This article introduces a new mathematical concept of illiquidity that goes hand in hand with credit risk. The concept is not volume- but constraint-based, i.e., certain assets cannot be shorted and are ineligible as num\'eraire. If those assets are still chosen as num\'eraire, we arrive at a two-price economy. We utilise Jarrow & Turnbull's foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of non-defaultable foreign counterparts. In the language of structured derivatives, the impact of credit risk is disabled through quanto-ing. In a similar fashion, we look at bond prices as if perfect liquidity was given. This corresponds to asset pricing with respect to an ineligible num\'eraire and necessitates F\"ollmer measures.

We build the time series of optimal realized portfolio weights from high-frequency data and we suggest a novel Dynamic Conditional Weights (DCW) model for their dynamics. DCW is benchmarked against popular model-based and model-free specifications in terms of weights forecasts and portfolio allocations. Next to portfolio variance, certainty equivalent and turnover, we introduce the break-even transaction costs as an additional measure that identifies the range of transaction costs for which one allocation is preferred to another. By comparing minimum-variance portfolios built on the components of the Dow Jones 30 Index, the proposed DCW overall attains the best allocations with respect to the measures considered, for any degree of risk-aversion, transaction costs and exposure.

We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $\mathcal{P}$ nor on the structure of the state space. Several aspects of modeling under Knightian Uncertainty are considered and analyzed. We show the need for a suitable adaptation of the notion of No Free Lunch with Vanishing Risk and discuss its relation to the choice of an appropriate filtration. In an abstract setup, we show that absence of arbitrage is equivalent to the existence of \emph{approximate} martingale measures sharing the same polar set of $\mathcal{P}$. We then specialize the results to a discrete-time framework in order to obtain true martingale measures.

Using data on 17 listed public banks from Russia over the period 2008 to 2016, we analyze whether international oil prices affect the bank stability in an oil-dependent country. We posit that a decrease in international oil prices has a negative long-run macroeconomic impact for an oil-exporting country, which further deteriorates the bank financial stability. More specifically, a decrease in international oil prices leads for an oil-exporting country as Russia to a currency depreciation and to a deterioration of the fiscal stance. In addition, given the positive correlation of oil and stock prices documented by numerous previous studies, a decrease in international oil prices represents a negative signal for the stock markets investors, negatively affecting banks' share prices and thus, their capacity to generate sustainable earnings. In this context, the bank financial stability can be menaced. With a focus on public listed banks and using a Pool Mean Group (PMG) estimator, we show that an increase in international oil prices and in the price to book value ratio has a long-run positive effect on Russian public banks stability, and conversely. While positive oil-price shocks contribute to bank stability in the long run, an opposite effect is recorded for negative shocks. However, no significant impact is documented in the short run. Our findings are robust to different bank stability specifications, different samples and control variables.

In this research, we have empirically investigated the key drivers affecting liquidity in equity markets. We illustrated how theoretical models, such as Kyle's model, of agents' interplay in the financial markets, are aligned with the phenomena observed in publicly available trades and quotes data. Specifically, we confirmed that for small signed order-flows, the price impact grows linearly with increase in the order-flow imbalance. We have, further, implemented a machine learning algorithm to forecast market impact given a signed order-flow. Our findings suggest that machine learning models can be used in estimation of financial variables; and predictive accuracy of such learning algorithms can surpass the performance of traditional statistical approaches.

Understanding the determinants of price impact is crucial for several reasons. From a theoretical stance, modelling the impact provides a statistical measure of liquidity. Practitioners adopt impact models as a pre-trade tool to estimate expected transaction costs and optimize the execution of their strategies. This further serves as a post-trade valuation benchmark as suboptimal execution can significantly deteriorate a portfolio performance.

More broadly, the price impact reflects the balance of liquidity across markets. This is of central importance to regulators as it provides an all-encompassing explanation of the correlation between market design and systemic risk, enabling regulators to design more stable and efficient markets.

The takeoff point of this paper is to generalize the existing stock trading results for a class of affine feedback controller to include consideration of a stop-loss order. Using the geometric Brownian motion as the underlying stock price model, our main result is to provide a closed-form expression for the cumulative distribution function for the trading profit or loss. In addition, we show that the affine feedback controller with stop-loss order indeed generalizes the result without stop order in the sense of distribution function. Some simulations and illustrative examples are also provided as supporting evidence of the theory. Moreover, we provide some technical results aimed at addressing the issues about survivability, cash-financing considerations, long-only property, and lower bound of the expected gain or loss.

Existing research argues that countries increase their production basket by adding products which require similar capabilities to those they already produce, a process referred to as path dependency. Green economic growth is a global movement that seeks to achieve economic expansion while at the same time mitigating environmental risks. We postulate that countries engaging in green economic growth are motivated to invest strategically to develop new capabilities that will help them transition to a green economy. As a result, they could potentially increase their production baskets not only by a path dependent process but also by the non path dependent process we term, high investment structural jumps. The main objective of this research is to determine whether countries increase their green production basket mainly by a process of path dependency, or alternatively, by a process of structural jumps. We analyze data from 65 countries and over a period from years 2007 to 2017. We focus on China as our main case study. The results of this research show that countries not only increase their green production baskets based on their available capabilities, following path dependency, but also expand to products that path dependency does not predict by investing in innovating and developing new environmental related technologies.

We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular, we introduce multi-curve models driven by a flow of CBI processes. Such models are especially parsimonious and tractable, and can generate contagion effects among different spreads. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed approach allows for explicit valuation formulae for all linear interest rate derivatives and semi-closed formulae for non-linear derivatives via Fourier techniques and quantization. We show that a simple specification of the model can be successfully calibrated to market data.

In this paper, we consider a discrete-time portfolio with $m \geq 2$ assets optimization problem which includes the rebalancing~frequency as an additional parameter in the maximization. The so-called Kelly Criterion is used as the performance metric; i.e., maximizing the expected logarithmic growth of a trader's account, and the portfolio obtained is called the frequency-based Kelly optimal portfolio. The focal point of this paper is to extend upon the results of our previous work to obtain various optimality characterizations on the portfolio. To be more specific, using Kelly's criterion in our frequency-based formulation, we first prove necessary and sufficient conditions for the frequency-based Kelly optimal portfolio. With the aid of these conditions, we then show several new optimality characterizations such as expected ratio optimality and asymptotic relative optimality, and a result which we call the Extended Dominant Asset Theorem. That is, we prove that the $i$th asset is dominant in the portfolio if and only if the Kelly optimal portfolio consists of that asset only. The word "extended" on the theorem comes from the fact that it was only a sufficiency result that was proved in our previous work. Hence, in this paper, we improve it to involve a proof of the necessity part. In addition, the trader's survivability issue (no bankruptcy consideration) is also studied in detail in our frequency-based trading framework. Finally, to bridge the theory and practice, we propose a simple trading algorithm using the notion called dominant asset condition to decide when should one triggers a trade. The corresponding trading performance using historical price data is reported as supporting evidence.

This paper investigates the finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markov regime-switching process is assumed to be unobservable, which has countable states that affect default intensities of surviving assets. The stochastic control problem is formulated under partial observations of asset prices and default events. By proving a novel martingale representation theorem based on incomplete and phasing out filtration, we characterize the value function in an equivalent form. This allows us to connect the control problem to a new type of quadratic BSDE with jumps, in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and establishing a uniform a priori estimates, we obtain the existence of a solution to this BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

We present a natural extension of the SABR model to price both backward and forward-looking RFR caplets in a post-Libor world. Forward-looking RFR caplets can be priced using the market standard approximations of Hagan et al. (2002). We provide closed-form effective SABR parameters for pricing backward-looking RFR caplets. These results are useful for smile interpolation and for analyzing backward and forward-looking smiles in normalized units.

While the coronavirus spreads, governments are attempting to reduce contagion rates at the expense of negative economic effects. Market expectations plummeted, foreshadowing the risk of a global economic crisis and mass unemployment. Governments provide huge financial aid programmes to mitigate the economic shocks. To achieve higher effectiveness with such policy measures, it is key to identify the industries that are most in need of support. In this study, we introduce a data-mining approach to measure industry-specific risks related to COVID-19. We examine company risk reports filed to the U.S. Securities and Exchange Commission (SEC). This alternative data set can complement more traditional economic indicators in times of the fast-evolving crisis as it allows for a real-time analysis of risk assessments. Preliminary findings suggest that the companies' awareness towards corona-related business risks is ahead of the overall stock market developments. Our approach allows to distinguish the industries by their risk awareness towards COVID-19. Based on natural language processing, we identify corona-related risk topics and their perceived relevance for different industries. The preliminary findings are summarised as an up-to-date online index. The CoRisk-Index tracks the industry-specific risk assessments related to the crisis, as it spreads through the economy. The tracking tool is updated weekly. It could provide relevant empirical data to inform models on the economic effects of the crisis. Such complementary empirical information could ultimately help policymakers to effectively target financial support in order to mitigate the economic shocks of the crisis.

