We propose a modelling framework for the optimal selection of crypto assets. Crypto assets differ by two essential features: security (technological) and stability (governance). Investors make choices over crypto assets similarly to how they make choices by using a recommender app: the app presents each investor with a pair of crypto assets with certain security-stability characteristics to be compared. Each investor submits its preference for adopting one of the two assets to the app. The app, in turn, provides a recommendation on whether the proposed adoption is sensible given the assets' essential features, information about the adoption choices of all other investors, and expected future economic benefits of adoption. Investors continue making their adoption choices over all pairs of crypto assets until their expected future economic benefits can no longer be improved upon. This constitutes an optimal selection decision. We simulate optimal selection decisions considering the behaviour of different types of investors, driven by their attitudes towards assets' features. We find a variety of possible emergent outcomes for the investments in the crypto-ecosystem and the future adoption of the crypto assets.

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

Financial undertakings often have to deal with liabilities of the form 'non-hedgeable claim size times value of a tradeable asset', e.g. foreign property insurance claims times fx rates. Which strategy to invest in the tradeable asset is risk minimal? We generalize the Gram-Charlier series for the sum of two dependent random variable, which allows us to expand the capital requirements based on value-at-risk and expected shortfall. We derive a stable and fairly model independent approximation of the risk minimal asset allocation in terms of the claim size distribution and the moments of asset return. The results enable a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component.

In this paper we investigate price and Greeks computation of a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochastic interest rate are considered together in the Heston Hull-White model. We consider a numerical method the solves the dynamic control problem due to the computing of the optimal withdrawal. Moreover, in order to speed up the computation, we employ Gaussian Process Regression (GPR). Starting from observed prices previously computed for some known combinations of model parameters, it is possible to approximate the whole price function on a defined domain. The regression algorithm consists of algorithm training and evaluation. The first step is the most time demanding, but it needs to be performed only once, while the latter is very fast and it requires to be performed only when predicting the target function. The developed method, as well as for the calculation of prices and Greeks, can also be employed to compute the no-arbitrage fee, which is a common practice in the Variable Annuities sector. Numerical experiments show that the accuracy of the values estimated by GPR is high with very low computational cost. Finally, we stress out that the analysis is carried out for a GMWB annuity but it could be generalized to other insurance products.

Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a $\sigma$-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003).

Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios.

In the first part of the paper we characterize these generalized statistical no-arbitrage notions. In the second part of the paper we construct several profitable generalized strategies with respect to various choices of the information system. In particular, we consider several forms of embedded binomial strategies and follow-the-trend strategies as well as partition-type strategies. We study and compare their behaviour on simulated data. Additionally, we find good performance on market data of these simple strategies which makes them profitable candidates for real applications.

We utilize a fundamentally different model of trading costs to look at the effect of the opening of the Hong Kong Shanghai Connect that links the stock exchanges in the two cities, arguably the biggest event in international business and finance since Christopher Columbus set sail for India. We design a novel methodology that compensates for the lack of data on trading costs in China. We estimate trading costs across similar positions on the dual listed set of securities in Hong Kong and China, hoping to provide useful pieces of information to help scale 'The Great Wall of Chinese Securities Trading Costs'. We then compare actual and estimated trading costs on a sample of real orders across the Hong Kong securities in the dual listed pair to establish the accuracy of our measurements. The primary question we seek to address is 'Which market would be better to trade to gain exposure to the same (or similar) set of securities or sectors?' We find that trading costs on Shanghai, which might have been lower than Hong Kong, might have become higher leading up to the Connect. What remains to be seen is whether this increase in trading costs is a temporary equilibrium due to the frenzy to gain exposure to Chinese securities or whether this phenomenon will persist once the two markets start becoming more and more tightly coupled. It would be interesting to see if this pioneering policy will lead to securities exchanges across the globe linking up one another, creating a trade anything, anywhere and anytime marketplace. Looking beyond mere trading costs, such studies can be used to gather some evidence on what effect the mode of governance and other aspects of life in one country have on another country, once they start joining up their financial markets.

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method.

