相关论文: Trading Strategy Adipted Optimization of European …

This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a…

Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…

In this paper we analyze a nonlinear Black--Scholes model for option pricing under variable transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a function of the underlying…

We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…

In this paper we present a locally one-dimensional (LOD) splitting method to solve numerically the two-dimensional Black-Scholes equation, arising in the Hull & White model for pricing European options with stochastic volatility,…

We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or…

In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign…

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…

Optimal trading is a recent field of research which was initiated by Almgren, Chriss, Bertsimas and Lo in the late 90's. Its main application is slicing large trading orders, in the interest of minimizing trading costs and potential…

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction…

In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure…

In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier…

Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…

We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…

There exist several methods how more general options can be priced with call prices. In this article, we extend these results to cover a wider class of options and market models. In particular, we introduce a new pricing formula which can…