Series Representations for Multivariate Time-Changed Lévy Models

Panov, Vladimir

doi:10.1007/s11009-015-9461-8

Cited by 3 publications

(9 citation statements)

References 37 publications

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“…Remark Some conditions, which guarantee that (A2) holds, can be found in the work of Panov . For instance, it is sufficient to assume that there exists a density function

p^{*} : {double-struckR}_{+}^{d - 1} \to double-struckR

and ( d − 1) functions

f_{j}^{*} : {double-struckR}_{+}^{2} \to {double-struckR}_{+}, j = 1, …, false(d - 1 false)

, such that for any u , x > 0,

\int_{- \infty}^{f_{1}^{*} false(u_{1}, v false)} … \int_{- \infty}^{f_{d - 1}^{*} false(u_{d - 1}, v false)} p^{*} false(z_{1}, …, z_{d - 1} false) d z_{d - 1}, …, d z_{1} = \overset{F}{true} false(u_{1}, …, u_{d - 1} false| v false);

the functions

f_{j}^{*} false(u_{j}, v false), j = 1, …, false(d - 1 false)

monotonically increase in u j for any fixed v , and moreover, for any j = 1,…,( d − 1) and any y > 0, the equation

f_{j}^{*} (u_{j}, v) = y

has a closed‐form solution with respect to u j ; we denote this solution by

h_{j}^{*} false(y, v false)

. In fact, in this case, …”

Section: Multivariate Subordination Of Stable Processesmentioning

confidence: 99%

“…Some conditions, which guarantee that (A2) holds, can be found in the work of Panov. 22 For instance, it is sufficient to assume that there exists a density function p * ∶ R d−1 + → R and (d − 1) functions * ∶ R 2 + → R + , = 1, … , (d − 1), such that 1. for any u, x > 0,…”

Section: Multivariate Subordination Of Stable Processesmentioning

confidence: 99%

“…Another idea is to take a multivariate subordinator , a Lévy process

bold-scriptT false(s false) = ((), {scriptT}_{1} false(s false), …, {scriptT}_{d} false(s false))

, independent of L ( t ), such that

boldX false(s false) = ((), L_{1} false({scriptT}_{1} false(s false) false), …, L_{d} false({scriptT}_{d} false(s false) false)) .

This concept, known as the multivariate subordination, was introduced by Barndorff‐Nielsen et al In our paper, we consider model for the situation when L ( t ) is a multivariate stable process, and dependence between the components of

bold-scriptT false(s false)

is described via a Lévy copula , another popular concept in the theory of jump‐type processes. This construction was considered by Panov for the partial case when L ( t ) is, in fact, a multivariate Brownian motion. Nevertheless, as we show below, the generalization to the class of stable processes leads to the construction of the model, which is more appropriate for describing stock returns.…”

Section: Introductionmentioning

confidence: 99%

“…This concept, known as the multivariate subordination, was introduced by Barndorff-Nielsen et al 21 In our paper, we consider model (2) for the situation when L(t) is a multivariate stable process, and dependence between the components of  (s) is described via a Lévy copula, another popular concept in the theory of jump-type processes. This construction was considered by Panov 22 for the partial case when L(t) is, in fact, a multivariate Brownian motion. Nevertheless, as we show below, the generalization to the class of stable processes leads to the construction of the model, which is more appropriate for describing stock returns.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multivariate asset‐pricing model based on subordinated stable processes

Panov

Samarin

2019

Appl Stoch Models Bus & Ind

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In this paper, we consider a multidimensional time‐changed stochastic process in the context of asset‐pricing modeling. The proposed model is constructed from stable processes, and its construction is based on two popular concepts: multivariate subordination and Lévy copulas. From a theoretical point of view, our main result is Theorem 1, which yields a simulation method from the considered class of processes. Our empirical study shows that the model represents the correlation between asset returns quite well. Moreover, we provide some evidence that this model is more appropriate for describing stock prices than classical time‐changed Brownian motion, at least if the cumulative amount of transactions is used for a stochastic time change.

