Related papers: Modeling Stock Return Distributions and Pricing Op…
This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the…
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are…
The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is…
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
It is proved that the sum of n independent but non-identically distributed doubly truncated Normal distributions converges in distribution to a Normal distribution. It is also shown how the result can be applied in estimating a constrained…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations,…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
Time-series with volatility clustering pose a unique challenge to uncertainty quantification (UQ) for returns forecasts. Methods for UQ such as Deep Evidential regression offer a simple way of quantifying return forecast uncertainty without…
The real options approach is now considered an effective alternative to the corporate DCF model for a feasibility study. The current paper offers a practical methodology employing binomial trees and real options techniques for evaluating…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As…
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…