We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimiz…
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48 results for “Locally Risk-Minimizing Strategies”
We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential Lévy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly model-independent upper estimations for the difference. In addition we show numerical example…
Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard modelsq-fin.CP
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
problem Calculating locally risk-minimizing strategies for non-martingale BNS models with infinite active jumps.
method Modified Malliavin calculus expression and Monte Carlo method for non-martingale BNS models.
result Proposes a numerical method for LRM strategies in non-martingale BNS models with infinite active jumps.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the optimal strategy in terms of suitable decompositions of a given contingent claim, wit…
New method for valuing and hedging credit risk when defaults cannot be hedged.
problem Valuation and hedging of counterparty credit risk when there's no protection available.
method Local risk-minimization approach via BSDE (Backward Stochastic Differential Equation)
result Optimal strategy computed for valuing and hedging credit risk.
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure …
Enhanced Gordon growth model for valuing financial products.
problem Valuation of financial products with time-varying interest rates and dividends.
method Dynamic Gordon growth model with time-varying spot interest rate and dividends, risk-neutral valuation, locally risk-minimizing strategy.
result Pricing and hedging formulas for dividend-paying European options and equity-linked life insurance products.
In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of in…
This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer-Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes the situation where the correlation between the market model and the time o…
The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extre…
We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal m…
We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are paid continuously and symmetrically and introduce the concept of tax- and expense-modified risk-minimization. Risk-minim…
A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatilityq-fin.PR
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and constructive methodology w…
Local risk-minimization with multiple assets under illiquidity with applications in energy marketsq-fin.MF
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and inc…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minim…
BSDEs driven by cylindrical martingales with application to approximate hedging in bond marketsmath.PR
We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs and prove that the sequence of solutions of corresponding finite-dimensional BSDEs…
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]
Hedging of defaultable claims in a structural model using a locally risk-minimizing approachq-fin.MF
In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on…
In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and [16], we introduce risk indifference price, marginal risk price and derivative he…
This guide simplifies high-probability regret bounds in empirical risk minimization.
problem High-probability regret bounds in empirical risk minimization.
method Modular presentation, three-step recipe, localized Rademacher complexity, local maximal inequalities, metric-entropy integrals.
result Recover familiar rates for various function classes and derive regret bounds for nuisance components.
In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the numéraire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in…
We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Merton…
Paper studies pricing and hedging of nonreplicable insurance contracts using benchmark-neutral approach.
problem Pricing and hedging of long-term insurance contracts like variable annuities.
method Benchmark-neutral pricing framework using stock growth optimal portfolio as numéraire.
result Prices can be significantly lower than risk-neutral ones, offering attractive long-term risk-management.
Empirical Risk Minimization in the Interpolating Regime with Application to Neural Network Learningstat.ML
A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the presence of lots of label noise, corroborate such a procedure. On the other hand, in…
Taylor Learningstat.ML
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
Paper analyzes minimax risks of personalized federated learning algorithms.
problem Statistical heterogeneity among clients in federated learning.
method Minimax analysis of FedAvg and local training approaches.
result Threshold for optimality between FedAvg and local training depends on data heterogeneity.
Optimizes exp-concave losses with a new risk bound.
problem Optimizing exp-concave losses with stochastic convex optimization.
method Empirical Risk Minimization with a unified geometric assumption and local norms.
result Provides an excess risk bound.
The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: …
Risk-minimization and hedging claims on a jump-diffusion market model, Feynman-Kac Theorem and PIDEq-fin.PR
At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratings on which prices are influenced by additional factors and rating, and behavior of this system is described by SDE driven by Wiener process…
We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using the Galtchouk-Kunita-Watanabe decomposition of the counterparty risk price paymen…
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malliavin derivatives. Our goal is to extend it to random variables which a…
Paper shows robust estimators converge to true risk minimizers at optimal rates.
problem Understanding asymptotic properties of robust risk minimizers.
method Investigates robust analogues of empirical risk minimization, focusing on median of means estimator.
result Robust minimizers converge to true minimizers at optimal rates and have similar asymptotic variance.
The paper develops fair machine learning models using causal path-specific effects.
problem Fairness in machine learning models under causal constraints.
method Lagrange multiplier approach for infinite-dimensional functional estimation, closed-form solutions for constrained optimization.
result Theoretical and flexible semiparametric estimation strategies for fair predictions.
Deep Quadratic Hedgingq-fin.CP
Deep learning solves high-dimensional quadratic hedging problems.
problem High-dimensional incomplete markets with mean-variance and local risk minimization.
method Deep learning-based BSDE solver for optimal hedging strategies.
result High-dimensional quadratic hedging is efficiently computed with deep learning.
Local risk-minimization for Barndorff-Nielsen and Shephard models with volatility risk premiumq-fin.MF
We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two par…
Study on optimal strategies for minimizing shortfall risk in game options.
problem Existence of optimal hedging strategies for shortfall risk in game options.
method Continuous time Black--Scholes model, finite and infinite exercise times.
result Optimal strategies exist for finite exercise times but not for all time intervals.
Decentralized learning achieves centralized performance via Gibbs measures.
problem Achieving centralized performance in decentralized machine learning.
method ERM-RER learning framework with Gibbs measures and relative-entropy regularization.
result Achieving centralized performance with Gibbs measures and specific scaling of regularization factors.
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a non-trivial exercise due…
Deep Hedging to Manage Tail Riskq-fin.PM
Deep neural networks reduce portfolio tail-risk by 99% in crisis-era simulations.
problem Managing tail risk in financial portfolios.
method Parameterizing convex-risk minimization with deep neural networks.
result Significant reduction in one-day 99% CVaR.
Improved ADMM for convex distributed learning with differential privacy.
problem Privacy concerns in distributed learning with sensitive data.
method Approximate multi-step ADMM with calibrated noise.
result Higher utility and error bounds asymptotic to state-of-the-art.
On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regressionmath.OC
Accelerates ERM problems with LPI-GD and improved oracle complexity.
problem Empirical Risk Minimization (ERM) problems with strong convexity and smoothness.
method Local Polynomial Interpolation-based Gradient Descent (LPI-GD) and accelerated methods.
result Oracle complexity improved to $ ilde{O}\left(\sqrtσ m^d \log(1/\varepsilon)
ight)$.
The paper analyzes local minima in high-dimensional empirical risk minimization.
problem Understanding local minima in high-dimensional data models.
method Using Kac-Rice formula and proportional asymptotics, the paper derives bounds on local minima.
result Sharp asymptotics on estimation and prediction errors are derived.