Related papers: Deep Hedging: Learning Risk-Neutral Implied Volati…
We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which…
Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this…
We propose a deep hedging framework for index option portfolios, grounded in a realistic market simulator that captures the joint dynamics of S&P 500 returns and the full implied volatility surface. Our approach integrates surface-informed…
Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging…
In most real scenarios the construction of a risk-neutral portfolio must be performed in discrete time and with transaction costs. Two human imposed constraints are the risk-aversion and the profit maximization, which together define a…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
Extracting the risk neutral density (RND) function from option prices is well defined in principle, but is very sensitive to errors in practice. For risk management, knowledge of the entire RND provides more information for Value-at-Risk…
Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can…
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash…
Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting…
The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…
Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter…