Semi-static trading strategies can lead to non-closed outcome spaces, complicating optimal investment.
problem Non-closed outcome spaces of semi-static trading strategies.
method Analyzing the space of outcomes of semi-static trading strategies with static options trading.
result The space of outcomes of semi-static trading strategies can be non-closed.
Investors with extra info can price securities in semi-statically complete models.
problem Pricing securities in markets with dynamic and static trading options.
method Introduces semi-static completeness and uses robust pricing framework.
result Semi-static completeness is equivalent to an extremality property.
Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.
problem Optimal pricing of exotic derivatives in illiquid markets with bid-ask spreads.
method Use Galerkin method and integration quadratures to approximate hedging problem as convex optimization, solved by interior point method.
result Semi-static hedging improves pricing and reduces transaction costs compared to static or dynamic trading alone.
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time and are modeled as locally-bounded semi-martingales. Using a general util…
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work w…
New method for super-hedging American options under model uncertainty.
problem Super-hedging American options in a market with dynamic and static trading strategies.
method Supremum over prices under randomized models, where European options are static and stocks are dynamic.
result Super-hedging price is the supremum of prices under randomized models.
Develops a hedging method for multi-asset derivatives with correlation risk.
problem Hedging multi-asset derivatives exposed to correlation and covariance risk.
method Combines dynamic trading with static hedging instruments using Galtchouk--Kunita--Watanabe decomposition.
result Explicit semi-static replication formulas for covariance swaps and geometric dispersion trades.
Study dynamic trading in options to improve price bounds for exotic derivatives.
problem Improving price bounds for exotic derivatives through dynamic option trading.
method Extend semi-static trading strategies to include dynamic option trading, analyze duality results and pricing rules.
result Improved price bounds for exotic derivatives compared to conventional methods.
Develops a semi-static strategy for hedging renewable PPAs, separating price and volume risks.
problem Risk exposure in pay-as-produced power purchase agreements (PPAs) due to joint power prices and renewable production.
method Uses a semi-static hedging strategy combining liquid futures for price risk and fixed renewable-linked claims for volume and covariance risk.
result Pricing and hedging of PPAs can be decomposed into a baseload forward level, a deterministic production-profile correction, and a stochastic price-volume covariance correction.
Investigates model risk and semi-static hedging for martingale constrained models.
problem Model risk distributionally robust sensitivities for functionals on the Wasserstein space.
method Introduces distributionally robust problem with semi-static hedging strategies.
result Explicit characterizations of model risk optimal semi-static hedging strategies.
The study examines the supports of extremal martingale measures with given marginals in a two-period setting.
problem Investigating the supports of extremal martingale measures with pre-specified marginals in a two-period setting.
method Established equivalence between extremality and denseness in L1(Q), provided combinatorial sufficient conditions for weak exact predictable representation property (WEP), and studied the relation between cycles and extremality. result Developed necessary and sufficient conditions for the weak exact predictable representation property (WEP) in terms of 2-net and deadlock for finite support of the first marginal. The paper redefines semi-static hedging as derivatives and calculates hedging errors.
problem The costs of maintaining hedging portfolios and the limitations of semi-static hedging.
method New integral representations, approximations, and efficient numerical methods for calculating Wiener-Hopf factors and Laplace-Fourier inversion.
result The hedging error of static hedging portfolios can be larger than variance-minimizing portfolios.
Optimizes hedging strategy using Fourier-integration for variance-optimality.
problem Finding optimal hedging strategy under variance-optimality criterion.
method General representations and Fourier-integration for Heston model; sparse hedging selection.
result Sparse semi-static hedging strategy using Fourier-integration.
The paper develops a Fourier-based method for optimal hedging in stochastic volatility models.
problem Optimal hedging in financial markets with stochastic volatility.
method Fourier representation in a semimartingale factor model.
result A tractable formula for expected squared hedging error and optimal strategy.
A semi-static approach efficiently replicates and prices callable interest rate derivatives.
problem Efficiently replicating and pricing callable interest rate derivatives under dynamic market conditions.
method Proposes a semi-static hedging algorithm that updates the replication portfolio on a finite number of instances, rather than continuously.
result The hedging error can be made arbitrarily small with a sufficiently large replication portfolio, and closed-form error margins are determined.
Study robust optimization for discrete strategies under uncertain conditions.
problem Optimizing decisions in uncertain environments with discrete strategies.
method Nonconcave robust optimization with discrete constraints.
result Existence of maximizers under specific conditions.
It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of Brownian subordination. In order to increase the liquidity of the hedging instrume…
On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge.
Paper mathematically extends timing risk hedging for barrier options.
problem Timing risk in barrier options under multi-dimensional models.
method Semi-static hedge using barrier options and asymptotic expansions.
result Higher order semi-static hedges can reduce hedging cost by over 90%.
Model-free financial market proves superhedging duality with dynamic strategies.
problem Proves superhedging duality in a model-free financial market.
method Dynamic and semi-static trading strategies, no-arbitrage prices analysis.
result Initial cost of cheapest portfolio can exceed no-arbitrage upper bound.
