Related papers: A data-reconstructed fractional volatility model
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
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…
Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered…
Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic…
This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
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…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\--Scholes\--type equation whose spatial domain for the logarithmic stock price $x\in \RR$ and the variance $v\in (0,\infty)$ is the…
We introduce a new model of financial market with stochastic volatility driven by an arbitrary H\"older continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the…
In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between…