diffusions

Ding, Kailin; Cui, Zhenyu; Wang, Yongjin

doi:10.1080/14697688.2020.1781235

Cited by 18 publications

(6 citation statements)

References 74 publications

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“…We simulate the threshold OU process using the Euler scheme (Bokil et al, 2020) (an alternative approach for simulation consists in discretizing space instead of time, cf. (Ding et al, 2020)) and use the estimator based on discrete observations. The implementation has been done using R. Parameters are as in Table 1.…”

Section: Threshold Estimation Testing and Interest Ratesmentioning

confidence: 99%

Drift Estimation of the Threshold Ornstein-Uhlenbeck Process From Continuous and Discrete Observations

Mazzonetto¹,

Pigato²

2024

STAT SINICA

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We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift parameters, both assuming continuous and discrete time observations. In the ergodic case, we derive consistency and speed of convergence of these estimators in long time and high frequency. Based on these results, we develop a test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to short-term US interest rates modeling.

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Section: Threshold Estimation Testing and Interest Ratesmentioning

confidence: 99%

Drift Estimation of the Threshold Ornstein-Uhlenbeck Process From Continuous and Discrete Observations

Mazzonetto¹,

Pigato²

2024

STAT SINICA

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“…Markov chains (finite state space Markov processes) can be used to approximate Markov processes in a continuous state space (Kushner and Dupuis 2001). This approach is developed in finance in work such as Lo and Skindilias (2014), Cui et al (2018), Cui et al (2019aCui et al ( , 2019b and Ding et al (2020). For instance, the work of Mijatovic and Pistorius (2013) describes equity and credit derivatives of firms susceptible to default through the device of time-changed Markov processes with killing.…”

Section: Related Literaturementioning

confidence: 99%

Implied Markov transition matrices under structural price models

Defourny

Moazeni

2021

Quantitative Finance

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This paper proposes an approach to compute the implied transition matrices from observations of market data on financial derivatives, when the price of the underlying originates from a structural model and the payoffs are received over a period of time. The structural price model involves a price formation mechanism which computes the price based on a set of Markovian inputs and constrained optimization processes. The developed inference method relies on a linear description of the derivative values in terms of occupation measures of the payoff duration. We establish closed-form expressions between occupation measures and state transitions, which then enable us to characterize implied state transition probabilities consistent with the market data on the derivative values. We develop methods to solve the optimization problem with the resulting nonlinear occupation measure equation. Numerical illustrations of the approach are presented for financial derivatives on network capacities. By applying the method to an electric network, we investigate the relation between financial transmission correct contract values and a range of implied probabilities of congestion in the network.

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“…In this paper, we focus the spotlight on a key matrix function that appears in several CTMC applications, that is, a matrix exponential, which emerges, for example, in distributions of first passage times, running extrema and stochastic time integrals, in bond prices and generally option price formulations as well as their sensitivities (see Cai et al 2020 andDing et al 2021). Here, we give prominence to a practically useful quantity that features in various applications, that of a stochastic time integral.…”

Section: Introductionmentioning

confidence: 99%

Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

Das

Tsai

Kyriakou

et al. 2022

Operations Research

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On Modeling the Probability Distribution of Stochastic Sums In the “Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions,” Das, Tsai, Kyriakou, and Fusai propose an efficient methodology for approximating the unknown probability distribution of a weighted stochastic sum or time integral. Resulting from earlier contributions based on continuous-time Markov chain approximations of one-dimensional Markov processes is the Laplace transform of the unknown distribution available in exponential matrix form. In this paper, the authors develop a bona fide Pearson curve-fitting approach to this distribution based on the moments, which they recover from the derivatives of the Laplace transform. Motivated by the computational hurdles toward this, they derive computationally efficient closed-form expressions for the derivatives of the matrix exponential. They then apply to pricing average-based options.

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A Markov chain approximation scheme for option pricing under skew diffusions

Cited by 18 publications

References 74 publications

Drift Estimation of the Threshold Ornstein-Uhlenbeck Process From Continuous and Discrete Observations

Drift Estimation of the Threshold Ornstein-Uhlenbeck Process From Continuous and Discrete Observations

Implied Markov transition matrices under structural price models

Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

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