The paper analyzes drawdowns in Lévy processes, focusing on magnitude, asymptotics, and duration.
problem Magnitude, asymptotics, and duration of drawdowns in Lévy processes.
method Approximation and asymptotic analysis of drawdown quantities for spectrally negative Lévy processes.
result The law of duration of drawdowns for a wide class of Lévy processes, including TTR.
Study optimizes portfolio to minimize relative drawdown duration, penalizing unfavorable performance states.
problem Minimizing relative drawdown duration in portfolio optimization relative to a benchmark.
method Introduces a benchmark-relative drawdown-duration criterion penalizing unfavorable performance states. Uses a one-dimensional Markovian representation and Hamilton-Jacobi-Bellman equation.
result Derives explicit projection-based characterization of the optimal feedback control and identifies geometric settings for unique strong solutions.
New method ranks assets better than traditional methods by considering drawdown durations.
problem Traditional asset ranking methods are biased and less robust.
method Uses total drawdown durations to estimate Sharpe ratios.
result New method yields significantly different rankings, especially in volatile periods.
Method simulates drawdown and duration in Lévy models using Gaussian approximation.
problem Simulating drawdown and duration in Lévy models with high jump activity.
method Stick-breaking Gaussian approximation for simulation, bounds on Wasserstein distances.
result Good agreement between theoretical bounds and numerical performance.
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture the risks to which invest…
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with respect to the bulk of drawdown price movement distribution. This paper goes on dee…
The study tests a functional-form restriction on risk exposure dynamics using margin debt data.
problem Understanding risk exposure dynamics under capital constraints and slack.
method Testing a regime-conditional functional-form restriction on aggregate risk-exposure dynamics implied by VaR-constrained intermediary models.
result The contraction and growth of exposures under capital constraints and slack are observed and tested.
Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension associated with the passage of time. In this paper, the concept of temporal pat…
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the asset value. We first consider a vanilla insurance contract whereby the protectio…
Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side of severity by studying the first drawdown over certain pre-specified size. In th…
The paper optimizes portfolios to minimize drawdown, outperforming market indices.
problem Minimizing drawdown in financial portfolios.
method Formulated as a nonlinear program, partially linearized, solved using SCIP.
result Minimal drawdown portfolios outperform market indices in return, Sharpe ratio, maximum and average drawdown.
Develops a method to manage drawdown risk in Kelly gambling.
problem Managing drawdown risk in Kelly gambling with uncertain outcomes.
method Develops a convex optimization problem to bound drawdown probability, trading off growth rate and risk.
result Shows that the convex optimization method outperforms fractional-Kelly bets for the same drawdown risk level or growth rate.
Paper adds a restart mechanism to a drawdown control policy for better trading performance.
problem Missed profitable opportunities when drawdown limit is close to reality.
method Integrates a data-driven restart mechanism into the drawdown modulation trading system.
result The restart mechanism improves trading performance even with transaction costs.
The paper studies drawdown times in Lévy risk processes, generalizing previous results.
problem Analyzing the time of drawdown in spectrally negative Lévy risk processes.
method Using the joint distribution of drawdown times, maximums, and other related quantities.
result Obtained semi-explicit expressions for the joint distribution in terms of scale functions and Lévy measure.
New control strategy mitigates stock trading drawdowns.
problem Mitigating drawdowns in stock trading.
method Drawdown-modulated feedback control using control theory.
result Optimal investment strategy that maximizes logarithmic growth.
Develops a new framework for drawdown risk beyond Gaussian assumptions.
problem Understanding drawdowns in systematic trading strategies.
method Monte-Carlo simulation, non-Gaussian extensions, fractional Brownian motion.
result Drawdowns and related measures vary differently under non-Gaussian assumptions.
The paper calculates fair premiums and optimal stopping rules for equity-linked contracts tied to drawdown and drawup events.
problem Fair valuation of equity-linked contracts tied to drawdown and drawup events.
method Fluctuation theory of Lévy processes and optimal stopping theory.
result Calculation of fair premiums and optimal stopping rules for equity-linked contracts.
Modeling maximum drawdown records in capital markets using PDMP.
problem Capturing the statistical properties of maximum drawdown records in financial markets.
method Piecewise Deterministic Markov Process (PDMP) for modeling, statistical analysis of mean and variance, simulation study, parameter estimation techniques.
result Derivation of statistical results including mean and variance of maximum drawdown records.
Paper improves fractional trading for risk-averse investors by considering current drawdowns.
problem Optimizing trading strategies for risk-averse investors.
method Reconsidered fractional trading ansatz with current drawdown risk measure.
result Optimal fraction solutions better reflect risk-averse investor needs.
We study the risk criterion for investments based on the drawdown from the maximal value of the capital in the past. Depending on investor's risk attitude, thus his risk exposure, we find that the distribution of these drawdowns follows a general power law. In particular, if the risk exposure is Kelly-optimal, the expo…
The paper quantifies when a trading strategy's drawdown becomes a cause for concern.
problem Detecting when a profitable trading strategy starts to degrade over time.
method Quantitative analysis of drawdown length and depth for upward drifting Brownian motions.
result Drawdowns lasting too long or being too deep indicate a need to revise the strategy's Sharpe ratio.
Investment strategy to minimize drawdown time in a financial market.
problem Minimizing the expected time in drawdown during lifetime.
method Optimal investment strategy in a Black-Scholes market for proportional consumption.
result Individual is myopic in investing, as shown by comparing with related problems.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
Unified approach for drawdown and drawup of Markov processes.
problem Study of drawdown and drawup in time-homogeneous Markov processes.
method Short-time pathwise analysis, integral equation solution.
result Unified approach to study various drawdown quantities.
