Related papers: Discrete Time vs Continuous Time Stock-price Dynam…

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…

This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive…

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…

The mean objective of this paper is to derive an explicit formula for a price of an European option associated to the underlying delayed stock price which follows a linear differential equation with a general delay in the drift term. We use…

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…

In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…

We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…

A bubble is characterized by the presence of an underlying asset whose discounted price process is a strict local martingale under the pricing measure. In such markets, many standard results from option pricing theory do not hold, and in…

This paper studies how to price and hedge options under stock models given as a path-dependent SDE solution. When the path-dependent SDE coefficients have Fr\'{e}chet derivatives, an option price is differentiable with respect to time and…

Stochastic processes time-changed by an inverse subordinator have been suggested as a way to model the price of assets in illiquid markets, where the jumps of the subordinator correspond to periods of time where one is unable to sell an…

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis…

Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for…

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…

Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an…

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The…

We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…

We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard (2013), where the price dynamics are endogenous, resulting from market transactions. We also show that the…

This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing…

Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency…