A single social media post can trigger a 10% drop in an asset’s price within a day, as demonstrated by Elon Musk’s ”Tesla stock price is too high imo” post. With the growth of social media and advances in language models, sentiment analysis becomes increasingly relevant and computationally achievable in financial markets. From a behavioral finance perspective, it is a well-established result that asset price changes stemming from sentiment shifts exhibits meanreversion. This property motivates the construction of a risk measure by separating sentimentinduced excess volatility from the total volatility.
This thesis aims to quantify this sentiment-induced volatility using a dataset of StockTwits posts from Kaggle. We began by analysing the data, where it was revealed that the posting activity displays properties that are associated with information diffusion, including heavy-tailed activity, burstiness and temporal autocorrelation. Accordingly, FinBERT and TwitterRoBERTa were employed to classify the posts as bullish, bearish or neutral, and the classifications were compared to the user-provided labels. These two BERT-based language models provide a wide coverage by specializing in Finance and colloquial language, respectively.
The predictive power of the resulting sentiment features was evaluated using (Bi-)LSTM and (Bi-)GRU. This power was measured by comparing only lagged-returns models to models enriched with attention-, calendar- and sentiment-based features. It was found that the returns-only models outperformed the enriched feature sets across all five assets and two distinct evaluation approaches. Inspecting the learning and validation curves further showed that the enriched features reduced model generalizability, rather than improving predictive performance.
The findings do not indicate that the constructed sentiment features provide any additional predictive information within the proposed framework. As a result, the evidence does not support proceeding with the construction of the proposed risk measure. This could potentially be the result of the choice of the selected target variable, log-squared returns, which is closely related to the lagged returns. Consequently, future research could consider a different volatility proxy; one that considers intraday price ranges. Such a quantity would not be as directly related to lagged returns and may allow sentiment-based features to contribute more meaningfully to the modeling process. ... Read more

In this thesis, we study spectral bias, the tendency of gradient-based training to learn the low-frequency part of a target before its high-frequency part. We work in a setting simple enough to analyse explicitly: regression on the unit circle with a shallow
ReLU network. In the infinite-width limit, the residual dynamics are governed by the Neural Tangent Kernel. Under the uniform measure on the circle this kernel depends only on the angle between two points, so the associated operator is a convolution and the Fourier modes are its eigenfunctions, each decaying at a rate set by its eigenvalue, and the lower the frequency, the larger the eigenvalue, so low frequencies are learned first.

Away from this idealised limit the picture degrades only gradually. On a fixed low-frequency subspace, both finite sampling and frozen finite width keep the operator close to the continuum Fourier prediction, with error of order O(n^(-1/2)) in the sample size n and O(m^(-1/2)) in the width m. The description breaks only once the kernel is allowed to evolve during training. At small width the evolving kernel reaches a lower loss by strengthening its lowest-frequency components, even as its alignment with the Fourier basis fails to improve. This reinforces the low-frequency bias rather than approximating the fixed-kernel dynamics. A formal theory of this evolving-kernel regime remains the main open problem. ... Read more

In this master thesis, we introduce a new multifractional stable motion, which we refer to as the Itô multifractional stable motion. The definition of the Itô multifractional stable motion is inspired by a relatively recently proposed alternative to the multifractional Brownian motion. The Itô multifractional stable motion is defined as

Y(t) = ∫_R(t-x)₊^H(x)-1/α - (-x)₊^H(x)-1/α dL(x).

Here (x)₊ = max(x, 0), α ∈ (0, 2), L is a standard symmetric α-stable Lévy process and finally, the multifractional parameter H is a jointly measurable stochastic process, adapted to the natural filtration generated by L, taking values in [H_-,H^-] ⊆ (0, 1). Under the assumption that H admits a deterministic modulus of continuity w and that H is strictly bounded from below by 1/α, it is proven that the uniform Hölder exponent ρ_Y^unif([a,b]) over a compact interval satisfies

 ρ_Y^unif([a,b]) ≥ min_t∈[a,b]H(t)-1/α.

Under the further assumption that w(h) log h → 0 as h ↓ 0, it is shown that Y is locally self-similar and that the pointwise Hölder exponent ρ_Y(t) satisfies

ρ_Y(t) ≤ H(t). ... Read more

Physics-informed neural networks (PINNs) provide a powerful framework for solving differential equations but often encounter difficulties when addressing high-frequency solutions. Finite basis physics-informed neural networks (FBPINNs) improve PINN performance through uniform overlapping domain decomposition, yet they may still struggle with problems involving non-uniform frequency solutions. In this work, we introduce a novel framework called adaptive domain decomposition-based FBPINNs (Adaptive DD FBPINNs), which incorporates partition of unity networks (POUnets) to learn domain partitions that adaptively decompose the domain in a data-driven manner. This dynamic decomposition significantly enhances the accuracy and efficiency of PDE solvers, particularly for problems with high-frequency components and complex geometries. Furthermore, the framework integrates a residual-based adaptive distribution (RAD) resampling strategy that concentrates training on regions with high residuals, further boosting performance. Experimental results demonstrate that the Adaptive DD FBPINN outperforms standard FBPINN in terms of accuracy, providing a flexible and robust solution for both regular and complex-shaped domains, while efficiently enforcing Dirichlet boundary conditions as hard constraints. Overall, this work provides an exploratory contribution, presenting a promising approach for adaptively learning partitions by combining data-driven POUnets and FBPINNs, which can be further generalized to complex-shaped domains. ... Read more

Modern electronic markets reward liquidity providers that can continuously quote competitive bid–ask spreads while dynamically controlling risk. This thesis investigates whether Reinforcement Learning (RL) can produce robust market-making strategies when an agent is trained in two settings that have so far received little attention in the literature: Domain Randomization (DR) and Self-Play (SP).
We first design MMakr, an extension of the ABIDES-Gym Limit Order Book (LOB) simulator that (i)
exposes a dimensionless, continuous control interface, (ii) supports per-component reward shaping,
(iii) gives the option to randomise liquidity, volatility and order-flow regimes on every episode, and (iv) allows earlier policy snapshots to be injected as adaptive opponents, thus natively enabling DR and SP training.
Using MMakr, we train Soft Actor-Critic (SAC) and Proximaly Policy Optimization (PPO) agents
under three curricula: a fixed single configuration, DR, and SP. A carefully tuned six-term reward—
combining directional profit, spread capture, fill ratio, inventory cost, quote-cliff and terminal inventory penalties—guides learning towards realistic quoting behaviour while keeping risk in check.
Experiments on six previously unseen market scenarios show that SAC learns profitable policies in
the single-configuration setting but over-fits and degrades out-of-sample. DR substantially improves
PPO’s stability and generalisation, while forcing SAC to adopt more conservative quoting, thereby
degrading its performance. SP introduces non-stationarity that current SAC was not able to overcome, whereas on-policy PPO shows promise in solving the problem but fails to find meaningful information in the time allocated.
The thesis contributes (a) the open-source MMakr environment, (b) an optimisation framework for
reward-component weight search, and (c) a systematic comparison of DR and SP in a realistic multi-
agent LOB simulator. While results reveal clear benefits of environmental diversity, they also highlight the brittleness of current RL algorithms under adversarial liquidity conditions, pointing to the need for curriculum-based randomisation, risk-aware objectives and more carefully configured and realistic simulators in future work. ... Read more

