Related papers: A Note on Delta Hedging in Markets with Jumps
We study super-replication of contingent claims in markets with delayed filtration. The first result in this paper reveals that in the Black--Scholes model with constant delay the super-replication price is prohibitively costly and leads to…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient…
We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage…
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…
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…
The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical…
We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the…
We develop deep learning models to learn the hedge ratio for S&P500 index options directly from options data. We compare different combinations of features and show that a feedforward neural network model with time to maturity,…
This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We examine the effect of different market…
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss…
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 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 consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him…
We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of…
This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A…