pwc-archive/papers-with-abstracts huggingface dataset:
Model order reduction for parametric high dimensional models in the analysis of financial risk
Authors: Andreas Binder, Onkar Jadhav, Volker Mehrmann
Date: 2020-02-27 00:00:00

This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the underlying product. These simulations are expensive and create a need for efficient computational performance. Thus, to tackle this problem, we establish a MOR approach based on a proper orthogonal decomposition (POD) method. The study involves the computations of high dimensional parametric convection-diffusion reaction partial differential equations (PDEs). POD requires to solve the high dimensional model at some parameter values to generate a reduced-order basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set that is analyzed, implemented, and tested on the industrial data. The results obtained for the numerical example of a floater with cap and floor under the Hull-White model indicate that the MOR approach works well for short-rate models.
Algorithmic market making for options
Authors: Bastien Baldacci, Philippe Bergault, Olivier Guéant
Date: 2019-07-29 00:00:00

In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model -- e.g. the Heston model -- the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.
Sig-SDEs model for quantitative finance
Authors: Imanol Perez Arribas, Cristopher Salvi, Lukasz Szpruch
Date: 2020-05-30 00:00:00
Tasks: model, Model Selection, Time Series, Time Series Analysis

Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach. Leveraging the properties of the signature, a well-known path-transform from stochastic analysis that recently emerged as leading machine learning technology for learning time-series data, we develop the Sig-SDE model. Sig-SDE provides a new perspective on neural SDEs and can be calibrated to exotic financial products that depend, in a non-linear way, on the whole trajectory of asset prices. Furthermore, we our approach enables to consistently calibrate under the pricing measure $\mathbb Q$ and real-world measure $\mathbb P$. Finally, we demonstrate the ability of Sig-SDE to simulate future possible market scenarios needed for computing risk profiles or hedging strategies. Importantly, this new model is underpinned by rigorous mathematical analysis, that under appropriate conditions provides theoretical guarantees for convergence of the presented algorithms.
More Robust Pricing of European Options Based on Fourier Cosine Series Expansions
Authors: Fabien Le Floc'h
Date: 2020-05-27 00:00:00

We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model. It is more robust across strikes and as fast as the original COS method.
Pricing Path-Dependent Derivatives under Multiscale Stochastic Volatility Models: a Malliavin Representation
Authors: Yuri F. Saporito
Date: 2020-05-08 00:00:00
Tasks: Form

In this paper we derive a efficient Monte Carlo approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models of Fouque \textit{et al}. Using the formulation of this pricing problem under the functional It\^o calculus framework and making use of Greek formulas from Malliavin calculus, we derive a representation for the first-order approximation of the price of path-dependent derivatives in the form $\mathbb{E}[\mbox{payoff} \times \mbox{weight}]$. The weight is known in closed form and depends only on the group market parameters arising from the calibration of the multiscale stochastic volatility to the market's implied volatility. Moreover, only simulations of the Black-Scholes model is required. We exemplify the method for a couple path-dependent derivatives.
Asymptotic Smiles for an Affine Jump-Diffusion Model
Authors: Nian Yao, Zhiqiu Li, Zhichao Ling, Junfeng Lin
Date: 2020-02-29 00:00:00
Tasks: model

In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work.
Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations
Authors: Takaaki Koike, Marius Hofert
Date: 2019-09-25 00:00:00

We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.
SABR smiles for RFR caplets
Authors: Sander Willems
Date: 2020-04-09 00:00:00

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.
A neural network model for solvency calculations in life insurance
Authors: Lucio Fernandez-Arjona
Date: 2020-05-05 00:00:00
Tasks: Feature Engineering, feature selection

Insurance companies make extensive use of Monte Carlo simulations in their capital and solvency models. To overcome the computational problems associated with Monte Carlo simulations, most large life insurance companies use proxy models such as replicating portfolios. In this paper, we present an example based on a variable annuity guarantee, showing the main challenges faced by practitioners in the construction of replicating portfolios: the feature engineering step and subsequent basis function selection problem. We describe how neural networks can be used as a proxy model and how to apply risk-neutral pricing on a neural network to integrate such a model into a market risk framework. The proposed model naturally solves the feature engineering and feature selection problems of replicating portfolios.
Bartlett's delta in the SABR model
Authors: Patrick S. Hagan, Andrew Lesniewski
Date: 2017-04-11 00:00:00
Tasks: model

We refine the analysis of hedging strategies for options under the SABR model carried out in [2]. In particular, we provide a theoretical justification of the empirical observation made in [2] that the modified delta ("Bartlett's delta") introduced there provides a more accurate and robust hedging strategy than the conventional SABR delta hedge.
Epidemic control via stochastic optimal control
Authors: Andrew Lesniewski
Date: 2020-04-14 00:00:00
Tasks: Epidemiology

