This thesis contains three essays on mathematical finance. The first discusses approximation methods for pricing swaptions based on moment expansions with multi-factor affine jump-diffusion models in Chapter 2. Two methods are examined. One is based on a Gram-Charlier expansion and the other is based on a generalized Edgeworth expansion. The density function of the forward swap is replaced with more tractable functions and their moments. Numerical simulations are conducted to confirm their accuracy. Models with a Gaussian-type or CIR-type volatility with an exponentially, normally or truncated normally distributed jump size are employed. The second essay proposes a framework to study the spot and forward relationship in carbon allowances markets and the third deals with the same problem in a different setting. The framework is based on the no-arbitrage principle. The value of the spot price depends on two underlying variables: the forward price and the net position of the zone defined as the difference between allocated carbon allowances and emissions. In Chapter 3, the net position of the market is modelled as a Markov chain and in Chapter 4, as a linear diffusion. Two kinds of filtration used in pricing are considered: complete information where market participants observe both processes continuously and incomplete information where they observe the forward price continuously and the net position of the zone periodically. Pricing problems occur in an incomplete market, since the net position of the zone is not tradable. A locally risk-minimization approach is used to fix the martingale measure. Under the complete information setting, The analytical spot price is obtained. Under the incomplete information setting, a filtered process is used for pricing, leading to the use of filtering theory. The spot price is computed numerically. Chapter 5 concludes.

The excursion time of a Levy process measures the time it spends continuously below or above a given barrier. This thesis contains five papers dealing with the excursions of different Levy processes and their applications in mathematical finance and insurance. Each of the five papers is presented in one of the chapters of this thesis starting from Chapter 2. In Chapter 2 the excursions of a Brownian motion with drift below or above a given barrier are studied by using a two-state semi-Markov model. Based on the results single barrier two-sided Parisian options are studied and the explicit expressions for the Laplace transforms of their price formulae are given. In Chapter 3 the excursion time of a Brownian motion with drift outside a corridor is considered by using a four-state semi-Markov model. The results are used to obtain the explicit expressions for the Laplace transforms of the prices of the double barrier Parisian options. In Chapter 4 Parisian corridor options are introduced and priced by using the results of the excursion time of a Brownian motion with drift inside a corridor. In Chapter 5 the main focus is the excursions of a Levy process with negative exponential jumps below a given barrier. Based on the results, a Parisian option whose underlying asset price follows this process is priced, as well as a Parisian type digital option. This is the first ever attempt to price Parisian options involving jump processes. Furthermore, the concept of ruin in risk theory is extended to the Parisian type of ruin. In Chapter 6 the excursions of a risk surplus process with a more general claim distribution are considered. For the processes without initial reserve, the Parisian ruin probability in an infinite time horizon is calculated. For the positive initial reserve case, only the asymptotic form can be obtained for very large initial reserve and small claim distributions.

This thesis provides a novel empirical treatment of the dynamics of financial market risk and liquidity, two very important areas both for financial research as well as to practitioners in the financial markets: We devise empirical non-linear time series models of the two concepts that specifically take into account 'explosive', self-reinforcing dynamic patterns. While 'conventional' empirical models are often 'linear' and tend to neglect these effects, real-life evidence such as e.g. the 1987 crash, the large stock market drops on February 27th, 2007 or the huge losses posted by investment banks and hedge funds during July and August 2007, suggest that such an approach is warranted: In the first part of the thesis we extend a time series model of Value-at-Risk (VaR) with non-linear multiplicative features and endogenous regime thresholds. When estimated with a Markov Chain Monte Carlo (MCMC) method against real data, the resulting 'Self- Exciting Threshold CAViaR' (Conditional Autoregressive Value-at- Risk) model is able to detect trigger thresholds for explosive market risk as well as the scale of such a possible expansion in risk. The second part of the thesis is dedicated to the 'Conditional Autoregressive Liquidity' (CARL) model, a multiplicative time series approach to the empirical modelling of market liquidity. The newly con-ceptualised model is capable of picking up self-reinforcing dynamics, i.e. autoregressive patterns in liquidity, which is in accordance with theoretical research on the topic. Moreover, by incorporating a multidimensional liquidity proxy, the model CARL is explicitly designed to take into account the fact that liquidity is a concept with many facets, unlike other empirical treatments that often view liquidity only along a single dimension (e.g. the bid-ask spread, volume, trade duration). In this thesis, we demonstrate the empirical versatility of the model using both fixed interval data (daily and weekly) as well as tick-by-tick intraday data, for which we propose a filtering technique in order to be able to use the model in such a data environment. We note that the model is able to pick up autocorrelation structures in liquidity rather well and find the forecast performance very encouraging for practical use.

