The Heston stochastic volatility model in Hilbert space

@article{Benth2017TheHS,
  title={The Heston stochastic volatility model in Hilbert space},
  author={Fred Espen Benth and Iben Cathrine Simonsen},
  journal={Stochastic Analysis and Applications},
  year={2017},
  volume={36},
  pages={733 - 750}
}
ABSTRACT We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein–Uhlenbeck process with itself. The volatility process is then defined by a Cholesky decomposition of the variance process. We define a Hilbert-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this stochastic volatility, and compute the characteristic functional and covariance operator of… 

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References

SHOWING 1-10 OF 21 REFERENCES

Representation of Infinite-Dimensional Forward Price Models in Commodity Markets

We study the forward price dynamics in commodity markets realised as a process with values in a Hilbert space of absolutely continuous functions defined by Filipović (Consistency problems for

A multifactor volatility Heston model

We model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana. As in standard Duffie and Kan affine

Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes

We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by Levy processes. The emphasis is on the different contexts in which these processes arise, such as

Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics

Non‐Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures.

A space-time random field model for electricity forward prices

Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In

Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

TLDR
This work connects empirical evidence about energy forward prices known from the literature to propose stochastic models, and analyzes the covariance operator and representations of such variables, as well as presenting applications to the pricing of spread and energy quanto options.

A maximal inequality for stochastic convolution integrals on hilbert spaces and space-time regularity of linear stochastic partial differential equations

We consider optimal control problems for one-dimensional diffusion processes [ILM0001] where the control processes υt are increasing, positive, and adapted. Several types of expected cost structures

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and

Wishart Processes

Based on a student research project this article gives a short review on Wishart processes. A Wishart procces is a matrix valued continuous time stochastic process with a marginal Wishart