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets …
Paper presents a machine learning algorithm for hedging ETF options, outperforming static hedging methods.
problem Semi-static hedging of ETF options with transaction costs and varying market conditions.
method Data-driven machine learning algorithm considering transaction costs, automated portfolio management, and PnL attribution analysis.
result The static hedging approach outperforms dynamic hedging methods in terms of profit and loss.
Unified framework for hedging American options, including shorting.
problem Generalizing hedging principles to American options, especially shorting.
method Unified framework, enlarging probability spaces, converting shorted options to European options.
result Unified FTAP and hedging dualities for American options, including shorting.
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile he…
New trading strategies yield gains on average in various market scenarios.
problem Developing trading strategies that consistently yield positive gains in different market conditions.
method Introducing generalized statistical arbitrage concepts and profitable strategies based on information systems.
result Constructed profitable generalized strategies with good performance on simulated and real market data.
In this article we consider the problem of giving a robust, model-independent, lower bound on the price of a forward starting straddle with payoff ∣FT1−FT0∣ where 0<T0<T1. Rather than assuming a model for the underlying forward price (Ft)t≥0, we assume that call prices for maturities $T_0<T_1…
Continuous-time pricing-hedging duality for European options.
problem Finding the minimal superhedging price of path-dependent European options.
method Formulates a duality between analytic and probabilistic problems, using simple trading strategies and semi-continuous claims.
result The minimal superhedging price equals the supremum of expectations over all martingale measures.
In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that th…
Detecting real-time price impact in algo trading
problem Identifying the impact of traders' actions on market prices
method Measuring timing synchronicity between trader actions and adverse market events
result Detecting price impact on a per-action basis
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
Neural networks improve pricing and hedging of complex financial claims.
problem Pricing and hedging of high-dimensional, path-dependent contingent claims.
method Regress later Monte Carlo approach using neural networks for interpretability.
result Any contingent claim can be semi-statically hedged using a portfolio of short maturity options.
Study optimizes financial strategies for various options globally.
problem Optimizing financial strategies for different types of options.
method Martingale optimal transport duality for càdlàg processes.
result Existence of robust semi-static superhedging strategies.
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular atten…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. T…
The paper analyzes optimal overbetting strategies for a satellite investment account.
problem Optimal control of leverage in a satellite investment account with limited leverage.
method Recursive overbetting strategy to maximize growth rate, solved via HJB equation.
result Optimal overbetting strategy balances growth rate of satellite and composite bankroll.
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…
Study utility maximization with costs under uncertain models.
problem Maximizing utility in a market with transaction costs and model uncertainty.
method Transformed semi-static utility maximization problem on an enlarged space using randomization techniques and dynamic programming.
result Existence of optimal strategy and convex duality theorem proved.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential Lévy processes such that the resulting market does not admit arbitrage opportunities. We derive …
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance, the European call-put parity corresponds to the central symmetry property, while…
This paper examines how regional trade agreements affect global trade relationships.
problem The relationship between regional trade agreements and global trade purity.
method Defined and decomposed synthesized trade resistance, separated natural and artificial factors, used expectation maximization algorithm to optimize parameters, and quantified trade purity indicator.
result Regional trade agreements contribute to the relative prosperity of EU and NAFTA countries, but weaken the role of trade unions and accelerate multilateral trade liberalization.
This study analyzes stock trading networks to quantify price impacts based on trader positions.
problem Quantifying the immediate price impact of trades in stock markets.
method Constructed stock trading networks using k-shell decomposition to classify traders and compare different market segments. result Institutional traders have lower price impacts compared to individuals at the same positions in the trading network.
World trade atlas reveals hyperbolic geometry of international connections.
problem Understanding the complex architecture of international trade networks.
method Gravity model predicting trade channels and analysis of trade distances.
result Trade distances are hyperbolic, not flat, reflecting a hierarchical international trade system.
Paper predicts international trade flows using machine learning and factorization models.
problem Predicting international bilateral trade flows with PTAs.
method Two-stage approach combining SHAP Explainer and Factorization Machine models.
result Enhanced predictive accuracy and deeper insights into trade dynamics.
Analysis shows preference for Chinese yuan in global trade network.
problem Analyzing the preference of countries to trade in US dollars or Chinese yuan.
method Mathematical analysis of world trade network using Ising spin interactions.
result Majority of countries prefer trading in Chinese yuan due to network structure.
Complex financial instruments allow insider trading without actual trades.
problem How to commit insider trading without executing a trade.
method Use of financial instruments to replicate the economic effect of trading.
result Insider trading can be committed without an actual trade.
Model predicts trading strategies based on latent demand and price impact.
problem Predicting strategic trading behavior of investors with private targets.
method Equilibrium model of dynamic trading, learning, and pricing by strategic investors.
result Trading strategies are a combination of target following, liquidity provision, and front-running based on latent demand and price pressure.
Optimizes trading pairs of stocks to reduce cross-impact costs.
problem Minimizing costs from trades of one stock affecting another.
method Develops a strategy to minimize cross-impacts by optimizing trading rates and periods.
result An optimal trading strategy for stock pairs is found.