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum principle. This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. We present a number of numerical solutions of the system under a variety of scenarios.
Quantization-based Bermudan option pricing in the $FX$ world
Authors: Jean-Michel Fayolle, Vincent Lemaire, Thibaut Montes, Gilles Pagès
Date: 2019-11-13 00:00:00
Tasks: Quantization

This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods.
The illiquidity network of stocks in China's market crash
Authors: Xiaoling Tan, Jichang Zhao
Date: 2020-04-04 00:00:00

The Chinese stock market experienced an abrupt crash in 2015, and over one-third of its market value evaporated. Given its associations with fear and the fine resolution with respect to frequency, the illiquidity of stocks may offer a promising perspective for understanding and even signaling a market crash. In this study, by connecting stocks with illiquidity comovements, an illiquidity network is established to model the market. Compared to noncrash days, on crash days, the market is more densely connected due to heavier but more homogeneous illiquidity dependencies that facilitate abrupt collapses. Critical stocks in the illiquidity network, particularly those in the finance sector, are targeted for inspection because of their crucial roles in accumulating and passing on illiquidity losses. The cascading failures of stocks in market crashes are profiled as disseminating from small degrees to high degrees that are usually located in the core of the illiquidity network and then back to the periphery. By counting the days with random failures in the previous five days, an early signal is implemented to successfully predict more than half of the crash days, especially consecutive days in the early phase. Additional evidence from both the Granger causality network and the random network further testifies to the robustness of the signal. Our results could help market practitioners such as regulators detect and prevent the risk of crashes in advance.
AutoAlpha: an Efficient Hierarchical Evolutionary Algorithm for Mining Alpha Factors in Quantitative Investment
Authors: Tianping Zhang, Yuanqi Li, Yifei Jin, Jian Li
Date: 2020-02-09 00:00:00
Tasks: Diversity, Ensemble Learning, Learning-To-Rank

The multi-factor model is a widely used model in quantitative investment. The success of a multi-factor model is largely determined by the effectiveness of the alpha factors used in the model. This paper proposes a new evolutionary algorithm called AutoAlpha to automatically generate effective formulaic alphas from massive stock datasets. Specifically, first we discover an inherent pattern of the formulaic alphas and propose a hierarchical structure to quickly locate the promising part of space for search. Then we propose a new Quality Diversity search based on the Principal Component Analysis (PCA-QD) to guide the search away from the well-explored space for more desirable results. Next, we utilize the warm start method and the replacement method to prevent the premature convergence problem. Based on the formulaic alphas we discover, we propose an ensemble learning-to-rank model for generating the portfolio. The backtests in the Chinese stock market and the comparisons with several baselines further demonstrate the effectiveness of AutoAlpha in mining formulaic alphas for quantitative trading.
Copula-based local dependence between energy, agriculture and metal commodity markets
Authors: Claudiu Albulescu, Aviral Tiwari, Qiang Ji
Date: 2020-03-09 00:00:00
Tasks: Management

This paper studies the extreme dependencies between energy, agriculture and metal commodity markets, with a focus on local co-movements, allowing the identification of asymmetries and changing trend in the degree of co-movements. More precisely, starting from a non-parametric mixture copula, we use a novel copula-based local Kendall's tau approach to measure nonlinear local dependence in regions. In all pairs of commodity indexes, we find increased co-movements in extreme situations, a stronger dependence between energy and other commodity markets at lower tails, and a 'V-type' local dependence for the energy-metal pairs. The three-dimensional Kendall's tau plot for upper tails in quantiles shows asymmetric co-movements in the energy-metal pairs, which tend to become negative at peak returns. Therefore, we show that the energy market can offer diversification solutions for risk management in the case of extreme bull market events.
Coronavirus and financial volatility: 40 days of fasting and fear
Authors: Claudiu Albulescu
Date: 2020-03-09 00:00:00

40 days after the start of the international monitoring of COVID-19, we search for the effect of official announcements regarding new cases of infection and death ratio on the financial markets volatility index (VIX). Whereas the new cases reported in China and outside China have a mixed effect on financial volatility, the death ratio positively influences VIX, that outside China triggering a more important impact. In addition, the higher the number of affected countries, the higher the financial volatility is.
Convex Optimization Over Risk-Neutral Probabilities
Authors: Shane Barratt, Jonathan Tuck, Stephen Boyd
Date: 2020-03-05 00:00:00

We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in particular, any risk neutral distribution can be interpreted as a certificate establishing that no arbitrage exists. We are interested in the case when there are multiple risk-neutral probabilities. We describe a number of convex optimization problems over the convex set of risk neutral price probabilities. These include computation of bounds on the cumulative distribution, VaR, CVaR, and other quantities, over the set of risk-neutral probabilities. After discretizing the underlying price, these problems become finite dimensional convex or quasiconvex optimization problems, and therefore are tractable. We illustrate our approach using real options and futures pricing data for the S&P 500 index and Bitcoin.
Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs
Authors: Yongyang Cai, Kenneth Judd, Rong Xu
Date: 2020-03-03 00:00:00
Tasks: Portfolio Optimization