With the introduction of the Solvency II regulatory framework, insurers face the challenge of managing the risk arising from selling unit-linked products on the market. In this thesis two approaches to this problem are considered: Firstly, an insurer could project the value of their liabilities to some future time using Monte Carlo simulation in order to reserve adequate capital to cover these with a high level of confidence. However, the complex nature of many liabilities means that valuation is a task requiring further simulation. The resulting `nested-simulation' is computationally inefficient and a regression-based approximation technique known as least-squares Monte Carlo (LSMC) simulation is a possible solution. In this thesis, the problem of configuring the LSMC method to efficiently project complex insurance liabilities is considered. The findings are illustrated by applying the technique to a realistic unit-linked life insurance product. Secondly, an insurer could implement a hedging strategy to mitigate their exposure from such products. This requires the calculation of market risk sensitivities (or `Greeks'). For complex, path-dependent liabilities, these sensitivities are typically estimated using simulation. Standard practice is to use a `bump and revalue' method. As well as requiring multiple valuations, this approach can be unreliable for higher order Greeks. In this thesis some alternative estimators are developed. These are implemented for a realistic unit-linked life insurance product within an advanced economic scenario generator model, incorporating stochastic interest rates and stochastic equity volatility.

Freud maintained that psychoanalysis was not only to be a clinical discourse of the interpersonal and the subjective, however dynamic and necessary therapeutically, but that its principles could be taken from those contexts and applied to wider global, societal, and cultural issues. Since the 1960s, financial corruption has grown into what has become a serious and entrenched problem, albeit this is seldom addressed in psychoanalytic terms. The ultimate aim of this research study is to enquire into the psychoanalytic roots of financial corruption and to ask whether it is possible to attempt a psychoanalytic investigation and explanation of acts of financial corruption committed in particular given circumstances, such as those existing in a developing, emerging, or transitional society, more precisely in the historical period of 1960s Africa. To address this, particular attention will be paid to writings pertaining to Nigeria in its period of decolonisation, when the issue of financial corruption began gain international attention. However, a series of initial steps are necessary in order to approach these issues. In the line of argumentation that this thesis will follow, two main aspects of financial corruption will be examined in depth: firstly, ‘money’, in its multi-layered significance and secondly, the internal desires of the individual with respect to ‘money’ and the external social environment within which this individual is located. Thus, first of all this dissertation will begin by asking two interrelated questions. What has been a psychoanalytic theory on ‘money’? And how did psychoanalysis determine the role that ‘money’ played in the unconscious? The first three chapters of the thesis are devoted to answering these and following a survey of the field, return to pre-World War Two classical psychoanalytic theoretical writings, the correspondence of pioneering psychoanalysts and Ferenczi’s Clinical Diary, in order to arrive at a starting point for a further examination of psychoanalysis and financial corruption. Centrally, the status of the ‘anal theory of money’, derived from Freud’s indicative papers on anal erotism and elaborated by Ferenczi and others, will be put to the test. Close readings of classical psychoanalytic writings led to the central argument of this thesis: that there arises the possibility of contesting the enshrined status of the relation of faeces to ‘money’ on the grounds of this not being a truly unconscious symbolic relation, as ‘money’ is a construct that has to be taught. It is argued that the theorists of the classical period did not do justice to the possible connections between orality and ‘money’ – despite strong pointers within their writings to the oral developmental stage. The final chapters attempt to close a gap by setting out an alternative hypothesis to anality based on the unconscious and orality. Karl Abraham’s work provides a key theoretical scaffolding in this respect. An oral hypothesis, taking seriously the actual and fantasmatic aspects of hunger and greed, is argued to be important for the psychoanalytic understanding of the unconscious motivations and impulses that could underlie financial corruption. With recourse to both the anal theory and the alternative oral hypothesis, which taken together enable a deeper analysis, a reading is undertaken of selected texts on 1960s’ corruption in order to explore the question of what could have been taking place psychoanalytically and to lay the building blocks towards a psychoanalytic theory of financial corruption.

This thesis is concerned with the modeling of financial time series data. It introduces to the economics literature a set of techniques for this purpose that are rooted in engineering and physics, but almost unheard of in economics. The key feature of these techniques is that they combine the available information in the time and frequency domains simultaneously, making it possible to enjoy the advantages of both forms of analysis. The thesis is divided into three sections. First, after briefly outlining the Fourier methods, a more exible technique that allows for the study of time-scale dependent phenomena (motivated from a discussion on Heisenberg's uncertainty principle) namely Wavelet method is defined. A complete account of discrete and continuous wavelet transformations, and wavelet variation is provided and the advantages of wavelet-multiresolution analysis over Fourier methods are demonstrated. In the second section, the statistical properties of financial returns at 1-day, 5-day and 10-day sampling intervals are studied using S&P500 index for over a decade, and the links between dependence properties of financial returns at lower sampling frequencies are explored. The concepts of temporal aggregation and skip sampling are discussed and the effects of temporal aggregation on long range dependent time series are theoretically outlined and then tested through simulations and empirically via S&P500. In the third section, the variation of two years of five-minute GBP/USD exchange rate is analysed and the notion of realised variation is explored. The characteristics of the intraday data at different sampling frequencies (5-minute, 30-minute, 60-minute, 10-hour, 1-day, and 5-day) are compared with each other and filtered out from seasonalities using the wavelet multiscaling technique. We find that temporal aggregation does not change the decay rate of autocorrelation functions of long-memory data of certain frequencies, however the level at which the autocorrelation functions start from move upward for daily data. This thesis adds to the literature by outlining and comparing the effects of aggregation between daily and intra-daily frequencies for the realised variances, which to our knowledge is a first. The effect temporal aggregation has on daily data is different from intra-daily data, and we provide three reasons why this might be. First, at higher frequencies strong periodocities distort the autocorrelation functions which could bring down the decay rate and mask the long memory feature of the data. Second, the choice of realised variance is crucial in this matter and different functions can result in contradictory outcomes. Third, as the order of aggregation increases the decay rate does not depend on the order of the aggregation.

