Related papers: Statistical Arbitrage in the Black-Scholes Framewo…
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…
The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a…
This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated…
In this paper, a general framework is developed for continuous-time financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a num\'eraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the…
Black-Scholes equation as one of the most celebrated mathematical models has an explicit analytical solution known as the Black-Scholes formula. Later variations of the equation, such as fractional or nonlinear Black-Scholes equations, do…
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…
This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of…
We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…
We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it…
In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error…
A market model with $d$ assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a num\`eraire is not assumed. It is shown that robust no arbitrage…