pwc-archive/papers-with-abstracts huggingface dataset:
Pricing and Hedging the No-Negative-Equity Guarantee in Equity-Release Mortgages
Authors: Kevin Engelbrecht, Saul Jacka
Date: 2020-10-06 00:00:00

We provide a practical superhedging strategy for the pricing and hedging of the No-Negative-Equity-Guarantee (NNEG) found in Equity-Release Mortgages (ERMs), or reverse mortgages, using a discrete-time model. In contrast to many papers on the NNEG and industry practice we work in an incomplete market setting so that deaths and property prices are not independent under most pricing measures. We give theoretical results and numerical illustrations to show that the assumption of market completeness leads to a considerable undervaluation of the NNEG. By introducing an Excess-of-Loss reinsurance asset, we show that it is possible to reduce the cost of the superhedge for a portfolio of ERMs with the average cost decreasing rapidly as the number of lives in the portfolio increases. All the hedging assets, with the exception of cash, have a term of one year making the availability of a property hedging asset from over-the-counter derivative providers more realistic. We outline how a practical multi-period ERM pricing and hedging model can be built. Although the prices identified by this model will be higher than prices under the completeness assumption, they are considerably lower than those under the Equivalent Value Test mandated by the UK's Prudential Regulatory Authority.
Group cohesion under individual regulatory constraints
Authors: Delia Coculescu, Freddy Delbaen
Date: 2020-10-03 00:00:00

We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures.
Convergence of utility indifference prices to the superreplication price in a multiple-priors framework
Authors: Romain Blanchard, Laurence Carassus
Date: 2017-09-27 00:00:00

This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion.
Risk-neutral pricing for APT
Authors: Laurence Carassus, Miklos Rasonyi
Date: 2019-04-25 00:00:00

We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity.
Equilibrium concepts for time-inconsistent stopping problems in continuous time
Authors: Erhan Bayraktar, Jingjie Zhang, Zhou Zhou
Date: 2019-09-03 00:00:00

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.
X-Value adjustments: accounting versus economic management perspectives
Authors: Alberto Elices
Date: 2020-09-09 00:00:00
Tasks: Management

This paper provides a mathematical framework based on the principle of invariance to classify institutions in two paradigms according to the way in which credit, debit and funding adjustments are calculated: accounting and management perspectives. This conceptual classification helps to answer questions such as: In which paradigm each institution sits (point of situation)? Where is the market consensus and regulation pointing to (target point)? What are the implications, pros and cons of switching perspective to align with future consensus (design of a transition)? An improved solution of the principle of invariance equations is presented to calculate these metrics avoiding approximations and irrespective of the discounting curve used in Front Office systems. The perspective is changed by appropriate selection of inputs always using the same calculation engine. A description of balance sheet financing is presented along with the justification of the funding curves used for both perspectives.
Fairness principles for insurance contracts in the presence of default risk
Authors: Delia Coculescu, Freddy Delbaen
Date: 2020-09-09 00:00:00
Tasks: Fairness

We use the theory of cooperative games for the design of fair insurance contracts. An insurance contract needs to specify the premium to be paid and a possible participation in the benefit (or surplus) of the company. It results from the analysis that when a contract is exposed to the default risk of the insurance company, ex-ante equilibrium considerations require a certain participation in the benefit of the company to be specified in the contracts. The fair benefit participation of agents appears as an outcome of a game involving the residual risks induced by the default possibility and using fuzzy coalitions.
Multi-utility representations of incomplete preferences induced by set-valued risk measures
Authors: Cosimo Munari
Date: 2020-09-09 00:00:00

We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that are both parsimonious (the family of representing functionals is indexed by a tractable set of parameters) and well behaved (the representing functionals satisfy nice regularity properties with respect to the structure of the underlying space of alternatives). The key to our results is a general dual representation of set-valued risk measures that unifies the existing dual representations in the literature and highlights their link with duality results for scalar risk measures.
Alòs type decomposition formula for Barndorff-Nielsen and Shephard model
Authors: Takuji Arai
Date: 2020-05-15 00:00:00
Tasks: Vocal Bursts Type Prediction

