pwc-archive/papers-with-abstracts huggingface dataset:
Best Portfolio Management Strategies For Synthetic and Real Assets
Authors: Jarosław Gruszka, Janusz Szwabiński
Date: 2019-04-23 00:00:00
Tasks: Econometrics, Management

Managing investment portfolios is an old and well know problem in multiple fields including financial mathematics and financial engineering as well as econometrics and econophysics. Multiple different concepts and theories were used so far to describe methods of handling with financial assets, including differential equations, stochastic calculus and advanced statistics. In this paper, using a set of tools from the probability theory, various strategies of building financial portfolios are analysed in different market conditions. A special attention is given to several realisations of a so called balanced portfolio, which is rooted in the natural "buy-low-sell-high" principle. Results show that there is no universal strategy, because they perform differently in different circumstances (e.g. for varying transaction costs). Moreover, the planned time of investment may also have a significant impact on the profitability of certain strategies. All methods have been tested with both simulated trajectories and real data from the Polish stock market.
Multiscale Asymptotic Analysis for Portfolio Optimization under Stochastic Environment
Authors: Jean-Pierre Fouque, Ruimeng Hu
Date: 2019-02-19 00:00:00
Tasks: Portfolio Optimization

Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian setting under each single scale, the slow one in [Fouque and Hu, SIAM J. Control Optim., 55 (2017), 1990-2023], and the fast one in [Hu, Proceedings of IEEE CDC 2018, accepted]. This paper is dedicated to the analysis when the two scales coexist in a Markovian setting. We study the terminal wealth utility maximization problem when the volatility is driven by both fast- and slow-scale factors. We first propose a zeroth-order strategy, and rigorously establish the first order approximation of the associated problem value. This is done by analyzing the corresponding linear partial differential equation (PDE) via regular and singular perturbation techniques, as in the single-scale cases. Then, we show the asymptotic optimality of our proposed strategy within a specific family of admissible controls. Interestingly, we highlight that a pure PDE approach does not work in the multi-scale case and, instead, we use the so-called epsilon-martingale decomposition. This completes the analysis of portfolio optimization in both fast mean-reverting and slowly-varying Markovian stochastic environments.
Statistical Arbitrage for Multiple Co-Integrated Stocks
Authors: T. N. Li, A. Papanicolaou
Date: 2019-08-06 00:00:00
Tasks: parameter estimation

In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.
A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formula
Authors: Aurélien Alfonsi, Adel Cherchali, Jose Arturo Infante Acevedo
Date: 2019-08-02 00:00:00
Tasks: Management, Specificity

The aim of this paper is to introduce a synthetic ALM model that catches the main specificity of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule. Second, it introduces a determination of the crediting rate to policyholders that is close to the practice and is a trade-off between the regulatory rate, a competitor rate and the available profits. Third, it considers an investment in bonds that enables to match a part of the cash outflow due to surrenders, while avoiding to store the trading history. We use this model to evaluate the Solvency Capital Requirement (SCR) with the standard formula, and show that the choice of the interest rate model is important to get a meaningful model after the regulatory shocks on the interest rate. We discuss the different values of the SCR modules first in a framework with moderate interest rates using the shocks of the present legislation, and then we consider a low interest framework with the latest recommandation of the EIOPA on the shocks. In both cases, we illustrate the importance of matching cash-flows and its impact on the SCR.
Artificial Intelligence Alter Egos: Who benefits from Robo-investing?
Authors: Catherine D'Hondt, Rudy De Winne, Eric Ghysels, Steve Raymond
Date: 2019-07-08 00:00:00
Tasks: Decision Making

Artificial intelligence, or AI, enhancements are increasingly shaping our daily lives. Financial decision-making is no exception to this. We introduce the notion of AI Alter Egos, which are shadow robo-investors, and use a unique data set covering brokerage accounts for a large cross-section of investors over a sample from January 2003 to March 2012, which includes the 2008 financial crisis, to assess the benefits of robo-investing. We have detailed investor characteristics and records of all trades. Our data set consists of investors typically targeted for robo-advising. We explore robo-investing strategies commonly used in the industry, including some involving advanced machine learning methods. The man versus machine comparison allows us to shed light on potential benefits the emerging robo-advising industry may provide to certain segments of the population, such as low income and/or high risk averse investors.
Dynamic Mean-Variance Portfolio Optimisation
Authors: Xiang Meng
Date: 2019-07-06 00:00:00

The portfolio optimisation problem, first raised by Harry Markowitz in 1952, has been a fundamental and central topic to understanding the stock market and making decisions. There has been plenty of works contributing to development of the mean-variance optimisation (MVO) so far. In this paper, one kind of them, namely, dynamic mean-variance optimisation (DMVO) is mainly discussed. One can apply either precommitment or game-theoritical approach to address time-inconsistency in DMVO. We use the second approach to seek for a time-consistent strategy. After obtaining the optimal strategy, we extend the result to a CEV-driven economy. In order to prove the usefulness of them, strategies are fit into both real market data and simulated data. It turns out that the strategy whose assumptions are close to market conditions generally gives a better result. Lastly, a selected strategy is chosen to compare with another strategy came up by deep learning technique.
Learning Threshold-Type Investment Strategies with Stochastic Gradient Method
Authors: Zsolt Nika, Miklós Rásonyi
Date: 2019-07-04 00:00:00
Tasks: Portfolio Optimization, Vocal Bursts Type Prediction

In online portfolio optimization the investor makes decisions based on new, continuously incoming information on financial assets (typically their prices). In our study we consider a learning algorithm, namely the Kiefer--Wolfowitz version of the Stochastic Gradient method, that converges to the log-optimal solution in the threshold-type, buy-and-sell strategy class. The systematic study of this method is novel in the field of portfolio optimization; we aim to establish the theory and practice of Stochastic Gradient algorithm used on parametrized trading strategies. We demonstrate on a wide variety of stock price dynamics (e.g. with stochastic volatility and long-memory) that there is an optimal threshold type strategy which can be learned. Subsequently, we numerically show the convergence of the algorithm. Furthermore, we deal with the typically problematic question of how to choose the hyperparameters (the parameters of the algorithm and not the dynamics of the prices) without knowing anything about the price other than a small sample.
Smart network based portfolios
Authors: Gian Paolo Clemente, Rosanna Grassi, Asmerilda Hitaj
Date: 2019-07-02 00:00:00
Tasks: Portfolio Optimization

In this article we deal with the problem of portfolio allocation by enhancing network theory tools. We use the dependence structure of the correlations network in constructing some well-known risk-based models in which the estimation of correlation matrix is a building block in the portfolio optimization. We formulate and solve all these portfolio allocation problems using both the standard approach and the network-based approach. Moreover, in constructing the network-based portfolios we propose the use of two different estimators for the covariance matrix: the sample estimator and the shrinkage toward constant correlation one. All the strategies under analysis are implemented on two high-dimensional portfolios having different characteristics, covering the period from January $2001$ to December $2017$. We find that the network-based portfolio consistently better performs and has lower risk compared to the corresponding standard portfolio in an out-of-sample perspective.
Analytic formula for option margin with liquidity costs under dynamic delta hedging
Authors: Kyungsub Lee, Byoung Ki Seo
Date: 2021-03-29 00:00:00

This study derives the expected liquidity cost when performing the delta hedging process of a European option. This cost is represented by an integration formula that includes European option prices and a certain function depending on the delta process. We first define a unit liquidity cost and then show that the liquidity cost is a multiplication of the unit liquidity cost, stock price, supply curve parameter, and the square of the number of options. Using this formula, the expected liquidity cost before hedging can be calculated much faster than when using a Monte Carlo simulation. Numerically computed distributions of liquidity costs in special cases are also provided.
Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options
Authors: Andrew Papanicolaou
Date: 2021-01-01 00:00:00

This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX options, and vice versa. This relationship can be quantified using moment formulas in a model-free way. Comparisons are made between VIX and SPX implied volatilities along with various examples of stochastic volatility models.
A structural approach to default modelling with pure jump processes
Authors: Jean-Philippe Aguilar, Nicolas Pesci, Victor James
Date: 2021-02-11 00:00:00

We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump L\'evy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included.
Cross impact in derivative markets
Authors: Mehdi Tomas, Iacopo Mastromatteo, Michael Benzaquen
Date: 2021-02-04 00:00:00

Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. The empirical estimation of this effect on complex financial instruments, such as derivatives, is an open problem. To address this, we consider a setting in which the prices of derivatives is a deterministic function of stochastic factors where trades on both factors and derivatives induce price impact. We show that a specific cross-impact model satisfies key properties which make its estimation tractable in applications. Using E-Mini futures, European call and put options and VIX futures, we estimate cross-impact and show our simple framework successfully captures some of the empirical phenomenology. Our framework for estimating cross-impact on derivatives may be used in practice for estimating hedging costs or building liquidity metrics on derivative markets.
Quantum crypto-economics: Blockchain prediction markets for the evolution of quantum technology
Authors: Peter P. Rohde, Vijay Mohan, Sinclair Davidson, Chris Berg, Darcy Allen, Gavin K. Brennen, Jason Potts
Date: 2021-02-01 00:00:00

Two of the most important technological advancements currently underway are the advent of quantum technologies, and the transitioning of global financial systems towards cryptographic assets, notably blockchain-based cryptocurrencies and smart contracts. There is, however, an important interplay between the two, given that, in due course, quantum technology will have the ability to directly compromise the cryptographic foundations of blockchain. We explore this complex interplay by building financial models for quantum failure in various scenarios, including pricing quantum risk premiums. We call this quantum crypto-economics.
Mortgage Contracts and Underwater Default
Authors: Yerkin Kitapbayev, Scott Robertson
Date: 2020-05-07 00:00:00

We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the ``underwater'' effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline remove the default incentive, but may induce prepayment in low price states. However, low state prepayments vanish if the benefit from home ownership is sufficiently high. We also show that capital gain sharing features, such as prepayment penalties in high house price states, are ineffective as they virtually eliminate prepayment. For observed foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed-rate contracts at mortgage rate spreads between 20-50 basis points. We obtain these results for perpetual versions of the contracts using American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts' values and optimal decision rules are associated with free boundary problems, which admit semi-explicit solutions.
Analysis of the optimal exercise boundary of American put options with delivery lags
Authors: Gechun Liang, Zhou Yang
Date: 2018-05-08 00:00:00

A make-your-mind-up option is an American derivative with delivery lags. We show that its put option can be decomposed as a European put and a new type of American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and decides an optimal stopping time to terminate the contract. Based on this decomposition and using free boundary techniques, we show that the associated optimal exercise boundary exists and is a strictly increasing and smooth curve, and analyze the asymptotic behavior of the value function and the optimal exercise boundary for both large maturity and small time lag.
Deep Curve-dependent PDEs for affine rough volatility
Authors: Antoine Jacquier, Mugad Oumgari
Date: 2019-06-06 00:00:00
Tasks: Deep Learning

We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the whole path of the process, for which we develop a numerical scheme based on deep learning techniques. Numerical simulations suggest that the latter is a promising alternative to classical Monte Carlo simulations.
XVA Valuation under Market Illiquidity
Authors: Weijie Pang, Stephan Sturm
Date: 2020-11-06 00:00:00

Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' defaults, illiquidity problems, and the role of the sale and repurchase agreement (Repo) market. Recently, models were proposed to address this by computing a total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market. In this article, we include a possible crisis by using an alternating renewal process to describe the switching between a normal financial regime and a financial crisis. We develop a framework to price the XVA of a European claim in this state-dependent situation. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of the XVA.
Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate
Authors: Foad Shokrollahi, Marcin Marcin Magdziarz
Date: 2020-07-23 00:00:00

