Related papers: Statistical likelihood methods in finance
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…
We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more…
The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays financial mathematics is heavily based on the use…
We consider a pair of traders in a market where the information available to the second trader is a strict subset of the information available to the first trader. The traders make prices based on the information available concerning a…
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…
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are functions of positive Ornstein-Uhlenbeck(OU)…
A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during…
Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…
Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the…
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…
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed…
We compare the option pricing formulas of Louis Bachelier and Black-Merton-Scholes and observe -- theoretically as well as for Bachelier's original data -- that the prices coincide very well. We illustrate Louis Bachelier's efforts to…
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable.…