Related papers: Deep Hedging: Learning Risk-Neutral Implied Volati…
We show how D4PG can be used in conjunction with quantile regression to develop a hedging strategy for a trader responsible for derivatives that arrive stochastically and depend on a single underlying asset. We assume that the trader makes…
We consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which require applying significant local distortions to…
We consider model-free pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…
Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static…
Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By…
Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…
By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and…
Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
We price and replicate a variety of claims written on the log price $X$ and quadratic variation $[X]$ of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the…
Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…
This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal…
We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only…