The global crisis of 2008 challenged the functioning of the financial markets. In the aftershock era numerous repercussions were felt throughout the world, resulting from a plethora of cross-border and cross-entity interdependencies. An initially systemic banking crunch – where cash strapped banks stopped lending, liquidity abruptly dried up, and credit conditions deteriorated – metastasized into a sovereign debt crisis in the euro area which devastated public finances and provoked higher sovereign default risk. Motivated by the intensity, the magnitude and the speed with which shocks propagate in the entire financial system, this thesis presents five essays on applied financial econometrics and financial networks which examine, model and investigate: i) systemic risk and the resilience of the banking industry via employing financial networks and entropy maximization; ii) the role of credit derivatives and the two-way feedback ramification, triggered by government interventions, on financial stability; iii) the symptoms of acute liquidity withdrawal in emerging markets; iv) a Bayesian three state switching regime approach to price financial assets; v) tail risk management with portfolio asymmetries and asset monotonic volatility. More precisely, in Chapter three the Maximum Entropy method is employed to capture systemic risk, the resilience of the banking system in Europe and the propagation of financial contagion in a dynamic financial network framework. As conditions deteriorate, three channels (interbank loan, sovereign, asset-backed loan) trigger severe direct and indirect losses and cascades of defaults, whilst the dominance of the sovereign credit risk channel amplifies, as the primary source of financial contagion in the banking network. Systemic risk within the northern euro area banking system is less apparent, while the southern euro area is more prone and susceptible to bank failures. By modelling the contagion path the results demonstrate that the euro area banking system insists to be markedly vulnerable and conducive to systemic risks, implying that there is a need for additional policies to increase the resilience of the sector. Moreover, the thesis develops a Markov-Switching Bayesian Vector Autoregression (MSBVAR) model in Chapter four to study the two-way feedback hypothesis between credit default swaps and the role of government interventions on financial stability. The results demonstrate that a rise in sovereign debt due to the countercyclical discretionary fiscal policy measures, is perceived by stock markets as a catastrophe on economic growth prospects. Interestingly, government interventions in the banking sector deteriorate the credit risk of sovereign debt, whilst higher risk premium required by investors for holding riskier government bonds depresses the sovereign debt market, and attenuates the collateral value of loans, leading to bank retrenchment. The ensuing two-way banking-fiscal feedback loop indicates that government interventions do not necessarily stabilize the banking sector. Furthermore, the thesis employs several copula functions and the Extreme Value theory in Chapter five, to estimate and quantify joint downside risks and the transmission of shocks in emerging currencies, evolving from domestic emerging stock markets, liquidity (banks’ credit default swaps), credit risk (Volatility Index) and growth (commodity prices) channels. The models measure the time-varying shock spillover intensities to ascertain a significant increase in cross-asset linkages during periods of high volatility which is over and above any expected economic fundamentals, providing strong evidence of asymmetric investor induced contagion, triggered by cross asset rebalancing. The critical role of the credit crisis is amplified, as the beginning of an important reassessment of emerging market currencies which lead to changes in the dependence structure, a revaluation and recalibration of their risk characteristics. Additionally, the thesis employs a Markov-switching vector autoregression (MSVAR) model to capture the transmission of shocks from stock, commodity and credit markets to four shipping indices in Chapter six. By estimating the impulse response functions (IRF), the model identifies the episodes and documents the existence of three regimes and directional spillovers between low, intermediate and high volatility regimes. The estimation results obtained using a Gibbs sampler indicate that the S&P 500, the S&P GSCI, Banks’ CDS and the VIX behave as channels which transform and spread the risk to the shipping market with the propagation of shocks. Interestingly, higher risk premium that is required by investors for holding financial assets depresses the shipping market substantially. Finally, several copula functions are employed to model tail dependence during periods of extreme, asset monotonic volatility and reverse portfolio asymmetry conditions between shipping, stock, commodity and credit markets in Chapter seven. The findings reveal that shocks in the shipping market coincide with dramatic changes in other markets and document the existence of extreme co-movements during severe financial conditions. Lower tail dependence exceeds conditional upper tail dependence, indicating that during periods of economic turbulence, dependence increases and the crisis spreads in a domino fashion, causing asymmetric contagion which advances during market downturns. In the post crisis period the level of dependence drops systematically and shipping assets become more pronouncedly heavy-tailed in downward moves. According to the estimated results accelerated decreases in commodities and prompt variations in volatility, provoke accelerated decreases and function as a barometer of shipping market fluctuations. The global financial crisis has profoundly shaped modern finance. This thesis examines the prominent role of the crisis in financial markets, provides important implications for understanding systemic and liquidity risk, for analysing policies designed to mitigate financial contagion, and for capturing the fluctuations of emerging currencies and financial assets during distress economic conditions.

The role of the financial mathematician is to find solutions to problems in finance through the application of mathematical theory. The motivation for this work is specification of models to accurately describe the price evolution of a risky asset, a risky asset is for example a security traded on a financial market such as a stock, currency or benchmark index. This thesis makes contributions in two classes of models, namely activity time models and integer valued models, by the discovery of new real valued and integer valued stochastic processes. In both model frameworks applications to option pricing are considered.