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“…Remark Some conditions, which guarantee that (A2) holds, can be found in the work of Panov . For instance, it is sufficient to assume that there exists a density function

p^{*} : {double-struckR}_{+}^{d - 1} \to double-struckR

and ( d − 1) functions

f_{j}^{*} : {double-struckR}_{+}^{2} \to {double-struckR}_{+}, j = 1, …, false(d - 1 false)

, such that for any u , x > 0,

\int_{- \infty}^{f_{1}^{*} false(u_{1}, v false)} … \int_{- \infty}^{f_{d - 1}^{*} false(u_{d - 1}, v false)} p^{*} false(z_{1}, …, z_{d - 1} false) d z_{d - 1}, …, d z_{1} = \overset{F}{true} false(u_{1}, …, u_{d - 1} false| v false);

the functions

f_{j}^{*} false(u_{j}, v false), j = 1, …, false(d - 1 false)

monotonically increase in u j for any fixed v , and moreover, for any j = 1,…,( d − 1) and any y > 0, the equation

f_{j}^{*} (u_{j}, v) = y

has a closed‐form solution with respect to u j ; we denote this solution by

h_{j}^{*} false(y, v false)

. In fact, in this case, …”

Section: Multivariate Subordination Of Stable Processesmentioning

confidence: 99%

Section: Multivariate Subordination Of Stable Processesmentioning

confidence: 99%

“…Another idea is to take a multivariate subordinator , a Lévy process

bold-scriptT false(s false) = ((), {scriptT}_{1} false(s false), …, {scriptT}_{d} false(s false))

, independent of L ( t ), such that

boldX false(s false) = ((), L_{1} false({scriptT}_{1} false(s false) false), …, L_{d} false({scriptT}_{d} false(s false) false)) .

bold-scriptT false(s false)

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multivariate asset‐pricing model based on subordinated stable processes

Panov

Samarin

2019

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…Beyond the Gaussian world, some choices have been proposed to model dependence in the context of Lévy processes. Among others, Cont and Tankov (2003), Cherubini et al (2013), Panov and Samarin (2019), Panov and Sirotkin (2017) have discussed the use of Lévy copulas or of Lévy series representations.…”

Section: Introductionmentioning

confidence: 99%

Correlating Lévy processes with self-decomposability: applications to energy markets

Gardini

Sabino²,

Sasso

2021

Decisions Econ Finan

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Based on the concept of self-decomposability, we extend some recent multidimensional Lévy models built using multivariate subordination. Our aim is to construct multivariate Lévy processes that can model the propagation of the systematic risk in dependent markets with some stochastic delay instead of affecting all the markets at the same time. To this end, we extend some known approaches keeping their mathematical tractability, study the properties of the new processes, derive closed-form expressions for their characteristic functions and detail how Monte Carlo schemes can be implemented. We illustrate the applicability of our approach in the context of gas, power and emission markets focusing on the calibration and on the pricing of spread options written on different underlying commodities.

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Option pricing in time-changed Lévy models with compound Poisson jumps

Иванов¹,

Ano²

2018

Modern Stochastics: Theory and Applications

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The problem of European-style option pricing in time-changed Lévy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the time-changed Lévy models, the variance-gamma and the normal-inverse Gaussian models are discussed. Exact formulas are given for the price of digital asset-or-nothing call option on extra asset in foreign currency. The prices of simpler options can be derived as corollaries of our results and examples are presented. Various types of dependencies between stock prices are mentioned.

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Series Representations for Multivariate Time-Changed Lévy Models

Cited by 3 publications

References 37 publications

Multivariate asset‐pricing model based on subordinated stable processes

Multivariate asset‐pricing model based on subordinated stable processes

Correlating Lévy processes with self-decomposability: applications to energy markets

Option pricing in time-changed Lévy models with compound Poisson jumps

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