Related papers: Elements for a Theory of Financial Risks
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
Much research in systemic risk is focused on default contagion. While this demands an understanding of valuation, fewer articles specifically deal with the existence, the uniqueness, and the computation of equilibrium prices in structural…
In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility.…
A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
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…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Option pricing formulas are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index $q$. A generalized…