We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple assets, and many trading periods in a finite horizon problem. We also solve dynamic stochastic problems, with a portfolio including one risk-free asset, an option, and its underlying risky asset, under the existence of transaction costs and constraints. These examples show that it is now tractable to solve such problems.
Optimal exit decision of venture capital under time-inconsistent preferences
Authors: Yanzhao Li, Ju'e Guo, Yongwu Li, Xu Zhang
Date: 2021-03-22 00:00:00

This paper proposes two kinds of time-inconsistent preferences (i.e. time flow inconsistency and critical time point inconsistency) to further advance the research on the exit decision of venture capital. Time-inconsistent preference, different from time-consistent preference, assumes that decision makers prefer recent returns rather than future returns. Based on venture capitalists' understanding of future preferences, we consider four types of venture capitalists, namely time-consistent venture capitalists, venture capitalists who only realize critical time point inconsistency, naive venture capitalists and sophisticated venture capitalists, of which the latter three are time-inconsistent. All types of time-inconsistent venture capitalists are aware of critical time point inconsistency. Naive venture capitalists misunderstand time flow inconsistency while sophisticated ones understand it correctly. We propose an optimal exit timing of venture capital model. Then we derive and compare the above four types of venture capitalists' exit thresholds. The main results are as follows: (1) all types of time-inconsistent venture capitalists tend to exit earlier than time-consistent venture capitalists. (2) The longer the expire date are, the more likely venture capitalists are to delay the exit, but the delay degree decreases successively (venture capitalists who only realize critical time point inconsistency > naive venture capitalists > sophisticated venture capitalists).
Quantum propensity in economics
Authors: David Orrell, Monireh Houshmand
Date: 2021-03-13 00:00:00
Tasks: Decision Making

This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision-makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized to incorporate effects such as interference and entanglement that characterise human decision-making. Applications to some common problems in economics and finance are discussed.
Optimal Bookmaking
Authors: Matthew Lorig, Zhou Zhou, Bin Zou
Date: 2019-07-01 00:00:00

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks a price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or characterizations to the bookmaker's optimal bookmaking problem in various interesting models.
Liquidity in Competitive Dealer Markets
Authors: Peter Bank, Ibrahim Ekren, Johannes Muhle-Karbe
Date: 2018-07-22 00:00:00

We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market with finite liquidity. This endogenously leads to transient price impact in the dealer market. Smooth, diffusive, and discrete trades all incur finite but nontrivial liquidity costs, and can arise naturally from the liquidity takers' optimization.
The Origination and Distribution of Money Market Instruments: Sterling Bills of Exchange during the First Globalization
Authors: Olivier Accominotti, Delio Lucena-Piquero, Stefano Ugolini
Date: 2021-03-02 00:00:00
Tasks: Descriptive

This paper presents a detailed analysis of how liquid money market instruments -- sterling bills of exchange -- were produced during the first globalisation. We rely on a unique data set that reports systematic information on all 23,493 bills re-discounted by the Bank of England in the year 1906. Using descriptive statistics and network analysis, we reconstruct the complete network of linkages between agents involved in the origination and distribution of these bills. Our analysis reveals the truly global dimension of the London bill market before the First World War and underscores the crucial role played by London intermediaries (acceptors and discounters) in overcoming information asymmetries between borrowers and lenders on this market. The complex industrial organisation of the London money market ensured that risky private debts could be transformed into extremely liquid and safe monetary instruments traded throughout the global financial system.
Reducing the Volatility of Cryptocurrencies -- A Survey of Stablecoins
Authors: Ayten Kahya, Bhaskar Krishnamachari, Seokgu Yun
Date: 2021-03-01 00:00:00
Tasks: Survey

In the wake of financial crises, stablecoins are gaining adoption among digital currencies. We discuss how stablecoins help reduce the volatility of cryptocurrencies by surveying different types of stablecoins and their stability mechanisms. We classify different approaches to stablecoins in three main categories i) fiat or asset backed, ii) crypto-collateralized and iii) algorithmic stablecoins, giving examples of concrete projects in each class. We assess the relative tradeoffs between the different approaches. We also discuss challenges associated with the future of stablecoins and their adoption, their adoption and point out future research directions.
Stability of Equilibrium Asset Pricing Models: A Necessary and Sufficient Condition
Authors: Jaroslav Borovicka, John Stachurski
Date: 2019-10-02 00:00:00

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Finally, we discuss computation of the test value associated with our condition, providing a Monte Carlo method that is naturally parallelizable.