The digitalisation of financial markets has led to an increase in the share of trades being executed by algorithmic trading systems. A key application of these algorithms arises when a trader needs to buy or sell a large volume of shares within a fixed time window. The trader must decide between placing reliable but costly market orders or cheaper limit orders, at a risk of not filling her target amount within the desired time frame. This is known as the Optimal Placement Problem (OPP) and this thesis aims to provide a general solution to this problem. Our research builds forth upon two models. The first, proposed by Cont and Kukanov [2017] [15], formulates the problem as a stochastic convex optimization problem. This model provides a static solution to the OPP, where the trader can only place orders at the initial time. We extend their model beyond the best quote price-level to consider any number of price-levels. This generalization still allows us to derive analytical expressions for the optimal placement strategy, including a closed-form solution under the assumption that market and limit order arrivals follow exponential distributions. However, large deviations in the calibrated parameters or distributions can lead to substantially higher costs. A dynamic strategy that allows the trader to adjust her placement strategy at intermediate times offers increased flexibility and resilience against such unexpected order flow deviations. The second model, proposed by Cartea and Jaimungal [2015] [5], provides such a dynamic solution and frames the problem as a stochastic optimal stopping and control problem. We extend this model to include mid-price drift and a general running inventory penalty, and formulate a recursive expression for the general optimal strategy for an inventory of any size. The static solution gives an accurate, efficient and robust indication of the optimal allocation for larger inventories and longer trading windows. The dynamic solution, on the other hand, is more effective at liquidating (or acquiring) smaller inventories in shorter time frames at an optimal price, by providing a precise, adaptive strategy in volatile market conditions. Overall, this thesis improves our understanding of the Optimal Placement Problem by analytically deriving its solution under two distinct model setups: the static model of [15] and the dynamic model of [5]. In the static approach, we find the optimal allocation switches from limit orders at one price-level to the next at distinct critical points. This provides an intuitive and broadly applicable rule of thumb for practical implementation, leading to lower expected costs across the board. The optimal strategy, derived from the dynamic model, leads to higher average earnings per share than benchmark models like the Time Weighted Average Price, the solution only considering limit orders and the solution found in [5], by taking into account market orders and possible mid-price drift. Future extensions, such as testing on different arrival distributions, depth discretisation, parameter calibration and using heuristic methods to improve computational speed, could further assess the practical viability and performance trade-offs of these strategies in real-world trading systems. ... Read more

This thesis investigates efficient Monte Carlo methods for estimating the 99.9% Value-at-Risk of
concentrated credit portfolios modelled through a normal copula framework. Crude Monte Carlo
simulation is inefficient when estimating extreme loss levels. To address this inefficiency, variance
reduction techniques are applied, including importance sampling and its adaptive variant. This thesis
provides empirical evidence that these techniques make extreme quantile estimation computationally
feasible in a realistic portfolio credit risk setting.
Multiple methods from the literature are reviewed to approach an appropriate importance sampling
proposal. Bernoulli tilting conditional on the common factors is an effective method when obligors
are weakly correlated. However, when large losses are mainly driven by common factors in the credit
portfolio, shifting their means turns out to be more effective. This has to be done with care, since an
improper shift may increase the variance. To this end, a deterministic method that approaches the mode
of the zero-variance distribution is discussed. Furthermore, adaptive importance sampling is studied,
which aims to minimize the variance directly by iteratively updating the shift based on past samples.
This thesis introduces a method that uses the generalized Poisson–Binomial distribution, together with
an inverse Fourier transform, to approximate the zero-variance distribution nearly exactly for simple
portfolio cases.
A deterministic mean-shifted importance sampling (M-IS) and an adaptive importance sampling
(AIS) approach are applied on stylized portfolios. These portfolios are constructed such that they mimic
real-world conditions. The M-IS method achieves an estimated variance reduction factor of 175 on a
large portfolio with 20 000 obligors. Performance on the actual Triodos Bank portfolio delivered similar
performance, but detailed results are withheld for reasons of confidentiality. For a moderately sized
portfolio consisting of 1 000 obligors, M-IS is no more effective than crude Monte Carlo because of the
higher impact of idiosyncratic concentrations. In this case, AIS finds a better balance between the
various kinds of concentrations. With conservative parameters, AIS achieves an estimated variance
reduction factor of 5 on the moderately sized portfolio. Bernoulli tilting could further increase the
variance reduction in these portfolio scenarios. Moreover, as the number of samples increases, AIS further
reduces variance. Finally, this thesis investigates how to construct asymptotic confidence intervals for
the extreme quantile estimates of these stylized portfolios and demonstrates via experiments that they
exhibit asymptotic normal behaviour despite the discreteness of the loss distribution. ... Read more

Energy markets are characterized by unique features such as seasonality, mean reversion, and sudden price spikes, which make the valuation of related derivatives considerably more challenging than in traditional financial markets. This thesis investigates the use of the COS method, a Fourier-based numerical technique, for the efficient valuation of energy derivatives within a Markov-modulated framework.