We consider a financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow & Turnbull setting in order to account for these two intricately intertwined risk types. We utilise the foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of non-defaultable foreign counterparts. The relevant exchange rate is only partially observable in the market filtration, which leads us naturally to an application of the concept of platonic financial markets. We provide an example of tractable term structure models that are driven by a two-dimensional affine jump diffusion. Furthermore, we derive explicit valuation formulae for marketable products, e.g., for credit default swaps.

The aim of this paper is to reemphasize the money theory of exchange which is centered on the function of exchange medium of money, and make a contribution towards linearization of the quantity equation of exchange. A dynamical quantity equation is presented and an important balanced path of economic evolution is derived. To understand the business cycle we propose a hypothesis of natural cycle and driving cycle concerning the evolution of the balanced path and plentiful conclusions can be made.

We model the limit order book (LOB) as a continuous Markov process and develop an algebra to describe its dynamics based on the fundamental events of the book: order arrivals and cancellations. We show how all observables (prices, returns, and liquidity measures) are governed by the same variables which also drive arrival and cancellation rates. The sensitivity of our model is evaluated in a simulation study and an empirical analysis. We estimate several linearized model specifications based on the theoretical description of the LOB and conduct in- and out-of-sample forecasts on several frequencies. The in-sample results based on contemporaneous information suggest that our model describes up to 90% of the variation of close-to-close returns, the adjusted $R^2$ still ranges at around 80%. In the more realistic setting where only past information enters the model, we still observe an adjusted $R^2$ in the range of 15%. The direction of the next return can be predicted, out-of-sample, with an accuracy of over 75% for short time horizons below 10 minutes. Out-of-sample, on average, we obtain $R^2$ values for the Mincer-Zarnowitz regression of around 2-3% and an $RMSPE$ that is 10 times lower than values documented in the literature.

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundamental exponent in the study of multifractals. The consequence of this behavior is the non-monotonic behavior of the coarse H\"older exponent $\alpha (q)$ leading to multi-branchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multi-branchedness is tantamount in significance to extending multifractal analysis.

In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward stochastic differential equation. Moreover, we prove the uniqueness of the open-loop equilibrium pair by showing that the original time-inconsistent problem is equivalent to an associated time-consistent one.

We develop the optimal trading strategy for a foreign exchange (FX) broker who must liquidate a large position in an illiquid currency pair. To maximize revenues, the broker considers trading in a currency triplet which consists of the illiquid pair and two other liquid currency pairs. The liquid pairs in the triplet are chosen so that one of the pairs is redundant. The broker is risk-neutral and accounts for model ambiguity in the FX rates to make her strategy robust to model misspecification. When the broker is ambiguity neutral (averse) the trading strategy in each pair is independent (dependent) of the inventory in the other two pairs in the triplet. We employ simulations to illustrate how the robust strategies perform. For a range of ambiguity aversion parameters, we find the mean Profit and Loss (P&L) of the strategy increases and the standard deviation of the P&L decreases as ambiguity aversion increases.

The measured correlations of financial time series in subsequent epochs change considerably as a function of time. When studying the whole correlation matrices, quasi-stationary patterns, referred to as market states, are seen by applying clustering methods. They emerge, disappear or reemerge, but they are dominated by the collective motion of all stocks. In the jargon, one speaks of the market motion, it is always associated with the largest eigenvalue of the correlation matrices. Thus the question arises, if one can extract more refined information on the system by subtracting the dominating market motion in a proper way. To this end we introduce a new approach by clustering reduced-rank correlation matrices which are obtained by subtracting the dyadic matrix belonging to the largest eigenvalue from the standard correlation matrices. We analyze daily data of 262 companies of the S&P 500 index over a period of almost 15 years from 2002 to 2016. The resulting dynamics is remarkably different, and the corresponding market states are quasi-stationary over a long period of time. Our approach adds to the attempts to separate endogenous from exogenous effects.