Multivariate European option pricing in a Markov-modulated Lévy framework

Deelstra, Griselda; Simon, Matthieu

doi:10.1016/j.cam.2016.11.040

Cited by 12 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We start by stating a very useful result, which can be proved in a similar way as the analogous well‐known result without synchronous jumps; see, eg, Deelstra and Simon …”

Section: Markov‐modulated Lévy Modelmentioning

confidence: 89%

“…This lemma is a crucial step for adapting the approach of Caldana and Fusai and Caldana et al to regime‐switching models with synchronous jumps. We notice that an analogous lemma had also been very useful in the work of Deelstra and Simon on the pricing of exchange and quanto options in a MMLP framework without synchronous jumps.…”

Section: Introductionmentioning

confidence: 87%

“…Therefore, the approximations given in Theorem and Proposition are then expressed in terms of a European call option written on G n ( T ). Note that the price of the corresponding European call option can be easily computed by following similar arguments as in the case without synchronous jumps; see, eg, Deelstra and Simon …”

Section: Basket Option Pricing By the Arithmetic‐geometric Mean Inequmentioning

confidence: 99%

“…As far as we know, there are not so many papers focusing upon multivariate option pricing in a regime‐switching framework, especially not in a MMLP setting, and none of them considers synchronous jumps. Among others, we refer to Yoon et al, Chen et al, Fan and Wang, and Deelstra and Simon . In particular, Deelstra and Simon study the pricing of exchange and quanto options in a MMLP framework by using a fast Fourier transform method.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Deelstra

Kozpınar

Simon

2018

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov-modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime-switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov-modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime-switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision.

show abstract

“…We start by stating a very useful result, which can be proved in a similar way as the analogous well‐known result without synchronous jumps; see, eg, Deelstra and Simon …”

Section: Markov‐modulated Lévy Modelmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 87%

Section: Basket Option Pricing By the Arithmetic‐geometric Mean Inequmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Deelstra

Kozpınar

Simon

2018

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…Over intervals of time where J(t) remains constant, and equal to i say, the level behaves as the superposition of a Brownian motion and Poisson processes of jumps, with parameters dependent on i; when the phases switches from i to j = i, X(t) jumps by a random quantity Y ij . Applications are found in mathematical finance (Jobert and Rogers [18], Ballotta and Bonfiglioli [1], Deelstra and Simon [11]), risk theory (Lu and Tsai [22], Li and Ren [21]) and queueing theory (Prabhu [25]).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes

Бини¹,

Latouche²,

Meini³

2021

Preprint

View full text Add to dashboard Cite

Markov-modulated Lévy processes lead to matrix integral equations of the kind A 0 + A 1 X + A 2 X 2 + A 3 (X) = 0 where A 0 , A 1 , A 2 are given matrix coefficients, while A 3 (X) is a nonlinear function, expressed in terms of integrals involving the exponential of the matrix X itself.In this paper we propose some numerical methods for the solution of this class of matrix equations, perform a theoretical convergence analysis and show the effectiveness of the new methods by means of a wide numerical experimentation.

show abstract

Stochastic approach to model spot price and value forward contracts on energy markets under uncertainty

Pawłowski

Nowak

2021

J Ambient Intell Human Comput

View full text Add to dashboard Cite

The paper deals with a model of electricity spot prices. The proposed dynamics of electricity spot prices is driven by a mean reverting diffusion with jumps having hyperexponential distribution. The analytical formula for the forward contract’s price is derived in a crisp case. Inasmuch as the model parameters are considered to be evaluated imprecisely, their fuzzy counterparts are introduced. With usage of the fuzzy arithmetic, the analytical expression for the forward contract’s price is derived. Several numerical examples highlighting attributes of the fuzzy forward electricity prices are brought out.

show abstract

Multivariate European option pricing in a Markov-modulated Lévy framework

Cited by 12 publications

References 15 publications

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Numerical solution of a matrix integral equation arising in Markov Modulated Lévy processes

Stochastic approach to model spot price and value forward contracts on energy markets under uncertainty

Contact Info

Product

Resources

About