The study begins with energy quanto options, whose payoff depends on two correlated underlyings incorporating jumps and regime-switching dynamics. By deriving the characteristic functions for two benchmark models and implementing the COS method, the results demonstrate high accuracy and significant computational speed-ups compared to FFT- and Monte Carlo-based benchmarks.

The research work then extends to electricity storage contracts, which feature early-exercise opportunities and operational constraints. In line with the methodology presented by [1], this section replicates their integration of the COS method into a dynamic programming framework to evaluate the option values across multiple contract types and volatility regimes. The obtained prices fall within the confidence intervals of the LSMC benchmark, confirming the robustness of the COS approach in handling path-dependent and constrained problems.

Finally, the pricing framework is generalized to electricity storage under a two-state Markov-modulated model, to better capture the behavior of electricity prices. The extended COS-based algorithm accurately reproduces complex probability densities and achieves stable convergence of the prices while maintaining high computational efficiency even under this more complex setting.

In conclusion, this thesis demonstrates that the COS method is a powerful and computationally efficient alternative to stochastic simulation methods for pricing energy derivatives. It is capable of handling jump dynamics, regime switching, early-exercise features and operational constraints, highlighting its potential for broader applications in energy finance.

[1] Boris C Boonstra and Cornelis W Oosterlee. “Valuation of electricity storage contracts using the COS method”. In: Applied Mathematics and Computation 410 (2021), p. 126416 ... Read more

Financial crime is growing in scale and complexity, increasing the need for robust monitoring. Variational Autoencoders offer compact representations of transaction behavior that can support anomaly detection and related use cases in this domain, yet their adoption remains limited due to the lack of interpretability of their latent spaces.

To address this challenge, we formalize interpretability by quantifying the relationship between latent dimensions and aspects of transaction behavior, using explicitness, modularity, and compactness as complementary metrics. Based on these measures, we develop a framework and apply it in controlled experiments that vary regularization strength and latent dimensionality, in order to understand their influence on the structure and interpretability of latent spaces.

We find that weak regularization preserves detail but compromises modularity and compactness, intermediate values progressively improve these properties, until strong regularization forces the latent space to collapse. Latent dimensionality further shapes both the level of detail preserved and the conditions under which meaningful structure emerges. The results show that there is no universal optimum, but rather parameter regimes suited to different priorities. The framework offers a systematic way to align model design with these priorities, providing both empirical insights and a general tool to support the adoption of VAEs in financial crime detection. ... Read more

This study explores the application of risk-sensitive Reinforcement Learning (RL) in portfolio optimization, aiming to integrate asset pricing and portfolio construction into a unified, end-to-end RL framework. While RL has shown promise in various domains, its traditional risk-neutral approach is unsuitable for financial contexts where risk sensitivity is crucial. This research focuses on risk-sensitive RL methods that incorporate different risk measures to manage uncertainty and volatility in financial markets better. The project extends existing RL techniques by adapting the cross-sectional approach to risk-sensitive settings and introducing new variants like PPO-CVaR and PPO-Expectile for portfolio management. A comparative study of these methods is conducted to assess their performance with real market data and simulated environments. The research addresses key questions related to how different risk measures impact learned portfolio strategies, the influence of risk appetite on decision-making, and the performance gap between simulated and real market data. The findings aim to provide insights for practitioners looking to implement risk-sensitive RL in financial asset management. ... Read more

This thesis addresses the portfolio allocation problem within a financial market featuring one riskless asset and a risky asset exhibiting rough Bergomi volatility. The objective is to maximize the expected utility of terminal wealth with respect to power utility. The volatility process in the model is driven by fractional Brownian motion and does not fit within the Markovian or semimartingale frameworks. To address this issue, we explore Markovian approximations for fractional processes and apply them to the rough Bergomi model, resulting in a multi-factor stochastic volatility model. This approach facilitates the development of a practical simulation scheme employing Gaussian quadrature and Cholesky decomposition, and allows us to address the portfolio optimization problem within a Markovian context. We solve the optimization problem using the Hamilton-Jacobi-Bellman equation, deriving an implicit solution for the case where volatility and stock return are driven by correlated Brownian motions, and providing an explicit solution for the case where they are uncorrelated. The validity of these results is further confirmed through a numerical study. ... Read more

Blockchain-based payment systems typically assume a synchronous communication network and a limited workload to confirm transactions within a bounded timeframe. These assumptions make such systems less effective in scenarios where reliable network access is not guaranteed.
Offline payment systems are designed to allow users to register offline transactions and ensure their execution once network access is restored. However, these methods often rely on specialized hardware to remain secure and tamper-proof, preventing double-spending and invalid transactions.