The objective is to provide an Al\`os type decomposition formula of call option prices for the Barndorff-Nielsen and Shephard model: an Ornstein-Uhlenbeck type stochastic volatility model driven by a subordinator without drift. Al\`os (2012) introduced a decomposition expression for the Heston model by using Ito's formula. In this paper, we extend it to the Barndorff-Nielsen and Shephard model. As far as we know, this is the first result on the Al\`os type decomposition formula for models with infinite active jumps.
Skewing Quanto with Simplicity
Authors: George Hong
Date: 2020-09-05 00:00:00

We present a simple and highly efficient analytical method for solving the Quanto Skew problem in Equities under a framework that accommodates both Equity and FX volatility skew consistently. Ease of implementation and extremely fast performance of this new approach should benefit a wide spectrum of market participants.
An approximate solution for options market-making in high dimension
Authors: Bastien Baldacci, Joffrey Derchu, Iuliia Manziuk
Date: 2020-09-02 00:00:00
Tasks: Dimensionality Reduction, Vocal Bursts Intensity Prediction

Managing a book of options on several underlying involves controlling positions of several thousands of financial assets. It is one of the most challenging financial problems involving both pricing and microstructural modeling. An options market maker has to manage both long- and short-dated options having very different dynamics. In particular, short-dated options inventories cannot be managed as a part of an aggregated inventory, which prevents the use of dimensionality reduction techniques such as a factorial approach or first-order Greeks approximation. In this paper, we show that a simple analytical approximation of the solution of the market maker's problem provides significantly higher flexibility than the existing algorithms designing options market making strategies.
Optimal Hedging in Incomplete Markets
Authors: George Bouzianis, Lane P. Hughston
Date: 2020-06-23 00:00:00
Tasks: Position

We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of a L\'evy-Ito market, where assets are driven jointly by an $n$-dimensional Brownian motion and an independent Poisson random measure on an $n$-dimensional state space. Given a position in need of hedging and the instruments available as hedges, we demonstrate the existence of an optimal hedge portfolio, where optimality is defined by use of an expected least squared-error criterion over a specified time frame, and where the numeraire with respect to which the hedge is optimized is taken to be the benchmark process associated with the designated pricing kernel.
XVA Analysis From the Balance Sheet
Authors: Claudio Albanese, Stephane Crepey, Rodney Hoskinson, Bouazza Saadeddine
Date: 2020-09-01 00:00:00
Tasks: GPU

XVAs denote various counterparty risk related valuation adjustments that are applied to financial derivatives since the 2007--09 crisis. We root a cost-of-capital XVA strategy in a balance sheet perspective which is key in identifying the economic meaning of the XVA terms. Our approach is first detailed in a static setup that is solved explicitly. It is then plugged in the dynamic and trade incremental context of a real derivative banking portfolio. The corresponding cost-of-capital XVA strategy ensures to bank shareholders a submartingale equity process corresponding to a target hurdle rate on their capital at risk, consistently between and throughout deals. Set on a forward/backward SDE formulation, this strategy can be solved efficiently using GPU computing combined with deep learning regression methods in a whole bank balance sheet context. A numerical case study emphasizes the workability and added value of the ensuing pathwise XVA computations.
Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing
Authors: Will Hicks
Date: 2020-09-01 00:00:00

Financial models based on the Wick product, and White Noise formalism have previously been suggested in order to incorporate integrals with respect to fractional Brownian motion. It has also been pointed out that this leads naturally to a quantum mechanical interpretation of the financial market. In this article we pursue this idea further, and in particular show how the framework of quantum probability can be used to construct Martingales, without relying on Brownian integrals. We go on to suggest benefits of doing so, and avenues for future work.
Portfolio Optimization with Sparse Multivariate Modelling
Authors: Pier Francesco Procacci, Tomaso Aste
Date: 2021-03-28 00:00:00
Tasks: Portfolio Optimization

Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2. uncertainties resulting from parameters' sampling error; 3. intrinsic non-stationarity of these systems. For what concerns point 1. we propose a L0-norm sparse elliptical modeling and show that sparsification is effective. The effects of points 2. and 3. are quantifified by studying the models' likelihood in- and out-of-sample for parameters estimated over train sets of different lengths. We show that models with larger off-sample likelihoods lead to better performing portfolios up to when two to three years of daily observations are included in the train set. For larger train sets, we found that portfolio performances deteriorate and detach from the models' likelihood, highlighting the role of non-stationarity. We further investigate this phenomenon by studying the out-of-sample likelihood of individual observations showing that the system changes significantly through time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of lower likelihood in the short-term: the `optimal' fit in finance needs to be defined in terms of the holding period. Lastly, we show that sparse models outperform full-models in that they deliver higher out of sample likelihood, lower realized portfolio volatility and improved portfolios' stability, avoiding typical pitfalls of the Mean-Variance optimization.
A Deep Deterministic Policy Gradient-based Strategy for Stocks Portfolio Management
Authors: Huanming Zhang, Zhengyong Jiang, Jionglong Su
Date: 2021-03-21 00:00:00
Tasks: GPU, Management

With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel portfolio management strategy based on the framework of Deep Deterministic Policy Gradient, a policy-based reinforcement learning framework, and compare its performance to that of other trading strategies. In our framework, two Long Short-Term Memory neural networks and two fully connected neural networks are constructed. We also investigate the performance of our strategy with and without transaction costs. Experimentally, we choose eight US stocks consisting of four low-volatility stocks and four high-volatility stocks. We compare the compound annual return rate of our strategy against seven other strategies, e.g., Uniform Buy and Hold, Exponential Gradient and Universal Portfolios. In our case, the compound annual return rate is 14.12%, outperforming all other strategies. Furthermore, in terms of Sharpe Ratio (0.5988), our strategy is nearly 33% higher than that of the second-best performing strategy.
Multi-Period Portfolio Optimization using Model Predictive Control with Mean-Variance and Risk Parity Frameworks
Authors: Xiaoyue Li, A. Sinem Uysal, John M. Mulvey
Date: 2021-03-19 00:00:00
Tasks: Model Predictive Control, Portfolio Optimization

We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective, and provide a successive convex program algorithm that provides 30 times faster and robust solutions in the experiments. Computational results on the multi-asset universe show that multi-period models perform better than their single period counterparts in out-of-sample period, 2006-2020. The out-of-sample risk-adjusted performance of both mean-variance and risk-parity formulations beat the fix-mix benchmark, and achieve Sharpe ratio of 0.64 and 0.97, respectively.
Statistical Arbitrage Risk Premium by Machine Learning
Authors: Raymond C. W. Leung, Yu-Man Tam
Date: 2021-03-18 00:00:00
Tasks: BIG-bench Machine Learning, Position

How to hedge factor risks without knowing the identities of the factors? We first prove a general theoretical result: even if the exact set of factors cannot be identified, any risky asset can use some portfolio of similar peer assets to hedge against its own factor exposures. A long position of a risky asset and a short position of a "replicate portfolio" of its peers represent that asset's factor residual risk. We coin the expected return of an asset's factor residual risk as its Statistical Arbitrage Risk Premium (SARP). The challenge in empirically estimating SARP is finding the peers for each asset and constructing the replicate portfolios. We use the elastic-net, a machine learning method, to project each stock's past returns onto that of every other stock. The resulting high-dimensional but sparse projection vector serves as investment weights in constructing the stocks' replicate portfolios. We say a stock has high (low) Statistical Arbitrage Risk (SAR) if it has low (high) R-squared with its peers. The key finding is that "unique" stocks have both a higher SARP and higher excess returns than "ubiquitous" stocks: in the cross-section, high SAR stocks have a monthly SARP (monthly excess returns) that is 1.101% (0.710%) greater than low SAR stocks. The average SAR across all stocks is countercyclical. Our results are robust to controlling for various known priced factors and characteristics.
A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data
Authors: Sakae Oya
Date: 2021-03-10 00:00:00
Tasks: Management

