Related papers: Modeling Stock Return Distributions and Pricing Op…
Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to include…
We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that…
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…
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops that the…
A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can…
The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver…
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on $q$-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities…
We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion…
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the…
This paper introduced key aspects of applying Machine Learning (ML) models, improved trading strategies, and the Quasi-Reversibility Method (QRM) to optimize stock option forecasting and trading results. It presented the findings of the…
Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and…
Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a…
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…
Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on…
We propose the finite mixture of skewed sub-Gaussian stable distributions. The maximum likelihood estimator for the parameters of proposed finite mixture model is computed through the expectation-maximization algorithm. The proposed model…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under…