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.
The paper prices swaps on generalized variance measures for multiple assets.
problem Hedging risk in financial markets with multi-asset swaps.
method Pricing generalized variance swaps using Barndorff-Nielsen and Shephard model.
result Results have implications for commodity sector risk management.
This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigen-value and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with Markov-modulated volatilities. We consider multiple assets in the portfolio for …
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…
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.
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its anal…
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.
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.
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.
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.
Debt swaps improve financial networks by optimizing clearing payments and stability.
problem Improving financial network stability and efficiency through debt swaps.
method Analyzing computational complexity of debt swaps, focusing on semi-positive swaps and v-improving swaps.
result Polynomial length of sequences of semi-positive v-improving swaps for ranking-based clearing, but NP-hard for arbitrary v-improving swaps.
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.
Paper generalizes pricing and hedging of volatility swaps in stochastic models.
problem Pricing and hedging of volatility swaps in stochastic volatility models.
method Generalizes zero vanna approximation to seasoned swaps, derives hedges using vanilla options and variance swaps.
result Pricing and hedging of volatility swaps are made practical and robust.
Swapping debt contracts can mitigate risk in financial networks.
problem Mitigating risk in financial networks through debt swaps.
method Analysis of debt swapping operations in financial networks under various conditions.
result Positive debt swaps can exist in worst-case shock models to minimize losses.
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…
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…
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.
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.
We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.
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.
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.
This study reviews techniques to estimate volatility and price Variance Swaps.
problem Estimating historical volatility and pricing Variance Swaps.
method Review of existing techniques.
result Discussion of various methods to estimate volatility and price Variance Swaps.
F. Labourie [arXiv:1212.5015] characterized the Hitchin components for PSL(n,R) for any n>1 by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank n swapping algebra, which is the quotient of the swap…
In this paper, we model financial markets with semi-Markov volatilities and price covarinace and correlation swaps for this markets. Numerical evaluations of vari- nace, volatility, covarinace and correlations swaps with semi-Markov volatility are presented as well. The novelty of the paper lies in pricing of volatilit…
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.
Neural networks compute bounds on multi-asset derivatives.
problem Computing precise prices of complex financial derivatives.
method Using neural networks and constrained optimal transport.
result Neural networks provide tighter bounds on derivative prices.
An uncollateralized swap hedged back-to-back by a CCP swap is used to introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure market risk capital, a practical business concern. By dynamically trading the CCP swap, with t…
Exact relationships found between ATM slope, volatility swap, and zero vanna.
problem Understanding relationships between implied volatilities and swaps.
method Analyzes exact relationships between ATM slope, volatility swap, and zero vanna.
result Exact relationships between ATM slope, volatility swap, and zero vanna.
Paper derives formulas for volatility swap strike and zero vanna implied volatility.
problem Relationship between volatility swap strike and zero vanna implied volatility.
method Applied Malliavin calculus to derive exact formulas.
result Zero vanna implied volatility is a better approximation for volatility swap strike.
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.
A note on setting swap parameters for traders.
problem Determining optimal slippage parameters and trade size for wealth swapping.
method Theoretical solution and framework for optimal slippage parameters and trade size.
result Offers a method to solve optimal slippage parameters and trade size for wealth swapping.
Paper solves no-swap regret minimization for combinatorial bandits with polylogarithmic dependence on N.
problem Design efficient no-swap regret algorithms for combinatorial bandits with exponentially large action space.
method Introduces a no-swap-regret learning algorithm with polylogarithmic dependence on N and demonstrates efficient implementation.
result Achieves no-swap regret with polylogarithmic dependence on N, resolving an open problem.
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.
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.
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of computationally tractable sparse regression algorithms---such as the Lasso, Orthogonal Matchi…
The paper extends the market price of risk for electricity swap contracts, incorporating jump risk.
problem Pricing electricity swap contracts with consideration of jump risk.
method Introducing a Merton type model with jumps and transferring to the physical measure, comparing arithmetic and geometric averaging.
result A decomposition of swap's market price of risk into classical and market price of risk components.
Paper introduces a new pricing method for electricity swaps and options.
problem Pricing electricity swaps and options in markets with varying delivery periods.
method Introduces a weighted geometric averaging of futures prices over delivery periods.
result Arbitrage-free pricing framework for derivatives in electricity markets.
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-…
Improved bounds for multicalibration and omniprediction in online and distributional settings.
problem Achieving efficient multicalibration and omniprediction in fairness and loss minimization.
method Proposed an efficient algorithm achieving improved rates for multicalibration and omniprediction.
result Achieved O(T31) ℓ2-swap multicalibration error for convex Lipschitz functions. 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.