A Unified Framework for Computing Regime-Switching Models

Cai, Ning; Kou, Steven; Song, Yingda

doi:10.2139/ssrn.3310365

Cited by 15 publications

(13 citation statements)

References 50 publications

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“…We can convert the original two‐dimensional Markov chain into a one‐dimensional Markov chain

{MathClass-open{{\overset{true˜}{X}}_{t} MathClass-close}}_{0 \leq t \leq T}

. According to Theorem 1 in Cai et al (2019), the transition rate matrix of

{MathClass-open{{\overset{true˜}{X}}_{t} MathClass-close}}_{0 \leq t \leq T}

can be constructed by

()(, \begin{matrix} λ_{11} I_{N} + Λ_{1} & λ_{12} I_{N} \\ λ_{21} I_{N} & λ_{22} I_{N} + Λ_{2} \end{matrix}),

where

I_{N}

is the identity matrix. According to the algorithm in Section 3, we can generate the optimal exercise strategy and obtain the American option price.…”

Section: Pricing American Options Under the Cev‐rs Modelmentioning

confidence: 99%

Pricing and calibration of the futures options market: A unified approximation

Song

2021

Journal of Futures Markets

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The constant elasticity of variance (CEV) model is widely used in modeling commodity futures prices, but it may not perform well in calibrating corresponding futures options. We consider two variations of the CEV model, that is, CEV with jumps and CEV with regime switching, and compare their performance in calibrating the Chinese futures options market. In particular, we propose a unified framework for pricing American futures options by combining the continuous‐time Markov chain approximation and the dynamic programming method. Results show that the inverse leverage effect in the soybean meal options market can be better described by the CEV regime‐switching model.

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“…We can convert the original two‐dimensional Markov chain into a one‐dimensional Markov chain

{MathClass-open{{\overset{true˜}{X}}_{t} MathClass-close}}_{0 \leq t \leq T}

. According to Theorem 1 in Cai et al (2019), the transition rate matrix of

{MathClass-open{{\overset{true˜}{X}}_{t} MathClass-close}}_{0 \leq t \leq T}

can be constructed by

()(, \begin{matrix} λ_{11} I_{N} + Λ_{1} & λ_{12} I_{N} \\ λ_{21} I_{N} & λ_{22} I_{N} + Λ_{2} \end{matrix}),

where

I_{N}

is the identity matrix. According to the algorithm in Section 3, we can generate the optimal exercise strategy and obtain the American option price.…”

Section: Pricing American Options Under the Cev‐rs Modelmentioning

confidence: 99%

Pricing and calibration of the futures options market: A unified approximation

Song

2021

Journal of Futures Markets

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“…Most lately, Cui et al (2021) proposed a novel Monte Carlo simulation method for stochastic differential equation systems based on CTMC with applications to stochastic local volatility models and queue processes. Pointing up the importance of regime-switching models in areas such as healthcare and financial engineering, Cai et al (2020) also proposed an extended CTMC approximation to general regime-switching Markov models and presented relevant uses.…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…Cai et al (2015) pioneered a method for obtaining the unknown probability distribution of the stochastic sum (discrete and continuous) in general one-dimensional Markov models via an approximating CTMC based on the technique in Mijatović and Pistorius (2013). (This was extended later to general regime-switching Markov models in Cai et al 2020.). As part of their application, they focused on the prices of Asian options which they recovered by numerical inversion of the double Laplace transform related to the constructed CTMC with respect to the strike price and the maturity (or number of monitoring dates in the case of discrete averaging).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…For more general case, Cai et al [7] recently proposed a general framework for average option prices under general one-dimensional Markov processes. For continuous average options, Cai et al [8] derives analytical approximations under general regime-switching Markov models.…”

Section: Introductionmentioning

confidence: 99%

Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models

Shiraya

Takahashi

2018

Mathematics of OR

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This paper presents a new approximation formula for pricing multi-dimensional discretely monitored average options in a local-stochastic volatility (LSV) model with jumps by applying an asymptotic expansion technique. Moreover, it provides a justification of the approximation method with some asymptotic error estimates for general payoff functions. Particularly, our model includes local volatility functions and jump components in the underlying asset price as well as its volatility processes. To the best of our knowledge, the proposed approximation is the first one which achieves analytic approximations for the average option prices in this environment.In numerical experiments, by employing several models, we provide approximate prices for the listed average and calendar spread options on the WTI futures based on the parameters through calibration to the listed (plain-vanilla) futures options prices. Then, we compare those with the CME settlement prices, which confirms the validity of the method.Moreover, we show that the LSV with jumps model is able to replicate consistently and precisely listed futures option, calendar spread option and average option prices with common parameters.

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A Unified Framework for Computing Regime-Switching Models

Cited by 15 publications

References 50 publications

Pricing and calibration of the futures options market: A unified approximation

Pricing and calibration of the futures options market: A unified approximation

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

Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models

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