Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps

Itkin, Andrey

doi:10.1080/1350486x.2017.1409641

Cited by 4 publications

(16 citation statements)

References 36 publications

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“…The latter results in the FD approximation of the mixed derivative using a 9-points stencil while still providing the second order of approximation. However, as shown in [Itkin, 2017a], this discretization could be unstable. Therefore, instead a fully implicit scheme was proposed which, as applied to our problem, is discussed in the next Section.…”

Section: Backward Schemementioning

confidence: 99%

“…Since computation of matrix exponent is time-consuming, especially in case of a two-dimensional operator L, we proceed with using a splitting technique, see [Lanser and Verwer, 1999, Duffy, 2006, Itkin, 2017b] and references therein. For instance, in [Itkin, 2017a] an ADI (alternative direction implicit) scheme proposed in [In't Hout and Welfert, 2007] for the solution of a backward PDE was extended twofold. First, a similar ADI scheme has been proposed for the forward equation which equalizes the results obtained by solving backward and forward PDEs.…”

Section: Splitting In Spatial Dimensionsmentioning

confidence: 99%

“…However, the standard methods fail to provide discretization of the second order that guarantees this feature. Therefore, we need another approach, similar to what was proposed in [Itkin, 2017a]. We discuss this in Appendix A.…”

Section: Second Derivatives the First Termmentioning

confidence: 99%

“…As compared with [Itkin, 2017a], the method in this paper has two innovations. First, in [Itkin, 2017a] a first order approximation in time step was constructed, while here we provide the second order approximation.…”

Section: Second Derivatives the First Termmentioning

confidence: 99%

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A model-free backward and forward nonlinear PDEs for implied volatility

Carr¹,

Itkin²,

Stoikov³

2019

Preprint

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We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. We also discuss suitable initial and boundary conditions for those PDEs. Finally, we demonstrate how to solve them numerically by using an iterative finite-difference approach.

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Section: Backward Schemementioning

confidence: 99%

Section: Splitting In Spatial Dimensionsmentioning

confidence: 99%

Section: Second Derivatives the First Termmentioning

confidence: 99%

Section: Second Derivatives the First Termmentioning

confidence: 99%

See 2 more Smart Citations

A model-free backward and forward nonlinear PDEs for implied volatility

Carr¹,

Itkin²,

Stoikov³

2019

Preprint

Self Cite

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“…The extensive research options cover a wide range of applications of mathematics in many fields. In recent years, the number of publications has increased (G. Chen & Shen, 2007;Itkin, 2017).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Block Model Reveals Maps of In Applied Mathematics Studies Using VOS Viewer

Karim¹,

Soebagyo²,

Purwanto³

2021

IJoPME

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Bibliometric analysis is the mapping of research research trends by processing metadata from Google Scolar. The aim is to find out research trends in applied mathematics. The research was conducted on April 30, 2021 through searching the Google Scholar database with the keywords applied mathematics with the publication name journal and the maximum number of results is 500 journals as a sample. Metadata retrieval using the Publish or Perish (POP) application version 7.31. The PoP data were then analyzed descriptively based on the publication year, publisher name, researcher productivity, and journal ranking. To get an accurate map of research developments, PoP data is exported to Exel CSV and Result as RIS file formats. The CSV data was created in a pivot table and the RIS data was analyzed using the VOSViewer (VV) application. The results of the research show that the number of publications of research results in the years 2005-2021 has fluctuated and is mostly published in Elsevier. The most prolific foreign researcher in publishing research results is Biher Bist with 14 articles. The VV visualization shows that the map of the development of applied mathematics research is divided into 5 clusters. Cluster 1 consists of 27 topics, cluster 2 consists of 15 topics, cluster 3 consists of 10 topics, cluster 4 consists of 7 topics, and cluster 5 consists of 3 topics with the most research covering mathematics, paper, problem, solution, system, university, department, science.

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Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods

Hok

Tan

2019

Decisions Econ Finan

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Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually time-consuming because of the multi-dimensional nature of the problem. In this paper, we develop a calibration technique based on a partial differential equation (PDE) approach which allows an efficient implementation. The essential idea is based on solving the derived forward equation satisfied by P (t, S, r)Z(t, S, r), where P (t, S, r) represents the risk neutral probability density of (S(t), r(t)) and Z(t, S, r) the projection of the stochastic discounting factor in the state variables (S(t), r(t)). The solution provides effective and sufficient information for the calibration and pricing. The PDE solver is constructed by using ADI (Alternative Direction Implicit) method based on an extension of the Peaceman-Rachford scheme. Furthermore, an efficient algorithm to compute all the corrective terms in the local volatility function due to the stochastic interest rates is proposed by using the PDE solutions and grid points. Different numerical experiments are examined and compared to demonstrate the results of our theoretical analysis.

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Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps

Cited by 4 publications

References 36 publications

A model-free backward and forward nonlinear PDEs for implied volatility

A model-free backward and forward nonlinear PDEs for implied volatility

Stochastic Block Model Reveals Maps of In Applied Mathematics Studies Using VOS Viewer

Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods

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