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Florian Aichinger

Publications and source records attributed to Florian Aichinger.

4 recordsLinked to original sources
arXiv2024

Pricing of geometric Asian options in the Volterra-Heston model

Geometric Asian options are a type of options where the payoff depends on the geometric mean of the underlying asset over a certain period of time. This paper is concerned with the pricing of such options for the class of Volterra-Heston models, covering the rough Heston model. We are able to derive semi-closed formulas for the prices of geometric Asian options with fixed and floating strikes for this class of stochastic volatility models. These formulas require the explicit calculation of the conditional joint Fourier transform of the logarithm of the stock price and the logarithm of the geometric mean of the stock price over time. Linking our problem to the theory of affine Volterra processes, we find a representation of this Fourier transform as a suitably constructed stochastic exponential, which depends on the solution of a Riccati-Volterra equation. Finally we provide a numerical study for our results in the rough Heston model.

q-fin.PR↗
arXiv2023

A Comparative Study of Factor Models for Different Periods of the Electricity Spot Price Market

Due to major shifts in European energy supply, a structural change can be observed in Austrian electricity spot price data starting from the second quarter of the year 2021 onward. In this work we study the performance of two different factor models for the electricity spot price in three different time periods. To this end, we consider three samples of EEX data for the Austrian base load electricity spot price, one from the pre-crises from 2018 to 2021, the second from the time of the crisis from 2021 to 2023 and the whole data from 2018 to 2023. For each of these samples, we investigate the fit of a classical 3-factor model with a Gaussian base signal and one positive and one negative jump signal and compare it with a 4-factor model to assess the effect of adding a second Gaussian base signal to the model. For the calibration of the models we develop a tailor-made Markov Chain Monte Carlo method based on Gibbs sampling. To evaluate the model adequacy, we provide simulations of the spot price as well as a posterior predictive check for the 3- and the 4-factor model. We find that the 4-factor model outperforms the 3-factor model in times of non-crises. In times of crises, the second Gaussian base signal does not lead to a better fit of the model. To the best of our knowledge, this is the first study regarding stochastic electricity spot price models in this new market environment. Hence, it serves as a solid base for future research.

q-fin.MF↗
arXiv2021

Utility maximization in multivariate Volterra models

This paper is concerned with portfolio selection for an investor with power utility in multi-asset financial markets in a rough stochastic environment. We investigate Merton's portfolio problem for different multivariate Volterra models, covering the rough Heston model. First we consider a class of multivariate affine Volterra models introduced in [E. Abi Jaber et al., SIAM J. Financial Math., 12, 369-409, (2021)]. Based on the classical Wishart model described in [N. B\"auerle and Li, Z., J. Appl. Probab., 50, 1025-1043 (2013)], we then introduce a new matrix-valued stochastic volatility model, where the volatility is driven by a Volterra-Wishart process. Due to the non-Markovianity of the underlying processes, the classical stochastic control approach cannot be applied in these settings. To overcome this issue, we provide a verification argument using calculus of convolutions and resolvents. The resulting optimal strategy can then be expressed explicitly in terms of the solution of a multivariate Riccati-Volterra equation. We thus extend the results obtained by Han and Wong to the multivariate case, avoiding restrictions on the correlation structure linked to the martingale distortion transformation used in [B. Han and Wong, H. Y., Finance Res. Lett., 39 (2021)]. We also provide existence and uniqueness theorems for the occurring Volterra processes and illustrate our results with a numerical study.

math.PR↗