In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short rate follows the subdiffusive fractional Black-Scholes model. We obtain the pricing formula for zero-coupon bond in the introduced model and derive the partial differential equation with appropriate boundary conditions for the valuation of equity warrant. Finally, the pricing formula for equity warrant is provided under subdiffusive fractional Brownian motion model of the short rate.
Explicit option valuation in the exponential NIG model
Authors: Jean-Philippe Aguilar
Date: 2020-06-08 00:00:00
Tasks: Form, model

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier and Fast Fourier transforms, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.
Small-time, large-time and $H\to 0$ asymptotics for the Rough Heston model
Authors: Martin Forde, Stefan Gerhold, Benjamin Smith
Date: 2019-06-21 00:00:00

We characterize the behaviour of the Rough Heston model introduced by Jaisson\&Rosenbaum \cite{JR16} in the small-time, large-time and $\alpha \to 1/2$ (i.e. $H\to 0$) limits. We show that the short-maturity smile scales in qualitatively the same way as a general rough stochastic volatility model (cf.\ \cite{FZ17}, \cite{FGP18a} et al.), and the rate function is equal to the Fenchel-Legendre transform of a simple transformation of the solution to the same Volterra integral equation (VIE) that appears in \cite{ER19}, but with the drift and mean reversion terms removed. The solution to this VIE satisfies a space-time scaling property which means we only need to solve this equation for the moment values of $p=1$ and $p=-1$ so the rate function can be efficiently computed using an Adams scheme or a power series, and we compute a power series in the log-moneyness variable for the asymptotic implied volatility which yields tractable expressions for the implied vol skew and convexity. The limiting asymptotic smile in the large-maturity regime is obtained via a stability analysis of the fixed points of the VIE, and is the same as for the standard Heston model in \cite{FJ11}. Finally, using L\'{e}vy's convergence theorem, we show that the log stock price $X_t$ tends weakly to a non-symmetric random variable $X^{(1/2)}_t$ as $\alpha \to 1/2$ (i.e. $H\to 0$) whose mgf is also the solution to the Rough Heston VIE with $\alpha=1/2$, and we show that $X^{(1/2)}_t/\sqrt{t}$ tends weakly to a non-symmetric random variable as $t\to 0$, which leads to a non-flat non-symmetric asymptotic smile in the Edgeworth regime. We also show that the third moment of the log stock price tends to a finite constant as $H\to 0$ (in contrast to the Rough Bergomi model discussed in \cite{FFGS20} where the skew flattens or blows up) and the $V$ process converges on pathspace to a random tempered distribution.
Power-type derivatives for rough volatility with jumps
Authors: Liang Wang, Weixuan Xia
Date: 2020-08-24 00:00:00
Tasks: Vocal Bursts Type Prediction

In this paper we propose a novel pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Our model directly targets the instantaneous variance of a risky asset and consists of a generalized fractional Ornstein-Uhlenbeck process driven by a L\'{e}vy subordinator and an independent sinusoidal-composite L\'{e}vy process. The former component captures short-term dependence in the instantaneous volatility, while the latter is introduced expressly for rectifying the activity level of the average forward variance. Such a framework ensures that the characteristic function of average forward variance is obtainable in semi-closed form, without having to invoke any geometric-mean approximations. To analyze swaps and European-style options on average forward volatility, we introduce a general class of power-type derivatives on the average forward variance, which also provide flexible nonlinear leverage exposure. Pricing-hedging formulae are based on a modified numerical Fourier transform technique. A comparative empirical study is conducted on two independent recent data sets on VIX options, before and during the COVID-19 pandemic, to demonstrate that the proposed framework is highly amenable to efficient model calibration under various choices of kernels.