Related papers: Quadratic Hedging and Optimization of Option Exerc…
While deep reinforcement learning has achieved tremendous successes in various applications, most existing works only focus on maximizing the expected value of total return and thus ignore its inherent stochasticity. Such stochasticity is…
Using a fast numerical technique, we investigate a large database of investor suboptimal non-exercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend…
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of…
The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…
Market making of options with different maturities and strikes is a challenging problem due to its highly dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired…
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging…
We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its…
American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and…
We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove…
This paper is devoted to the pricing of Barrier options by optimal quadratic quantization method. From a known useful representation of the premium of barrier options one deduces an algorithm similar to one used to estimate nonlinear filter…
We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms…
It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…
The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal…
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling…
We present a dynamic hedging scheme for S&P 500 options, where rebalancing decisions are enhanced by integrating information about the implied volatility surface dynamics. The optimal hedging strategy is obtained through a deep policy…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{\star}$ which turns the dynamic asset allocation problem into a…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…