arXiv subjects

Sergei Fedotov

Publications and source records attributed to Sergei Fedotov.

45 records · Page 3Linked to original sources

arXiv2006

An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility

We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting from a discrete-time stochastic volatility model, we derive a recurrence equation for the variance of the innovation term in latent volatility equation. This equation describes a reduction of uncertainty in volatility which is crucial for option pricing. To implement the idea of adaptive control, we use the risk-minimization procedure involving random volatility with uncertainty. By using stochastic dynamic programming and a Bayesian approach, we derive a recurrence equation for the risk inherent in writing the option. This equation allows us to find the fair price of the European call option. We illustrate numerically that the adaptive procedure leads to a decrease in option price.

cond-mat.other↗

arXiv2004

Long memory stochastic volatility in option pricing

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 dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the fact the option price and random volatility change on different time scales, we find the asymptotic equation for the derivation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

cond-mat.other↗

arXiv2004

Volatility smile and stochastic arbitrage returns

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 stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility ``smile'' can also be explained in terms of random arbitrage opportunities.

cond-mat.other↗

arXiv2004

Stochastic Analysis of Subcritical Amplification of Magnetic Energy in a Turbulent Dynamo

We present and analyze a simplified stochastic $αΩ-$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $α-$% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the $α-$parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to $α-$fluctuations is found. We obtain numerical solutions of non-linear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the $α-$parameter.

astro-ph↗

arXiv2004

Stochastic arbitrage return and its implications for option pricing

The purpose of this work is to explore the role that 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 stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility "smile" can also be explained in terms of random arbitrage opportunities.

math.GM↗

arXiv2003

Non-normal and Stochastic Amplification in Turbulent Dynamo: Subcritical Case

Our attention focuses on the stochastic dynamo equation with non-normal operator that give an insight into the role of stochastics and non-normality in the galactic magnetic field generation. The main point of this Letter is a discussion of the generation of a large-scale magnetic field that cannot be explained by traditional linear eigenvalue analysis. We present a simple stochastic model for the thin-disk axisymmetric $αΩ$ dynamo involving three factors: (a) the non-normality generated by differential rotation, (b) the nonlinearity reflecting how the magnetic field affects the turbulent dynamo coefficients, and (c) stochastic perturbations. We show that even for \textit{subcritical case,} there are three possible mechanisms for the generation of magnetic field. The first mechanism is a deterministic one that describes an interplay between transient growth and nonlinear saturation of the turbulent $α-$effect and diffusivity. It turns out that the trivial state is nonlinearity unstable to small but finite initial perturbations. The second and third are the stochastic mechanisms that account for the interaction of non-normal effect generated by differential rotation and random additive and multiplicative fluctuations. In particular, we show that in \textit{subcritical case}the average magnetic energy can grow exponentially with time due to the multiplicative noise associated with $α-$effect.

astro-ph↗

arXiv2001

Memory Effects in Turbulent Dynamo: Generation and Propagation of Large Scale Magnetic Field

We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the growth rate several times compared to the conventional gradient transport expression. Moreover, the integral turbulent transport term leads to a large decrease of the speed of magnetic front propagation.

astro-ph↗

arXiv1998

Option Pricing Model for Incomplete Market

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces total risk inherent in writing the option. The basic purpose of paper is to present an effective algorithm that can be used in practice. Keywords: option pricing, incomplete market, transaction costs, stochastic optimization, Bellman equation.

cond-mat.stat-mech↗

arXiv1998

Traveling waves in reaction-diffusion system

A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.

cond-mat.stat-mech↗