scholarly journals A Non-Gaussian Pricing Model for Structured Products

2017 ◽  
Vol 11 (3) ◽  
pp. 45-58
Author(s):  
Denis Zuev
Keyword(s):  
Probability Distributions ◽  
Fair Value ◽  
Pricing Model ◽  
Fair Price ◽  
Gaussian Distributions ◽  
Structured Products ◽  
Market Participants ◽  
Market Framework ◽  
Non Gaussian ◽  
Value Pricing

The paper aims to reconstruct the empirical premia of the structured products with two underlying assets. We apply various models that differ in probability distributions of the underlying price processes. Pricing techniques, currently worldwide accepted, are based on the Black-Scholes model modifications with Gaussian distributions. Conventionally a correlation between underlying price processes is not considered. In order to achieve the overall objective the paper suggests a pricing model of structured products. The model considers a non-Gaussian realistic market framework for pricing the underlying assets and takes into account their correlation. The theoretical and methodological basis of our research is quantitative finance, evolutionary equations, dynamical systems and field theory. The paper presents an example of pricing a range of structured products. We find that the approach to the theoretical premium valuation of the complex financial instrument is interrelated bijec- tively with statistical properties of the underlying assets. In particular, the paper presents the effectiveness of our model with regard to the structured derivatives with the correlated assets that obey non-Gaussian distributions. The fair value of the structured product evaluated using our model outperforms estimates obtained by means of other methods as it allows lower fair price of the derivatives. The results of our research may be beneficial to academics, market participants including market analysts, risk-managers and developers of financial products. We have concluded that market participants carry extra costs due to the simple models of the structured products' fair value pricing they apply. The proposed model looks especially promising within the context of the complex derivatives market which growth has been accompanied by low liquidity and high premia, in the absence of a unique framework for pricing the structured products that would be consistent with financial market practice.

A robust pricing of specific structured bonds with coupons

2014 ◽  
Vol 15 (3) ◽  
pp. 234-247
Author(s):  
Anastasios Evgenidis ◽  
Costas Siriopoulos
Keyword(s):  
Interest Rates ◽  
Global Financial Crisis ◽  
Model Misspecification ◽  
Fair Value ◽  
Fair Price ◽  
Bond Price ◽  
Content Type ◽  
Structured Products ◽  
Innovative Model ◽  
Bond Issuers

Purpose – The purpose of this paper is to present an innovative model to evaluate the fair price of a subset of structured products for a hypothetical US structured bond. Design/methodology/approach – The authors assume that interest rates dynamics are described by the Cox–Ingersoll–Ross process. They conduct robustness checks by stress testing against parameter and model uncertainty. Findings – The fair value of the bond is robust under any parameter or model misspecification. In addition, a change in the price seems to be more sensitive to long-term yields rather than short-or mid-term yields. The authors provide a better understanding of the relationship between bond prices and business cycles: a slight change in the current structure would have a significant effect on the bond price only during economic expansions. Social implications – The recent global financial crisis has led policymakers and the financial press to blame financial innovation through accusations of structured products being highly complex. Much of the criticism is based on the fact that investors were not able to properly price and fully understand the risks of their investments. Regulators should ensure proper pricing of these products to protect both the investors and the system. Fair pricing is important for bond issuers, governments or corporations to design their product at an attractive price for investors. Originality/value – This paper fills a gap in the extant literature by providing an innovative model based on an Euler–Maruyama Monte Carlo scheme to price structured products.

scholarly journals Information theoretic measures of dependence, compactness, and non-gaussianity for multivariate probability distributions

2009 ◽  
Vol 16 (1) ◽  
pp. 57-64 ◽  
Author(s):  
A. H. Monahan ◽  
T. DelSole
Keyword(s):  
Probability Distributions ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Gaussian Distributions ◽  
Information Theoretic ◽  
Measures Of Dependence ◽  
Basic Task ◽  
Non Gaussian ◽  
Measure Of Dependence

Abstract. A basic task of exploratory data analysis is the characterisation of "structure" in multivariate datasets. For bivariate Gaussian distributions, natural measures of dependence (the predictive relationship between individual variables) and compactness (the degree of concentration of the probability density function (pdf) around a low-dimensional axis) are respectively provided by ordinary least-squares regression and Principal Component Analysis. This study considers general measures of structure for non-Gaussian distributions and demonstrates that these can be defined in terms of the information theoretic "distance" (as measured by relative entropy) between the given pdf and an appropriate "unstructured" pdf. The measure of dependence, mutual information, is well-known; it is shown that this is not a useful measure of compactness because it is not invariant under an orthogonal rotation of the variables. An appropriate rotationally invariant compactness measure is defined and shown to reduce to the equivalent PCA measure for bivariate Gaussian distributions. This compactness measure is shown to be naturally related to a standard information theoretic measure of non-Gaussianity. Finally, straightforward geometric interpretations of each of these measures in terms of "effective volume" of the pdf are presented.

scholarly journals Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels

2018 ◽  
Vol 2 (3) ◽  
pp. 20 ◽  
Author(s):  
Maike A. F. dos Santos
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Continuous Time ◽  
Probability Distributions ◽  
Diffusion Equations ◽  
Memory Kernel ◽  
Gaussian Distributions ◽  
Diffusive Process ◽  
Continuous Time Random Walks ◽  
Non Gaussian

The investigation of diffusive process in nature presents a complexity associated withmemory effects. Thereby, it is necessary new mathematical models to involve memory conceptin diffusion. In the following, I approach the continuous time random walks in the context ofgeneralised diffusion equations. To do this, I investigate the diffusion equation with exponential andMittag–Leffler memory-kernels in the context of Caputo–Fabrizio and Atangana–Baleanu fractionaloperators on Caputo sense. Thus, exact expressions for the probability distributions are obtained,in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class ofdiffusive behaviour. Moreover, I propose a generalised model to describe the random walk processwith resetting on memory kernel context.

scholarly journals Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Gaussian Distributions ◽  
Velocity Increments ◽  
Non Gaussian

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

Non-Gaussian probability distributions of solar wind fluctuations

1994 ◽  
Vol 12 (12) ◽  
pp. 1127-1138 ◽  
Author(s):  
E. Marsch ◽  
C. Y. Tu
Keyword(s):  
Solar Wind ◽  
Probability Distributions ◽  
Time Lag ◽  
Small Scale ◽  
Time Lags ◽  
Mhd Turbulence ◽  
Theoretical Concepts ◽  
Fluid Turbulence ◽  
Long Time ◽  
Non Gaussian

Abstract. The probability distributions of field differences ∆x(τ)=x(t+τ)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.

scholarly journals Industry Definition and Less Than Fair Value Pricing: an Analysis of ITC Practice

1994 ◽  
Vol 9 (1) ◽  
pp. 106-22
Author(s):  
Nestor M. Arguea ◽  
Richard K. Harper
Keyword(s):  
Fair Value ◽  
Value Pricing

scholarly journals A Study of Black–Scholes Model’s Applicability in Indian Capital Markets

Paradigm ◽  
2020 ◽  
Vol 24 (1) ◽  
pp. 73-92
Author(s):  
Anubha Srivastava ◽  
Manjula Shastri
Keyword(s):  
Stock Market ◽  
Option Pricing ◽  
Trading Volume ◽  
Stock Exchange ◽  
Market Price ◽  
Significant Degree ◽  
Pricing Model ◽  
Fair Price ◽  
Black Scholes ◽  
Indian Stock Market

Derivative trading, started in mid-2000, has become an integral and significant part of Indian stock market. The tremendous increase in trading volume in Indian stock market has reflected into high volatility in the option prices. The pricing of options is very complex aspect of applied finance and has been subject of extensive research. Black–Scholes option model is a scientific pricing model which is applied for determining the fair price for option contracts. This article examines if Black–Scholes option pricing model (BSOPM) is a good indicator of option pricing in Indian context. The literature review highlights that various studies have been conducted on BSOPM in various stock exchange across the world with mixed outcome on its relevance and applicability. This article is an empirical study to test the relevance of BSOPM for which 10 most popular industry’s stock listed on National Stock Exchange have been taken. Then the BSOPM has been applied using volatility and risk-free rate. Furthermore, t-test has been used to test the hypothesis and determine the significant relationship between BS model values and actual model values. This study concludes that BSOPM involves significant degree of mispricing. Hence, this model alone cannot be adopted as an indicator for option pricing. The variation from market price is synchronised with respect to moneyness and time to maturity of the option.

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