Black-Scholes in a CEV Random Environment: A New Approach to Smile Modelling

2015 ◽  
Author(s):  
Antoine Jacquier ◽  
Patrick Roome
Keyword(s):  
Random Environment ◽  
New Approach ◽  
Black Scholes

scholarly journals Black–Scholes in a CEV random environment

2018 ◽  
Vol 12 (3) ◽  
pp. 445-474 ◽  
Author(s):  
Antoine Jacquier ◽  
Patrick Roome
Keyword(s):  
Random Environment ◽  
Black Scholes

NEARLY EXACT OPTION PRICE SIMULATION USING CHARACTERISTIC FUNCTIONS

2012 ◽  
Vol 15 (07) ◽  
pp. 1250047 ◽  
Author(s):  
CAROLE BERNARD ◽  
ZHENYU CUI ◽  
DON MCLEISH
Keyword(s):  
Characteristic Function ◽  
Probability Density ◽  
Option Price ◽  
Probability Density Functions ◽  
Heston Model ◽  
Characteristic Functions ◽  
Density Functions ◽  
New Approach ◽  
Black Scholes ◽  
Unbiased Estimates

This paper presents a new approach to perform a nearly unbiased simulation using inversion of the characteristic function. As an application we are able to give unbiased estimates of the price of forward starting options in the Heston model and of continuously monitored Parisian options in the Black-Scholes framework. This method of simulation can be applied to problems for which the characteristic functions are easily evaluated but the corresponding probability density functions are complicated.

scholarly journals Application of the Trefftz method for option pricing

2020 ◽  
Vol 2020 (146) ◽  
pp. 37-49
Author(s):  
Katarzyna BRZOZOWSKA-RUP ◽  
◽  
Sylwia HOŻEJOWSKA ◽  
Leszek HOŻEJOWSKI ◽  
◽  
...  
Keyword(s):  
Option Pricing ◽  
Design Methodology ◽  
Number Of Solutions ◽  
Trefftz Method ◽  
New Approach ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Starting Point ◽  
Black Scholes ◽  
Computational Simplicity

Purpose: Option pricing is hardly a new topic, however, in many cases they lack an analytical 11 solution. The article proposes a new approach to option pricing based on the semi-analytical 12 Trefftz method. 13 Design/methodology/approach: An appropriate transformation makes it possible to reduce the 14 Black-Scholes equation to the heat equation. This admits the Trefftz method (which has shown 15 its effectiveness in heat conduction problems) to be employed. The advantage of such 16 an approach lies in its computational simplicity and in the fact that it delivers a solution 17 satisfying the governing equation. 18 Findings: The theoretical option pricing problem being considered in the paper has been solved 19 by means of the Trefftz method, and the results achieved appear to comply with those taken 20 from the Black-Scholes formula. Numerical simulations have been carried out and compared, 21 which has confirmed the accuracy of the proposed approach. 22 Originality/value: Although a number of solutions to the Black-Scholes model have appeared, 23 the paper presents a thoroughly novel idea of implementation of the Trefftz method for solving 24 this model. So far, the method has been applied to problems having nothing in common with 25 finance. Therefore the present approach might be a starting point for software development, 26 competitive to the existing methods of pricing options.

scholarly journals CONDITIONAL LEAST SQUARES ESTIMATION OF THE PARAMETERS OF HIGHER ORDER RANDOM ENVIRONMENT INAR MODElS

2019 ◽  
pp. 525
Author(s):  
Petra N. Laketa ◽  
Aleksandar S. Nastic
Keyword(s):  
Least Squares ◽  
Random Environment ◽  
Nonnegative Integer ◽  
Simulated Data ◽  
Higher Order ◽  
Counting Processes ◽  
Autoregressive Processes ◽  
New Approach ◽  
Conditional Least Squares ◽  
Parameter Values

Two different random environment INAR models of higher order, precisely RrNGINARmax(p) and RrNGINAR1(p), are presented as a new approach to modeling non-stationary nonnegative integer-valued autoregressive processes. The interpretation of these models is given in order to better understand the circumstances of their application to random environment counting processes. The estimation statistics, defined using the Conditional Least Squares (CLS) method, is introduced and the properties are tested on the replicated simulated data obtained by RrNGINAR models with different parameter values. The obtained CLS estimates are presented and discussed.

scholarly journals A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 760 ◽  
Author(s):  
Seda Gulen ◽  
Catalin Popescu ◽  
Murat Sari
Keyword(s):  
Current Method ◽  
Strong Stability ◽  
Computational Effort ◽  
Academic Community ◽  
Third Order ◽  
New Approach ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Linear And Nonlinear

Since financial engineering problems are of great importance in the academic community, effective methods are still needed to analyze these models. Therefore, this article focuses mainly on capturing the discrete behavior of linear and nonlinear Black–Scholes European option pricing models. To achieve this, this article presents a combined method; a sixth order finite difference (FD6) scheme in space and a third–order strong stability preserving Runge–Kutta (SSPRK3) over time. The computed results are compared with available literature and the exact solution. The computed results revealed that the current method seems to be quite strong both quantitatively and qualitatively with minimal computational effort. Therefore, this method appears to be a very reliable alternative and flexible to implement in solving the problem while preserving the physical properties of such realistic processes.

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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