Functionals of Multidimensional Diffusions with Applications to Finance

Baldeaux, Jan; Platen, Eckhard

doi:10.1007/978-3-319-00747-2

Cited by 34 publications

(26 citation statements)

References 156 publications

(452 reference statements)

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“…Xs ]: we recover the proposition 2.0.40 in Lennox (2011), see also corollary 5.9 in Craddock and Lennox (2009) and proposition 5.4.3. in Baldeaux and Platen (2013), p. 154, that is,…”

Section: Appendix Amentioning

confidence: 98%

“…Recently Baldeaux () implemented the Broadie and Kaya () algorithm to the exact simulation of the 3/2 model. This is possible because the Laplace transform of the integral of the inverse of a CIR process conditional to the terminal value of the process is known in closed form (see, e.g., Baldeaux and Platen , theorem 6.4.1).…”

Section: Exact Simulation Of the 4/2 Modelmentioning

confidence: 99%

“…ds Xs ]: we recover the theorem 5.10 in Craddock and Lennox (2009) (where we corrected as before the typo √ Axy → √ Ax/y in the first term of their proof, see also ch. 5.8), see also proposition 5.4.4. in Baldeaux and Platen (2013), p. 155 (for a Bessel process of dimension n). r μ = 0 or ν = 0: we get new explicit formulas for the transforms resp.…”

Section: Appendix Amentioning

confidence: 99%

See 2 more Smart Citations

The 4/2 Stochastic Volatility Model: A Unified Approach for the Heston and the 3/2 Model

Grasselli

2016

Mathematical Finance

132

101

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We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for partial differential equations; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model, which is useful for numerical applications.

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“…Xs ]: we recover the proposition 2.0.40 in Lennox (2011), see also corollary 5.9 in Craddock and Lennox (2009) and proposition 5.4.3. in Baldeaux and Platen (2013), p. 154, that is,…”

Section: Appendix Amentioning

confidence: 98%

Section: Exact Simulation Of the 4/2 Modelmentioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

See 1 more Smart Citation

The 4/2 Stochastic Volatility Model: A Unified Approach for the Heston and the 3/2 Model

Grasselli

2016

Mathematical Finance

132

101

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show abstract

“…Then for each T ∈ R ++ and n ∈ N, the random matrices Γ (1) T,n and Γ (2) T,n are invertible almost surely, and hence there exists a unique CLSE c T,n , d T,n , δ T,n , ε T,n , ζ T,n of (c, d, δ, ε, ζ) taking the form given in (3.5).…”

Section: Clse Based On Continuous Time Observationsmentioning

confidence: 99%

On conditional least squares estimation for affine diffusions based on continuous time observations

Bolyog

Pap

2018

Stat Inference Stoch Process

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We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For all the drift parameters, in the subcritical and supercritical cases, asymptotic normality and asymptotic mixed normality is proved, while in the critical case, non-standard asymptotic behavior is described.

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“…They find only limited reference to scientific papers or current research issues such as in the seminal book by [5] on Brownian Motion and Stochastic Calculus. Moreover, he mainly introduces standard theories and does not take into account new developments in probability theory or related fields, such as Lie algebra [6]. All in all, the positive impression outweighs.…”

Section: Positive Aspects Of the Bookmentioning

confidence: 99%

A Review on ‘Probability and Stochastic Processes’

Herzog

2016

AJTAS

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This paper is a commentary on the book 'Probability and Stochastic Processes' from Ionut Florescu. The book is an excellent introduction to both probability theory and stochastic processes. It provides a comprehensive discussion of the main statistical concepts including the theorems and proofs. The introduction to probability theory is easy accessible and a perfect starting point for undergraduate students even with majors in other subjects than science, such as business or engineering. The book is also up-to-date because it includes programming code for simulations. However, the book has some weaknesses. It is less convincing in more advanced topics of stochastic theory and it does not include solutions to excises and recent research trends.

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Functionals of Multidimensional Diffusions with Applications to Finance

Cited by 34 publications

References 156 publications

The 4/2 Stochastic Volatility Model: A Unified Approach for the Heston and the 3/2 Model

The 4/2 Stochastic Volatility Model: A Unified Approach for the Heston and the 3/2 Model

On conditional least squares estimation for affine diffusions based on continuous time observations

A Review on ‘Probability and Stochastic Processes’

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