A multifactor volatility Heston model

Fonseca, José Da; Grasselli, Martino; Tebaldi, Claudio

doi:10.1080/14697680701668418

Cited by 181 publications

(133 citation statements)

References 14 publications

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“…More generally, mathematical finance and biology provide examples of elliptic differential operators which become degenerate along the boundary of a 'quadrant', R d−m × R m + , and R d−m ×R m + is a state space for the corresponding Markov process. Examples primarily motivated by mathematical finance include affine processes [1,14,17,22,23,24,40,41], which may be viewed as extensions of geometric Brownian motion (see, for example, [71]), the Heston stochastic volatility process [51], and the Wishart process [14,42,45,46,47]. Examples of this kind which arise in mathematical biology include the multi-dimensional Kimura diffusions and their local model processes [27,Equations (1.5) and (1.20)].…”

Section: 2mentioning

confidence: 99%

Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators

Feehan

2013

Communications in Partial Differential Equations

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Abstract. We prove weak and strong maximum principles, including a Hopf lemma, for C 2 subsolutions to equations defined by second-order, linear elliptic partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the C 2 subsolutions along this boundary vanishing locus ensures that these maximum principles hold irrespective of the sign of the Fichera function. Boundary conditions need only be prescribed on the complement in the domain boundary of the principal symbol's vanishing locus. We obtain uniqueness and a priori maximum principle estimates for C 2 solutions to boundary value and obstacle problems defined by these boundary-degenerate elliptic operators with partial Dirichlet or Neumann boundary conditions. We also prove weak maximum principles and uniqueness for W 1,2 solutions to the corresponding variational equations and inequalities defined with the aide of weighted Sobolev spaces. The domain is allowed to be unbounded when the operator coefficients and solutions obey certain growth conditions. Contents List of

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Section: 2mentioning

confidence: 99%

Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators

Feehan

2013

Communications in Partial Differential Equations

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“…It is a direct multivariate extension of the Cox-Ingersoll-Ross model and has been extended and used for financial applications by e.g. Gourieroux & Sufana (2003Da Fonseca et al (2007, 2008 ;Buraschi et al (2010); Muhle-Karbe et al (2012). While these papers consider option pricing, hedging, credit risk and term structure models, we will investigate portfolio optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Optimal Portfolios for Financial Markets with Wishart Volatility

Bäuerle

2013

Journal of Applied Probability

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Abstract. We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain explicitly the optimal portfolio strategy and the value function in some parameter settings. In particular when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is indeed to identify when the solution of the HJB equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.

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“…In order to derive the conditional Laplace transform of p t , we use the matrix Riccati linearization technique suggested by Fonseca, Grasselli and Tebaldi (2008), instead the approach of Gourieroux and Sufana (2010). Proposition 1 shows the conditional Laplace transform of the log-price process, p t .…”

Section: Laplace Transformsmentioning

confidence: 99%

Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing

McAleer

2015

Journal of Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in 1 AbstractThe paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace transform of the AMWSV models. The paper also suggests estimating the AMWSV model by the generalized method of moments using information not only of stock prices but also of realized volatilities and covolatilities. The empirical results for the bivariate data of the NASDAQ 100 and S&P 500 indices show that the general AMWSV model is preferred among several nested models.

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A multifactor volatility Heston model

Cited by 181 publications

References 14 publications

Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators

Maximum Principles for Boundary-Degenerate Second Order Linear Elliptic Differential Operators

Optimal Portfolios for Financial Markets with Wishart Volatility

Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing

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