Stock price prediction is a challenging task, but machine learning methods have recently been used successfully for this purpose. In this paper, we extract over 270 hand-crafted features (factors) inspired by technical and quantitative analysis and tested their validity on short-term mid-price movement prediction. We focus on a wrapper feature selection method using entropy, least-mean squares, and linear discriminant analysis. We also build a new quantitative feature based on adaptive logistic regression for online learning, which is constantly selected first among the majority of the proposed feature selection methods. This study examines the best combination of features using high frequency limit order book data from Nasdaq Nordic. Our results suggest that sorting methods and classifiers can be used in such a way that one can reach the best performance with a combination of only very few advanced hand-crafted features.

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and L\'evy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional L\'evy based on polynomial jump-diffusions.

We derive valuations of a portfolio of financial instruments from a securities lending perspective, under different assumptions, and show a weighting scheme that converges to the true valuation. We illustrate conditions under which our alternative weighting scheme converges faster to the true valuation when compared to the minimum variance weighting. This weighting scheme is applicable in any situation where multiple forecasts are made and we need a methodology to combine them. Our valuations can be useful either to derive a bidding strategy for an exclusive auction or to design an appropriate auction mechanism, depending on which side of the fence a participant sits (whether the interest is to procure the rights to use a portfolio for making stock loans such as for a lending desk, or, to obtain additional revenue from a portfolio such as from the point of view of a long only asset management firm). Lastly, we run simulations to establish numerical examples for the set of valuations and for various bidding strategies corresponding to different auction settings.

We develop models to price long term loans in the securities lending business. These longer horizon deals can be viewed as contracts with optionality embedded in them and can be priced using established methods from derivatives theory, becoming to our limited knowledge, the first application that can lead to greater synergies between the operations of derivative and delta-one trading desks, perhaps even being able to combine certain aspects of the day to day operations of these seemingly disparate entities. We run numerical simulations to demonstrate the practical applicability of these models. These models are part of one of the least explored yet profit laden areas of modern investment management.

We develop a heuristic that can mitigate the loss of information that sets in when parameters are estimated first and then the valuation is performed by directly calculating the valuation using the historical time series. This can lead to reduced models errors and greater financial stability. We illustrate how the methodologies developed here could be useful for inventory management. All these techniques could have applications for dealing with other financial instruments, non-financial commodities and many forms of uncertainty. An unintended consequence of our efforts, has become a review of the vast literature on options pricing, which can be useful for anyone that attempts to apply the corresponding techniques to the problems mentioned here.

Admittedly, our initial ambitions to produce a normative theory on long term loan valuations are undone by the present state of affairs in social science modeling. Though we consider many elements of a securities lending system at face value, this cannot be termed a positive theory. For now, if it ends up producing a useful theory, our work is done.

We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous market impact, it is shown that transaction costs of optimal adaptive strategies are substantially lower than the corresponding costs of the optimal static strategy. In the same spirit, in the case of transient impact it is shown that strategies that observe the signal a finite number of times can dramatically reduce the transaction costs and improve the performance of the optimal static strategy.

Stock trading based on Kelly's celebrated Expected Logarithmic Growth (ELG) criterion, a well-known prescription for optimal resource allocation, has received considerable attention in the literature. Using ELG as the performance metric, we compare the impact of trade execution delay on the relative performance of high-frequency trading versus buy and hold. While it is intuitively obvious and straightforward to prove that in the presence of sufficiently high transaction costs, buy and hold is the better strategy, is it possible that with no transaction costs, buy and hold can still be the better strategy? When there is no delay in trade execution, we prove a theorem saying that the answer is ``no.'' However, when there is delay in trade execution, we present simulation results using a binary lattice stock model to show that the answer can be ``yes.'' This is seen to be true whether self-financing is imposed or not.

We compare performance of US stocks based on their size (market capitalization). We regress alpha and beta over size and other factors for individual stocks in Standard & Poor 500, for randomly generated portfolios. The novelty of our research is that we compare exchange-traded funds (ETFs) consisting of large-, mid- and small-cap stocks, including international ETFs. Conclusions: Size and market exposure (beta) are inversely related (strong evidence for ETFs, weaker for individual stocks). No conclusive evidence about dependence of excess return (alpha) on size, or international markets.