This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.
problem Finding minimum cost super-hedging strategies in a multi-asset, incomplete market model.
method Explicit formulas for minimum cost super-hedging strategies for various European type multi-asset contingent claims.
result Explicit formulas for non-negative local residuals of super-hedging strategies.
Deep learning improves portfolio optimization in volatile markets.
problem Challenges in long-only, multi-asset strategies across market cycles.
method Training DL models with limited regime data using pre-training techniques and transformer architectures.
result Models show resilience and improved predictive accuracy in volatile markets.
Generative Adversarial Network (GAN) simulates realistic multi-asset scenarios for tail risk.
problem Simulating realistic joint dynamics of multi-asset portfolios for tail risk estimation.
method Designing a GAN that preserves Value-at-Risk (VaR) and Expected Shortfall (ES) tail risk features.
result Correctly captures tail risk for a broad class of trading strategies and demonstrates strong generalization.
Closed-form pricing method for multi-asset options.
problem Pricing multi-asset contingent claims in an incomplete market.
method Proving extremal martingale measures and constructing algorithms for bounds and hedging.
result Closed-form formulas for no-arbitrage price intervals and hedging strategies.
Improved bounds for multi-asset options using deep learning and market prices.
problem Computing model-free bounds for multi-asset options with uncertainty in dependence structure.
method Fundamental theorem of asset pricing, superhedging duality, penalization approach, deep learning.
result Deep learning approximations improve computational efficiency and accuracy.
Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are L1. We present a mean-field approach that reduces the multi-asset problem to a single-asset problem, with an effective predictor that includes a risk avers…
Portfolio traders strive to identify dynamic portfolio allocation schemes so that their total budgets are efficiently allocated through the investment horizon. This study proposes a novel portfolio trading strategy in which an intelligent agent is trained to identify an optimal trading action by using deep Q-learning. …
In this article we study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but we specialise to a case where transaction costs are zero except for sales and purchases of …
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.
New automated market makers for multi-asset trading.
problem Liquidity management in multi-asset trading.
method Derived from self-financing transactions and rebalancing principles.
result Constant product market maker as a special case.
The paper addresses optimal execution for multi-asset portfolios using Ornstein-Uhlenbeck dynamics.
problem Optimal execution for multi-asset portfolios with Ornstein-Uhlenbeck dynamics.
method Stochastic optimal control and simplification of Hamilton-Jacobi-Bellman equation to ODEs.
result Existence and uniqueness of solution to the execution problem using extit{a priori} estimates.
A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functi…
SBCA optimizes portfolios by fusing price data and text sentiment.
problem Insufficient integration of multi-modal information in traditional portfolio optimization models.
method Cross-modal BERT-driven Actor-Critic framework with gated fusion and constraint embedding.
result SBCA outperforms benchmarks in portfolio value, return, Sharpe ratio, and maximum drawdown.
The paper develops bounds for multi-asset derivatives using option prices.
problem Computing model-free upper and lower bounds for multi-asset derivatives.
method Develops a fundamental theorem of asset pricing and superhedging duality, recasting the problem into a linear semi-infinite optimization problem and providing algorithms for exact computation.
result Provides ε-optimal upper and lower bounds for multi-asset derivatives, characterizing optimal pricing measures. Improved price bounds for multi-asset derivatives using market option data.
problem Creating robust price bounds for multi-asset derivatives under market-implied dependence.
method Extracting inter-asset dependence information from market option prices and applying modified martingale optimal transport.
result Improved price bounds for multi-asset derivatives, demonstrating relevance and tractability.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
problem Understanding price dynamics and bubbles in multi-asset markets.
method Derives sufficient and necessary conditions for average equilibrium price dynamics in a two-asset model.
result Assets with positive average dividends display hump-shaped bubbles, while those with constant fundamental values show misvaluation effects.
Efficient method for pricing multi-asset options with local volatility.
problem Pricing options on multiple assets with varying volatility.
method Generic hybrid numerical method for efficient pricing.
result Efficient pricing of multi-asset options with local volatility.
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.
Develops a novel framework for pricing variance swaps in multi-asset stochastic volatility models.
problem Pricing variance swaps in multi-asset stochastic volatility models.
method Determinant-based instantaneous generalized variance, Heston and BNS stochastic volatility frameworks.
result Analytical pricing expressions for multi-asset Heston and BNS formulations.
Paper proposes a CNN model for improved multi-asset portfolio risk prediction.
problem Challenges in risk management of multi-asset portfolios due to limited correlation capture.
method Uses CNN and image processing to convert financial data into images for enhanced feature extraction.
result CNN model significantly outperforms traditional methods in risk prediction accuracy.
Study solves DREs for trading strategies using signals and past prices.
problem Solving DREs for optimal trading strategies.
method Analyzes DREs with indefinite matrix coefficients and applies to trading problems.
result Derives optimal trading strategies using signals and past prices.