Managing a large-scale portfolio with many assets is one of the most challenging tasks in the field of finance. It is partly because estimation of either covariance or precision matrix of asset returns tends to be unstable or even infeasible when the number of assets $p$ exceeds the number of observations $n$. For this reason, most of the previous studies on portfolio management have focused on the case of$ p < n$. To deal with the case of $p > n$, we propose to use a new Bayesian framework based on adaptive graphical LASSO for estimating the precision matrix of asset returns in a large-scale portfolio. Unlike the previous studies on graphical LASSO in the literature, our approach utilizes a Bayesian estimation method for the precision matrix proposed by Oya and Nakatsuma (2022) so that the positive definiteness of the precision matrix should be always guaranteed. As an empirical application, we construct the global minimum variance portfolio of $p = 100$ for various values of n with the proposed approach as well as the non-Bayesian graphical LASSO approach, and compare their out-of-sample performance with the equal weight portfolio as the benchmark. In this comparison, the proposed approach produces more stable results than the non-Bayesian approach in terms of Sharpe ratio, portfolio composition and turnover. Furthermore, the proposed approach succeeds in estimating the precision matrix even if $n$ is much smaller than $p$ and the non-Bayesian approach fails to do so.
Portfolio Optimization Constrained by Performance Attribution
Authors: Yuan Hu, W. Brent Lindquist
Date: 2021-03-07 00:00:00
Tasks: Portfolio Optimization

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize expected tail loss and investigate both asset allocation (AA) and the selection effect (SE) as hard constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index; the benchmark is an equi-weighted portfolio of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures maximum drawdown, Sharpe ratio, and Rachev ratio. The results suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE, with SE constraints producing the larger performance enhancement.
Optimizing Expected Shortfall under an $\ell_1$ constraint -- an analytic approach
Authors: Gábor Papp, Imre Kondor, Fabio Caccioli
Date: 2021-03-07 00:00:00
Tasks: Time Series Analysis

Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio $r=N/T$, where $N$ is the number of different assets in the portfolio, and $T$ is the length of the available time series. The critical ratio depends on the confidence level $\alpha$, which means we have a line of critical points on the $\alpha-r$ plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an $\ell_1$ regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e. a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric $\ell_1$ regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio $r=N/T$, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters.
The Climate Extended Risk Model (CERM)
Authors: Josselin Garnier, Jean-Baptiste Gaudemet, Anne Gruz
Date: 2021-03-04 00:00:00
Tasks: model

This paper addresses estimates of climate risk embedded within a bank credit portfolio. The proposed Climate Extended Risk Model (CERM) adapts well known credit risk models and makes it possible to calculate incremental credit losses on a loan portfolio that are rooted into physical and transition risks. The paper provides detailed description of the model hypotheses and steps.
Climate Change Valuation Adjustment (CCVA) using parameterized climate change impacts
Authors: Chris Kenyon, Mourad Berrahoui
Date: 2021-02-21 00:00:00

We introduce Climate Change Valuation Adjustment (CCVA) to capture climate change impacts on CVA+FVA that are currently invisible assuming typical market practice. To discuss such impacts on CVA+FVA from changes to instantaneous hazard rates we introduce a flexible and expressive parameterization to capture the path of this impact to climate change endpoints, and transient transition effects. Finally we provide quantification of examples of typical interest where there is risk of economic stress from sea level change up to 2101, and from transformations of business models. We find that even with the slowest possible uniform approach to a climate change impact in 2101 there can still be significant CVA+FVA impacts on interest rate swaps of 20 years or more maturity. Transformation effects on CVA+FVA are strongly dependent on timing and duration of business model transformation. Using a parameterized approach enables discussion with stakeholders of economic impacts on CVA+FVA, whatever the details behind the climate impact.