Related papers: Optimization of Financial Instrument Parcels in St…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
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…
We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…
Based on geometrical considerations, we propose a new oscillator for technical market analysis, the tube oscillator. This oscillator measures the trending behavior of a fixed market instrument based on its past history. It is shown in an…
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.
The application of deep learning to time series forecasting is one of the major challenges in present machine learning. We propose a novel methodology that combines machine learning and image processing methods to define and predict market…
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than expected ones, in accordance with an existing extremum…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time…
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…
Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In option markets, the most popular way has been to extract implied volatilities to assess the…
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…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes…
Ito equations are derived for simple stochastic cellular automaton with parameters and compared with results obtained from the histogram method. Good agreement for various parameters supports wide applicability of the Ito equation as a…
This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account.…
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to…