In this work, we introduce a novel offline payment system that does not rely on trusted hardware. Our system enables users to determine transaction fees and accept offline payments based on the trustworthiness of their peers. Users can decide whether to accept offline payments from each other based on the information our system provides.

Our system employs a smart contract to manage transactions on a blockchain for its online component. We implemented the online part of our system as an Ethereum Solidity smart contract and deployed it on the Sepolia testnet. Our performance evaluation demonstrates our system’s practicality, handling 68 Transactions Per Second (TPS) with a confirmation latency of 12 seconds on the Sepolia testnet. The system’s scalability can improve with advanced layer-1 or layer-2 blockchain solutions, enhancing throughput, decreasing latency, and reducing fees. ... Read more

In this thesis, we aim to improve the application of deep reinforcement learning in portfo- lio optimization. Reinforcement learning has in recent years been applied to a wide range of problems, from games to control systems in the physical world and also to finance. While reinforcement learning has shown success in simulated environments (e.g. matching or exceeding human performance in games), its adoption in practical applications (non- simulated environments) has lagged. Dulac-Arnold et al. [2019] suggest this is caused by a discrepancy in the experimental set-up in research and the conditions in practice. Specifically, they present a list of challenges that make the application of reinforcement learning in real-world settings more difficult. One of these challenges is non-stationary environments, which is common in financial environments. It is a challenge since, given an observed state, the optimal action may not always be the same as it may change over time due to non-stationarity. Therefore, more specifically, the goal of this thesis is to overcome the challenge of non-stationarity in the application of reinforcement learning to portfolio optimization. In this thesis, we use reinforced deep Markov models (RDMM) introduced by Ferreira [2020] (applied to an optimal execution problem and later used by Cartea et al. [2021] for statistical arbitrage on simulated price movements of an FX triplet) for its data efficiency and ability to handle complex environments. RDMM involve a partially observ- able Markov decision process (POMDP) which is also the setting used by Xie et al. [2021] to model non-stationarity in reinforcement learning. We extend RDMM to incorporate non-stationarity, using the framework suggested by Xie et al. [2021], and apply it to port- folio optimization. Our implementation is sample efficient which allows for quick learning, by doing this we attempt to improve on another challenge of reinforcement learning — i.e. sample-inefficiency [Dulac-Arnold et al., 2019]. Moreover, our implementation can handle continuous state and action spaces.
We compare the performance of our algorithms to classical portfolio optimization tech- niques such as Mean-Variance (MV) and Equal Risk Contribution (ERC), and to popular reinforcement learning techniques such as Deep Deterministic Policy Gradient (DDPG) and Soft Actor-Critic (SAC). We observe our implementation has higher sample-efficiency compared DDPG and SAC, and higher cumulative returns on the test set compared to MV, ERC, DDPG, and SAC.
... Read more

Implied volatility surfaces (IVS) are essential for option pricing and risk management. Recently, generative deep learning models, such as the Denoising Diffusion Probabilistic Model (DDPM), have gained popularity for generating IVS. However, these machine-generated surfaces do not necessarily meet arbitrage-free constraints, e.g., calendar spread and butterfly arbitrage.
This thesis addresses this limitation by integrating arbitrage-free constraints into the DDPM generation process. We introduce a classifier specifically designed to detect violations of arbitrage-free conditions. During the DDPM’s iterative generation process, the classifier guides the formation of the IVS at each step, effectively minimizing potential arbitrage opportunities. To evaluate the effectiveness of our approach, we compare the extent of arbitrage violations in IVS generated by the standard DDPM with those produced by our enhanced DDPM-Classifier model. The results demonstrate that the DDPM-Classifier significantly reduces arbitrage opportunities and improves the quality of IVS.
... Read more

