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Dimension-wise scaled normal mixtures with application to finance and biometry. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Merkle R, Barth A. On Some Distributional Properties of Subordinated Gaussian Random Fields. Methodol Comput Appl Probab 2022. [DOI: 10.1007/s11009-022-09958-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
AbstractMotivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal distribution of the constructed random fields, derive a Lévy-Khinchin-type formula and semi-explicit formulas for the covariance function. Further, we study the pointwise stochastic regularity and present various numerical examples.
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Necessity of weak subordination for some strongly subordinated Lévy processes. J Appl Probab 2021. [DOI: 10.1017/jpr.2021.17] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
AbstractConsider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of the subordinator are indistinguishable within each stack, then strong subordination produces a Lévy process; otherwise it may not. Weak subordination was introduced to extend strong subordination, always producing a Lévy process even when strong subordination does not. Here we prove that strong and weak subordination are equal in law under the aforementioned condition. In addition, we prove that if strong subordination is a Lévy process then it is necessarily equal in law to weak subordination in two cases: firstly when the subordinator is deterministic, and secondly when it is pure-jump with finite activity.
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Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2021. [DOI: 10.1007/s11203-021-09254-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Xia Y, Grabchak M. Estimation and simulation for multivariate tempered stable distributions. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1962878] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Yunfei Xia
- Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC, USA
| | - Michael Grabchak
- Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC, USA
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Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices. JOURNAL OF RISK AND FINANCIAL MANAGEMENT 2021. [DOI: 10.3390/jrfm14080355] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first perspective uses a geometric two-dimensional Brownian motion model. The second inverts two-dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.
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Buchmann B, Lu KW, Madan DB. Self-decomposability of weak variance generalised gamma convolutions. Stoch Process Their Appl 2020. [DOI: 10.1016/j.spa.2019.02.012] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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