This thesis contains three essays exploring the asset pricing implications of asymmetric information and trading constraints. Chapter 1 studies how short-sale constraints affect the informational efficiency of market prices and the link between prices and economic activity. I show that under short-sale constraints security prices contain less information. However, short-sale constraints increase the informativeness of prices to some agents who learn about the quality of an investment opportunity from market prices and have additional private information. This, in turn, can lead to higher allocative efficiency in the real economy. My result thus implies that the decrease in average informativeness due to short-sale constraints can be more than compensated by an increase in informativeness to some agents. In Chapter 2, I develop an equilibrium model of strategic arbitrage under wealth constraints. Arbitrageurs optimally invest into a fundamentally riskless arbitrage opportunity, but if their capital does not fully cover losses, they are forced to close their positions. Strategic arbitrageurs with price impact take this constraint into account and try to induce the fire sales of others by manipulating prices. I show that if traders have similar proportions of their capital invested in the arbitrage opportunity, they behave cooperatively. However, if the proportions are very different, the arbitrageur who is less invested predates on the other. The presence of other traders thus creates predatory risk, and arbitrageurs might be reluctant to take large positions in the arbitrage opportunity in the first place, leading to an initially slow convergence of prices. Chapter 3 (joint with Dömötör Pálvölgyi) studies the uniqueness of equilibrium in a textbook noisy rational expectations economy model a la Grossman and Stiglitz (1980). We provide a very simple proof to show that the unique linear equilibrium of their model is the unique equilibrium when allowing for any continuous price function, linear or not. We also provide an algorithm to create a (non-continuous) equilibrium price that is different from the Grossman-Stiglitz price.

Sparse Weighted Norm Minimum Variance Portfolio. In this paper, I propose a weighted L1 and squared L2 norm penalty in portfolio optimization to improve the portfolio performance as the number of available assets N goes large. I show that under certain conditions, the realized risk of the portfolio obtained from this strategy will asymptotically be less than that of some benchmark portfolios with high probability. An intuitive interpretation for why including a fewer number of assets may be beneficial in the high dimensional situation is built on a constraint between sparsity of the optimal weight vector and the realized risk. The theoretical results also imply that the penalty parameters for the weighted norm penalty can be specified as a function of N and sample size n. An efficient coordinate-wise descent type algorithm is then introduced to solve the penalized weighted norm portfolio optimization problem. I find performances of the weighted norm strategy dominate other benchmarks for the case of Fama-French 100 size and book to market ratio portfolios, but are mixed for the case of individual stocks. Several novel alternative penalties are also proposed, and their performances are shown to be comparable to the weighted norm strategy. Bond Variance Risk Premia (Joint work with Philippe Mueller and Andrea Vedolin). Using data from 1983 to 2010, we propose a new fear measure for Treasury markets, akin to the VIX for equities, labeled TIV. We show that TIV explains one third of the time variation in funding liquidity and that the spread between the VIX and TIV captures flight to quality. We then construct Treasury bond variance risk premia as the difference between the implied variance and an expected variance estimate using autoregressive models. Bond variance risk premia display pronounced spikes during crisis periods. We show that variance risk premia encompass a broad spectrum of macroeconomic uncertainty. Uncertainty about the nominal and the real side of the economy increase variance risk premia but uncertainty about monetary policy has a strongly negative effect. We document that bond variance risk premia predict excess returns on Treasuries, stocks, corporate bonds and mortgage-backed securities, both in-sample and out-of-sample. Furthermore, this predictability is not subsumed by other standard predictors. Testing Jumps via False Discovery Rate Control. Many recently developed nonparametric jump tests can be viewed as multiple hypothesis testing problems. For such multiple hypothesis tests, it is well known that controlling type I error often unavoidably makes a large proportion of erroneous rejections, and such situation becomes even worse when the jump occurrence is a rare event. To obtain more reliable results, we aim to control the false discovery rate (FDR), an efficient compound error measure for erroneous rejections in multiple testing problems. We perform the test via a nonparametric statistic proposed by Barndorff-Nielsen and Shephard (2006), and control the FDR with a procedure proposed by Benjamini and Hochberg (1995). We provide asymptotical results for the FDR control. From simulations, we examine relevant theoretical results and demonstrate the advantages of controlling FDR. The hybrid approach is then applied to empirical analysis on two benchmark stock indices with high frequency data.