Insurers are required to have buffers to be able to meet financial obligations that result from their portfolios, which are determined using a cash flow model. The input of such a cash flow model consists among of things, of two mortality tables and the portfolio of an insurer. Mortality rates are simulated using the Lee-Carter model. These simulated rates are in turn used to simulate the cash flow corresponding to a portfolio. This results in one possibility of incoming and outgoing money over a period of time. Lots of simulations are required to get a reliable estimate for the future cash flow which is (depending on the number of simulations) computationally heavy and therefore time consuming. The calculation time is decreased by applying an extreme gradient boosting (XGBoost) machine learning method in which cash flows are considered target variables and the mortality tables are considered features of the model. The trained XGBoost model can predict the cash flows based on the mortality tables. The standard XGBoost model is extended to a multi-target regression model which is able to predict multiple target variables at once. This XGBoost model reduces the computation time and ensures that 99.5% of the predictions deviates within either 1% or 0.5% of the observed values. XGBoost gives a good method of determining a reliable estimate of the future cash flow. ... Read more

The computation of multivariate expectations is a common task in various fields related to probability theory. This thesis aims to develop a generic and efficient solver for multivariate expectation problems, with a focus on its application in the field of quantitative finance, specifically for the quantification of Counterparty Credit Risk (CCR).

The proposed COS-CPD method utilizes the COS method to recover the exposure distribution by its Fourier-cosine series expansion, from which measures such as the PFE and EE can be obtained. The key insight is that the corresponding Fourier coefficients are readily available from the characteristic function, which can be solved using numerical integration methods. However, the efficiency of standard quadrature rules is limited to only a few risk factors, as the dimension of integration is determined by the number of risk factors involved.

To address this limitation, the COS-CPD method reduces the dimension of integration of the characteristic function through two steps. Firstly, the joint density function of the risk factors in the characteristic function is replaced by a dimension-reduced Fourier-cosine series expansion, which is obtained through CPD. With CPD, the computational complexity of computing the Fourier coefficient tensor is reduced to a linear growth with respect to the number of dimensions. Secondly, the portfolio is divided into segments that share the same risk factors. These two steps reduces the evaluation of the characteristic function to the calculation of only one- and two-dimensional integrals, which are solved by the Clenshaw-Curtis quadrature rule. As a result, the COS-CPD method is suitable for portfolios with more than three risk factors.

Numerical comparisons of the COS-CPD method and Monte Carlo (MC) method are made for netting-set PFE and EE profiles of multiple derivative portfolios up to five risk factors. For similar accuracy levels, the COS-CPD method greatly outperforms the Monte Carlo method in computation time. This difference increases for larger portfolios, which makes the COS-CPD method a much more efficient alternative for the MC method, especially for large portfolios.

Furthermore, the COS-CPD method is applied in the context of multi-asset option pricing. A six-dimensional basket option is considered, and the results are compared to a recently developed sparse grid method. The comparison shows that the COS-CPD method outperforms the sparse grid method in both accuracy and computation time. Moreover, the COS-CPD method allows the computation of the option value for multiple strike prices simultaneously, with no significant additional computational cost. ... Read more

In this research a new method for pricing continuous Arithmetic averaged Asian options is proposed. The computation is based on Fourier-cosine expansion, namely the COS method. Therefore, we derive the characteristic function of Integrated Geometric Brownian Motion based on Bougerol's identity.

Extensive numerical error analysis on the CDF recovery of IGBM and the option prices is performed. Via numerical tests, the convergence of errors using our new method has been proved. We are able to price continuous Arithmetic averaged Asian options with a minimal error of order 10^-2, and a maximum precision of order 10^-5 within seconds.
... Read more