We employ perturbation analysis technique to study multi-asset portfolio optimisation with transaction cost. We allow for correlations in risky assets and obtain optimal trading methods for general utility functions. Our analytical results are supported by numerical simulations in the context of the Long Term Growth Mo…
Exponential Lévy processes have been used for modelling financial derivatives because of their ability to exhibit many empirical features of markets. Using their multidimensional analogue, a general analytic pricing formula is obtained, allowing for the direct valuation of multi-asset options on $n \in \z^+$ risky asse…
Paper uses RL to optimize multi-asset portfolios in fluctuating markets.
problem Optimizing multi-asset portfolios in time-varying financial markets.
method Soft Actor-Critic (SAC) algorithm for policy learning, policy iteration process.
result SAC algorithm outperforms in various criteria in simulated and real financial markets.
Detects arbitrage in multi-asset derivatives markets.
problem Identifying arbitrage opportunities in multi-asset derivative markets.
method Using bijection between equivalent martingale measures and copulas, derived sufficient conditions for no-arbitrage and formulated an optimization problem.
result Constructs a market where individual derivatives are no-arb but collectively an arbitrage opportunity exists.
Investment strategy in ambiguous financial markets with learning
problem Continuous time investment problem in multi-asset Black-Scholes market with model ambiguity
method Optimal dynamic investment strategy within the class of all adapted strategies which allow for learning
result Ambiguity averse investors invest less in risky assets
Extends return risk measures to multiple assets, proving properties and comparing different risk models.
problem Evaluating risk in financial markets with multiple assets.
method Develops multi-asset return risk measures (MARRMs), analyzes their properties, and compares them with other risk models.
result Proves that a positively homogeneous MARRM is quasi-convex if and only if it is convex, and provides conditions to avoid inconsistent risk evaluations.
Simulates multi-asset spot and option markets using normalizing flows.
problem High-dimensionality of market call prices and dynamic preservation across simulators.
method Normalizing flows for efficient low-dimensional representations, conditional invertibility for joint distribution calibration.
result Calibrated simulators maintain dynamics of each underlying and accurately represent market call prices.
Tensor trains speed up option pricing for multi-asset options.
problem Speeding up option pricing for multi-asset options.
method Tensor train learning algorithms to compress functions with parameter dependence.
result The proposed method outperforms Monte Carlo-based pricing in computational complexity.
CFMMs solve complex multi-asset trades via convex optimization.
problem Complex multi-asset trades in decentralized exchanges.
method Formulate multi-asset trades as convex optimization problems.
result Efficiently solve multi-asset trades using convex optimization.
New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
problem Efficiently pricing multi-asset options in Lévy models.
method Optimized damping parameters and hierarchical adaptive quadrature.
result Significant speed-up in computational time for up to six dimensions.
Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential we…
We consider a Black-Scholes type equation arising on a pricing model for a multi-asset option with general transaction costs. The pioneering work of Leland is thus extended in two different ways: on the one hand, the problem is multi-dimensional since it involves different underlying assets; on the other hand, the tran…
Quantum computing speeds up pricing multi-asset derivatives.
problem Exponential growth in complexity for multi-asset derivatives pricing.
method Quantum algorithm based on quantum linear system algorithms for FDM.
result Exponential speedup in derivative pricing compared to classical methods.
New method uses neural networks for better financial hedging.
problem Spanning multi-asset payoffs with vanilla options.
method One-hidden-layer feedforward neural networks for numerical solution.
result Better hedging results with neural networks compared to single-asset approaches.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
problem Efficient computation of Greeks for multi-asset options with high accuracy and low sample complexity.
method Tensor train (TT) representations of Fourier-based pricing functions, combined with numerical differentiation or analytical approaches.
result Significant speed-ups of up to 105imes over Monte Carlo simulations while maintaining comparable accuracy. In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-…
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with both static and dynamic components. They need indeed to propose bid and offer/ask prices in an optimal way for making money …
This paper solves hedging in incomplete markets using neural networks.
problem Hedging in incomplete markets with risk factor, illiquidity, and discrete transaction dates.
method Proposes a jump-diffusion model and uses RNN, LSTM, and Mogrifier-LSTM neural networks for hedging strategies.
result Mogrifier-LSTM is the fastest and most effective model for hedging.
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the …
In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The meth…
Study shows integrating OFI from multiple levels improves price impact explanation but not forecasting.
problem Explaining and forecasting price movements in equity markets using OFI.
method Systematic approach to combine OFIs from multiple levels into an integrated variable, testing multi-asset models with and without cross-impact terms.
result Lagged cross-asset OFIs improve future return forecasting but not contemporaneous price impact.
Study of a risk-averse informed trader in a multi-asset market with non-Gaussian prices.
problem Existence of equilibrium in a multi-asset market with non-Gaussian prices and a risk-averse informed trader.
method Constructed equilibrium using Fokker-Planck equation and coupled partial differential equations with an optimal transport constraint.
result Equilibrium exists in a market with multiple assets and non-Gaussian prices.
Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to be used in successful management of risk, uncertainty and leverage. The author ex…
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomised) stopping time, rather than instantly at an ordinary stopping time. Allo…