An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates

Gnoatto, Alessandro; Grasselli, Martino

doi:10.1137/130922902

Cited by 32 publications

(14 citation statements)

References 52 publications

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“…Similarly, for ξ > M, e − u,ξ 1 − e − h,ξ − h, ξ ≤ e − u,ξ − e − u+h,ξ + e − u,ξ h, ξ ≤ 2 | h, ξ | . (22) Combining (21) and (22) and applying Lemma 4.1, we get…”

Section: Lemma 42unclassified

“…In particular, they provide natural models for the evolution of the covariance matrix of multi-asset prices that exhibit random dependence, such as the Wishart process [10], the jump-type Wishart process [38], and a certain class of matrix-valued Ornstein-Uhlenbeck processes driven by Lévy subordinators [7]. Among these, the Wishart process is the most popular one, and it can be used as a multivariate covariance model that extends the well-known Heston model [26]; see also [3], [9], [11], [14], [21], [22], [23], [24], and [25]. The jump-type Wishart process was introduced by Leippold and Trojani [38] to provide additional model flexibility.…”

Section: Introductionmentioning

confidence: 99%

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Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

et al. 2020

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This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

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Section: Lemma 42unclassified

Section: Introductionmentioning

confidence: 99%

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

et al. 2020

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“…This symmetry is the key requirement for a model to be consistent for a currency pair and its inverse pair (see e.g. [10,11,8,15] and references therein).…”

Section: Preliminariesmentioning

confidence: 99%

Pricing FX Options under Intermediate Currency

Maurer¹,

Sharp²,

Tretyakov³

2019

Preprint

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We introduce a new pricing mechanism for FX options, which is based on the idea of an intermediate pseudo-currency market. This approach allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is sufficient to calibrate a model to the volatility smile on the domestic market as, due to the consistency of pricing formulas, the model automatically reproduces the correct smile for the inverse pair (the foreign market). We first consider the case of two currencies and then we extend the pricing mechanism to the multi-currency setting. We illustrate the new pricing mechanism by applying it to the Heston and SABR stochastic volatility models, to the model in which exchange rates are described by an extended skewed normal distribution, and also to the model-free approach of option pricing.

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“…Wishart and general positive semi-definite affine models have also been successfully used to model interest rates (e.g. [8,13,41,45]). For stochastic processes the existence and uniqueness of stationary solutions as well as convergence to the stationary solution is of high interest.…”

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confidence: 99%

Geometric ergodicity of affine processes on cones

Mayerhofer

Stelzer

Vestweber

2020

Stochastic Processes and their Applications

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For affine processes on finite-dimensional cones, we give criteria for geometric ergodicitythat is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of the limiting distribution, where we exploit the crucial affine property, and finite moments, where we invoke the polynomial property of affine semigroups. Furthermore, we elaborate sufficient conditions for aperiodicity and irreducibility. Our results are applicable to Wishart processes with jumps on the positive semidefinite matrices, continuous-time branching processes with immigration in high dimensions, and classical termstructure models for credit and interest rate risk.

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An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates

Cited by 32 publications

References 52 publications

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Pricing FX Options under Intermediate Currency

Geometric ergodicity of affine processes on cones

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