This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …
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48 results for “drawdown duration”
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.
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximationmath.PR
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…
On the maximum drawdown during speculative bubblesphysics.data-an
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 total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distrib…
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.
The Temporal Dimension of Riskq-fin.PM
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…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate the problem (minimising average drawdown, maximum drawdown, or a weighted combi…
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.
Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Marketsq-fin.RM
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.
Risk-Constrained Kelly Gamblingq-fin.PM
We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown probability; using this bound instead of the original risk constraint yields a conv…
Generalized Expected Discounted Penalty Function at General Drawdown for Lévy Risk Processesq-fin.PR
This paper considers an insurance surplus process modeled by a spectrally negative Lévy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution of the time of drawdown, the running maximum at drawdown, the last m…
Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the drawdown issue in a stock trading context. Although our analysis can be carried …
Probability distribution of drawdowns in risky investmentscond-mat.stat-mech
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…
Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functionsq-fin.PR
In this paper, we analyse some equity-linked contracts that are related to drawdown and drawup events based on assets governed by a geometric spectrally negative Lévy process. Drawdown and drawup refer to the differences between the historical maximum and minimum of the asset price and its current value, respectively. …
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.
Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial modelq-fin.PM
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…
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…
In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric Lévy process. We consider four contracts, three of which were introduced in Zhang et al. (2013) for a geometric Brownian motion. The first one is an i…
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.
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…
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.
Trading strategies that were profitable in the past often degrade with time. Since unlucky streaks can also hit "healthy" strategies, how can one detect that something truly worrying is happening? It is intuitive that a drawdown that lasts too long or one that is too deep should lead to a downward revision of the assum…
Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of …
In this paper the fractional trading ansatz of money management is reconsidered with special attention to chance and risk parts in the goal function of the related optimization problem. By changing the goal function with due regards to other risk measures like current drawdowns, the optimal fraction solutions reflect t…
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.
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
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to co…
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…
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 determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is less than some fixed pro…
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.
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.
We consider the portfolio choice problem for a long-run investor in a general continuous semimartingale model. We suggest to use path-wise growth optimality as the decision criterion and encode preferences through restrictions on the class of admissible wealth processes. Specifically, the investor is only interested in…
The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu, presented in Part I of this series (arXiv:1710.04579 [q-fin.PM]). As alternative to classical portfolio risk measures such as the standard devi…
Beyond the Mean: Limit Theory and Tests for Infinite-Mean Autoregressive Conditional Durationsecon.EM
Unified asymptotic theory and tests for ACD models reveal infinite-mean durations in cryptocurrency trading.
problem Challenges in asymptotic theory for ACD models, especially for integrated ACD.
method Unified asymptotic theory for quasi-maximum likelihood estimator, hypothesis testing framework.
result Infinite-mean durations in cryptocurrency trading, rejected integrated ACD hypothesis.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
Optimal dividend payout strategies with drawdown constraint identified.
problem Optimal dividend payout strategies under a drawdown constraint.
method Solving a two-dimensional optimal control problem using viscosity solutions and calculus of variations.
result A two-curve strategy is optimal for sufficiently large initial and maximum dividend rates, with a surprising limit result for large maximum dividend rates.
New conditions for ACD model consistency and normality.
problem Random number of durations in ACD model.
method Additional sufficient conditions for consistency and normality of QMLE.
result Finite mean of durations is required for consistency and normality.
New f-Betas for portfolio optimization using f-divergence risk measures.
problem Optimizing portfolio performance under varying market conditions.
method Derive f-Betas and Hellinger-Betas, using f-divergence risk measures.
result Demonstrated new Beta metrics provide better performance under stress.