This thesis investigates the estimation of option-implied probability density functions for inflation using inflation options, focusing not only on the expected value but the whole distribution. The aim is to identify the most effective method for measuring the market expectation of future inflation. The research explores both parametric and non-parametric approaches for deriving these density functions from inflation option prices. Methodologies include parametric models such as expansion, generalised distribution, and mixture methods, alongside non-parametric techniques using Breeden and Litzenberger’s result, such as curve-fitting and kernel methods. Implementing these methods involved analysing inflation option data sourced from the BVOL Bloomberg database, specifically for Harmonised Index of Consumer Prices excluding Tobacco (HICPxT) options from January 1, 2013. The study employed Shimko’s method, various spline methods, the Delta method, and Kernel method, assessing their effectiveness and challenges. Results reveal diverse implications for each method. Visual comparisons showcase the varying outcomes of the implemented methods, Likelihood-based assessments present a more numerical approach benefiting the Delta and Kernel methods due to higher scores and fewer negative likelihoods. Conclusions suggest that while multiple methods offer insights into inflation prediction, the Kernel method shows promise in its reliability while the Delta method scores highest in the numerical methods. However, challenges in accurately modelling extreme values and tail behaviours persist across methodologies. Recommendations for further research involve addressing these limitations and exploring enhancements to refine inflation prediction models.F ... Read more

The global push for renewable energy faces challenges due to the unpredictable and inconsistent nature of wind and solar sources. These inherent characteristics of renewable energy sources add volatility to the electricity markets. In response, electrical energy storage (EES) emerges as a solution for maintaining grid flexibility, stability, and reliability. Therefore, it is important to understand the potential interdependence of the wholesale electricity markets and the EESs.
This thesis focuses on short-term EES scheduling, comparing pumped hydropower storage (PHS), compressed air energy storage (CAES), and battery energy storage systems (BESS). This thesis aims to optimize EES scheduling, which includes charging and discharging actions, in the intraday electricity market, considering market price uncertainties. Storage decisions are optimized for one day (24 hours) from the perspective of the storage owner, and its objective is to maximize its profit through market operations. The research introduces a two-stage stochastic programming approach with a rolling horizon method (SORH) to adapt to changing conditions of the intraday market throughout the day.
The results of SORH, its deterministic counterpart (DORH), and simple deterministic optimization (DO) are compared by implementing a case study organized in four typical days based on trading data from the German electricity market. SORH consistently outperforms DORH and DO and is a suitable optimization strategy. SORH reaches on average 72 percentage of the theoretical optimum, where all prices are known in advance. Moreover, SORH offers opportunities for speculative trading using the storage as an option rather than only physically operating the storage. For a practical application of the model, future research could explore methods to match the current day with representative typical days to construct relevant price scenarios. ... Read more

Barrier options, although highly liquid financial derivatives, present notable pricing challenges. In this thesis, we present a novel pricing approach for valuing continuously-monitored knock-out barrier options within the framework of stochastic volatility models.

The underlying process is firstly modelled under geometric Brownian motion and, subsequently, under Heston's stochastic volatility model. A key insight is that the value of a barrier option can be expressed as a single-dimensional integral, whereby the integrand involves the so-called survival density function, which captures the barrier-brea-ching information. Therefore, the option can be valued using the one-dimensional COS method for European options, once the Fourier series coefficients of the survival density are obtained.

The coefficients of the sine series expansion of the survival density function are, in fact, a continuous function, which is closely related to the characteristic function of the density. This motivates us to directly recover that function, which we refer to as the target function herewith, by selecting an appropriate series expansion for it. Thereafter, we insert this series expansion into the partial differential equation (PDE) that the target function should satisfy, which can be derived from the pricing PDE. This results in a linear system, solving which we obtain the coefficients needed to reconstruct the target function. Notably, this approach is particularly advantageous when the reference values of option prices are limited or unavailable, as it relies solely on the PDE to calibrate the series coefficients.

Our choice of series expansion is driven by the need for precise global and local approximations. Our research shows that a proper expansion for the target function can be built up from integrating a two-dimensional Fourier series of its first derivative with respect to time, marking our second pivotal insight. That results in a trigonometric expansion that significantly enhances the accuracy compared to a direct Fourier series expansion on the target function. Finally, our third pivotal insight: applying a change of variables further improves error convergence.

Extensive testing results suggest that, for similar accuracy levels, our approach greatly outperforms Monte Carlo simulations in terms of computation time. It also demonstrates superior computational efficiency and accuracy compared to other advanced numerical methods in the existing literature.
The benefits of this method become even more prominent when pricing a large number of options simultaneously.

Numerical tests reveal algebraic convergence for the series expansion reconstruction. For the option price, theoretical error analysis aligns with our findings, also predicting algebraic convergence. ... Read more