Related papers: Ito calculus without probability in idealized fina…
Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$,…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
We introduce a Path Shadowing Monte-Carlo method, which provides prediction of future paths, given any generative model. At any given date, it averages future quantities over generated price paths whose past history matches, or `shadows',…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a…
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties…
In this paper we investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
Optimal pricing of European call option is described by linear stochastic differential equation. Trading strategy given by a twin of stochastic variables was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to tarading…
In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that…
Most finance studies are discussed on the basis of several hypotheses, for example, investors rationally optimize their investment strategies. However, the hypotheses themselves are sometimes criticized. Market impacts, where trades of…
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
We revisit optimal execution of an active portfolio in the presence of slippage (aka linear, proportional, or absolute-value) costs. Market efficiency implies a close balance between active alphas and trading costs, so even small changes to…
Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic…
We use pathwise It\^o calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of F\"ollmer's pathwise It\^o calculus and works for…
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study…