The paper calculates premiums and optimal stopping rules for insurance contracts with Lévy assets.
problem Calculating fair premiums and optimal stopping rules for insurance contracts with Lévy assets.
method Solving two-sided exit problems related to drawdown and drawup of spectrally negative Lévy processes, and optimal stopping theory.
result Fair premiums and optimal stopping rules identified for various insurance contracts.
Paper builds risk measures for portfolio theory, focusing on drawdown risk.
problem Calculating efficient portfolios with drawdown risk constraints.
method Develops convex risk measures for portfolio theory, including drawdown-based measures.
result Calculates efficient portfolios using drawdown risk constraints.
Unified framework for drawdown risk computation under Markov models.
problem High computational challenges in drawdown risk metrics.
method Unified framework for computing five drawdown quantities under general Markov models, using linear systems and efficient algorithms.
result Efficient algorithms achieve same complexity as path-independent problems, validated by rigorous convergence analysis and extensive experiments.
In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the dr…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…
Paper calculates perpetual put option pricing with drawdown cap.
problem Pricing perpetual American put options with drawdown constraints.
method Derives explicit formula using Black-Scholes model and martingale theory.
result Optimal exercise occurs at first drawdown below a threshold.
Investors with anxiety about drawdowns may use stop-loss and trailing stops as optimal selling strategies.
problem Investors' anxiety about drawdowns affects optimal selling strategies.
method Mathematical analysis of optimal stopping with random discounting.
result Stop-loss and trailing stops can be optimal selling strategies under anxiety about drawdowns.
This paper shows Markowitz-style strategies are inefficient when considering drawdown risk.
problem Inefficiency of Markowitz-style investment strategies in recursive betting scenarios.
method Use of drawdown as risk metric, time-varying linear feedback block K(k) called the drawdown modulator.
result Classical Markowitz-style strategies are inefficient when considering drawdown risk.
The study characterizes honest times and extends semimartingale class for option pricing.
problem Characterizing honest times and extending semimartingale class for option pricing.
method Characterization of honest times using drawdown and relative drawdown representations, extending semimartingale class to include jumps.
result Established Madan-Roynette-Yor option pricing formula for a broader class of processes.
Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum dr…
Bayesian analysis optimizes stop-loss thresholds based on drawdown distributions.
problem Arbitrary stop-loss levels in financial strategies.
method Bayesian analysis of drawdown distributions.
result Systematic selection of optimal stop-loss thresholds.
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
problem Pricing perpetual American put options with a drawdown event in a Lévy market.
method Derives explicit price using geometric Lévy process with downward jumps, optimal stopping rule, and martingale arguments.
result Optimal stopping rule is the first time asset price falls below a specific value.
The study identifies factors predicting stock returns and maximum drawdown using various models.
problem Predicting stock returns and maximum drawdown in the US equity market.
method Supervised learning with multiple models (OLS, penalized linear regressions, tree-based models, neural networks) over 49 years of data.
result Non-linear models outperformed linear models in predicting stock returns and maximum drawdown, especially during calm periods.
Study portfolio optimization with partial info and drawdown constraints using deep learning.
problem Optimizing portfolios with partial information and maximum drawdown constraints.
method Bayesian framework, dynamic programming, semi-explicit solutions, deep learning for stochastic control.
result Numerical solutions and performance analysis with deep learning, convergence to Merton problem.
Market valuation duration is 175 years, but drops to 46 years during crises.
problem Understanding the duration of market valuation and its impact on returns.
method Comparing market valuation ratios and dividends to estimate duration, analyzing the discount rate effect.
result Valuation duration is negatively correlated with market returns, with a robust out-of-sample R2 of 15%.
New model predicts financial transaction durations using quantiles.
problem Modeling financial transaction durations using traditional mean duration.
method Proposes a new autoregressive conditional duration model based on log-symmetric distributions reparametrized by quantiles.
result Proposed model allows for modeling different percentiles of financial transaction durations.
The paper develops bootstrap methods for ACD models with random durations.
problem Bootstrap inference for autoregressive duration models with random durations.
method Recursive schemes for fixed calendar span or realized event count.
result The bootstrap method reproduces the conditional Gaussian component for ACD models with 0<κ<1. A modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve and interest-bearing cash.
problem Drawdown control
method Continuous cash-overlay filters
result Earnings an 18.83% CAGR versus 16.62% for 100% R
In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting…
We study the class of Azéma-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown…
New model improves inference on asset market durations.
problem Statistical artifacts in trade aggregation.
method Flexible stochastic duration model with uncertainty in related trades.
result Conditional hazard function varies less than previous studies.
The paper proposes a trading strategy using Ornstein-Uhlenbeck processes and analyzes their maximum drawdown.
problem Analyzing the profitability of trading strategies based on currency exchange rate dynamics.
method Derives the maximum drawdown of Ornstein-Uhlenbeck processes and applies it to trading strategies.
result The proposed trading strategy is profitable and aligns with theoretical characteristics.
New econometric results for financial duration models under varying tail behaviors.
problem Estimation and inference challenges in financial durations models with random event counts.
method Analysis of likelihood estimators for ACD models, focusing on tail behavior and stationarity.
result Asymptotic normality breaks down for tail indices smaller than one, leading to mixed Gaussian estimators with non-standard rates of convergence.