Related papers: Hedging under arbitrage
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson…
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations…
An important revenue stream for electric battery operators is often arbitraging the hourly price spreads in the day-ahead auction. The optimal approach to this is challenging if risk is a consideration as this requires the estimation of…
We propose a model for hedging in a market with jumps for a large investor. The dynamics of the stock prices and the value process is governed by forward-backward SDEs driven by Teugels martingales. Unlike known FBSDE market models, ours…
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at…
Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's…
Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar…
We revisit the classical topic of quadratic and linear mean-variance equilibria with both financial and real assets. The novelty of our results is that they are the first allowing for equilibrium prices driven by general semimartingales and…
In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this…
In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via…
We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections…
We study a quadratic hedging problem for a sequence of contingent claims with random weights in discrete time. We obtain the optimal hedging strategy explicitly in a recursive representation, without imposing the non-degeneracy (ND)…
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…
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
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…
We provide some theoretical extensions and a calibration protocol for our former dynamic optimal execution model. The Hawkes parameters and the propagator are estimated independently on financial data from stocks of the CAC40.…
We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine…
We study scaled trinomial models converging to the Black--Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is…
We consider portfolio selection under nonparametric $\alpha$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are…
As soon as one accepts to abandon the zero-risk paradigm of Black-Scholes, very interesting issues concerning risk control arise because different definitions of the risk become unequivalent. Optimal hedges then depend on the quantity one…