Quantitative Finance

In the paper we consider the problem of valuation and hedging of American options written on dividend-paying assets whose price dynamics follow the multidimensional diffusion model. We derive a stochastic balance equation for the American option value function and its gradient. We prove that the latter pair is the unique solution of the stochastic balance equation as a result of the uniqueness in the related adapted future-supremum problem.

Risk capital allocations (RCAs) are an important tool in quantitative risk management, where they are utilized to, e.g., gauge the profitability of distinct business units, determine the price of a new product, and conduct the marginal economic capital analysis. Nevertheless, the notion of RCA has been living in the shadow of another, closely related notion, of risk measure (RM) in the sense that the latter notion often shapes the fashion in which the former notion is implemented. In fact, as the majority of the RCAs known nowadays are induced by RMs, the popularity of the two are apparently very much correlated. As a result, it is the RCA that is induced by the Conditional Tail Expectation (CTE) RM that has arguably prevailed in scholarly literature and applications. Admittedly, the CTE RM is a sound mathematical object and an important regulatory RM, but its appropriateness is controversial in, e.g., profitability analysis and pricing. In this paper, we address the question as to whether or not the RCA induced by the CTE RM may concur with alternatives that arise from the context of profit maximization. More specifically, we provide exhaustive description of all those probabilistic model settings, in which the mathematical and regulatory CTE RM may also reflect the risk perception of a profit-maximizing insurer.

In this paper aspects related to handling of intraday imbalances for hydro and wind power are addressed. The definition of imbalance cost is established and used to describe the potential benefits of shifting from plant-specific schedules to a common load requirement for wind and hydropower units in the same price area. The Nordpool intraday pay-as-bid market has been the basis for evaluation of imbalances, and some main characteristics for this market has been described. We consider how internal handling of complementary imbalances within the same river system with high inflow uncertainty and constrained reservoirs can reduce volatility in short-term marginal cost and risk compared to trading in the intraday market. We have also shown the the imbalance cost for a power producer with both wind and hydropower assets can be reduced by internal balancing in combination with sales and purchase in a pay-as-bid intraday market

The present study aims to establish the model of the cryptocurrency price trend based on financial theory using the LSTM model with multiple combinations between the window length and the predicting horizons, the random walk model is also applied with different parameter settings.

A volatility surface is an important tool for pricing and hedging derivatives. The surface shows the volatility that is implied by the market price of an option on an asset as a function of the option's strike price and maturity. Often, market data is incomplete and it is necessary to estimate missing points on partially observed surfaces. In this paper, we show how variational autoencoders can be used for this task. The first step is to derive latent variables that can be used to construct synthetic volatility surfaces that are indistinguishable from those observed historically. The second step is to determine the synthetic surface generated by our latent variables that fits available data as closely as possible. As a dividend of our first step, the synthetic surfaces produced can also be used in stress testing, in market simulators for developing quantitative investment strategies, and for the valuation of exotic options. We illustrate our procedure and demonstrate its power using foreign exchange market data.

Finding Bertram's optimal trading strategy for a pair of cointegrated assets following the Ornstein--Uhlenbeck price difference process can be formulated as an unconstrained convex optimization problem for maximization of expected profit per unit of time. This model is generalized to the form where the riskiness of profit, measured by its per-time-unit volatility, is controlled (e.g. in case of existence of limits on riskiness of trading strategies imposed by regulatory bodies). The resulting optimization problem need not be convex. In spite of this undesirable fact, it is demonstrated that the problem is still efficiently solvable. In addition, the problem that parameters of the price difference process are never known exactly and are imprecisely estimated from an observed finite sample is investigated (recalling that this problem is critical for practice). It is shown how the imprecision affects the optimal trading strategy by quantification of the loss caused by the imprecise estimate compared to a theoretical trader knowing the parameters exactly. The main results focus on the geometric and optimization-theoretic viewpoint of the risk-bounded trading strategy and the imprecision resulting from the statistical estimates.

The nonuniqueness of rational expectations is explained: in the stochastic, discrete-time, linear, constant-coefficients case, the associated free parameters are coefficients that determine the public's most immediate reactions to shocks. The requirement of model-consistency may leave these parameters completely free, yet when their values are appropriately specified, a unique solution is determined. In a broad class of models, the requirement of least-square forecast errors determines the parameter values, and therefore defines a unique solution. This approach is independent of dynamical stability, and generally does not suppress model dynamics. Application to a standard New Keynesian example shows that the traditional solution suppresses precisely those dynamics that arise from rational expectations. The uncovering of those dynamics reveals their incompatibility with the new I-S equation and the expectational Phillips curve.

Using the generalized extreme value theory to characterize tail distributions, we address liquidation, leverage, and optimal margins for bitcoin long and short futures positions. The empirical analysis of perpetual bitcoin futures on BitMEX shows that (1) daily forced liquidations to out- standing futures are substantial at 3.51%, and 1.89% for long and short; (2) investors got forced liquidation do trade aggressively with average leverage of 60X; and (3) exchanges should elevate current 1% margin requirement to 33% (3X leverage) for long and 20% (5X leverage) for short to reduce the daily margin call probability to 1%. Our results further suggest normality assumption on return significantly underestimates optimal margins. Policy implications are also discussed.

Financial portfolio management is one of the most applicable problems in reinforcement learning (RL) owing to its sequential decision-making nature. Existing RL-based approaches, while inspiring, often lack scalability, reusability, or profundity of intake information to accommodate the ever-changing capital markets. In this paper, we propose MSPM, a modularized and scalable, multi-agent RL-based system for financial portfolio management. MSPM involves two asynchronously updated units: an Evolving Agent Module (EAM) and Strategic Agent Module (SAM). A self-sustained EAM produces signal-comprised information for a specific asset using heterogeneous data inputs, and each EAM employs its reusability to have connections to multiple SAMs. An SAM is responsible for asset reallocation in a portfolio using profound information from the connected EAMs. With the elaborate architecture and the multi-step condensation of volatile market information, MSPM aims to provide a customizable, stable, and dedicated solution to portfolio management, unlike existing approaches. We also tackle the data-shortage issue of newly-listed stocks by transfer learning, and validate the indispensability of EAM with four different portfolios. Experiments on 8-year U.S. stock market data prove the effectiveness of MSPM in profit accumulation, by its outperformance over existing benchmarks.