Black–Scholes like closed form formulas and numerical solutions for American style options

2020 ◽  
Vol 550 ◽  
pp. 124379
Author(s):  
Fredrick Michael
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Black Scholes ◽  
American Style

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 156-165 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

scholarly journals Numerical Solutions of Black-Scholes Model by Du Fort-Frankel FDM and Galerkin WRM

2020 ◽  
Vol 9 (1) ◽  
pp. 1-10
Author(s):  
Md Shorif Hossan ◽  
A B M Shahadat Hossain ◽  
Md Shafiqul Islam
Keyword(s):  
Numerical Solutions ◽  
Black Scholes Model ◽  
Black Scholes

Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part I — Theory

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Closed Form ◽  
Structural Model ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Form Solution ◽  
Control Laws ◽  
Comparison Functions ◽  
Flexible Behavior

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact closed-form and numerical solutions are developed for the small elastic motions of a planar, flexible, single link system, in which the link is represented as an Euler-Bernoulli bar in transverse vibration. The link is connected to ground by a pin joint, and the articulation is controlled by proportional and proprotional/derivative (PD) feedback control laws. The characteristics of the closed-form solution are shown to consist of combinations of the characteristic expressions associated with classical end conditions. A large-articulation flexible body model of a controlled-articulation flexible link is then developed and linearized about an arbitrary reference angle. This model uses the method of assumed modes to represent the flexible behavior of the link. It is shown the model is analytically equivalent to a purely structural model which uses a hybrid set of assumed modes, and that numerical convergence can be investigated in terms of admissible functions and quasi-comparison functions. Numerical evaluation of the use of various types of assumed modes is presented in a companion paper.

Closed-Form Approximations to the Solution of V-Belt Force and Slip Equations

1985 ◽  
Vol 107 (2) ◽  
pp. 292-300 ◽  
Author(s):  
J. P. Dolan ◽  
W. S. Worley
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Design Practice ◽  
Tension Distribution ◽  
Analytical Approximations ◽  
Current Design

A method for generating accurate numerical solutions of the exact differential equations describing tension distribution and radial penetration of a flexible V-belt on driveN and driveR sheaves is presented and results are compared with approximate solutions reported in the literature. Analytical approximations for these solutions of higher accuracy than any previously published have been found and are presented. They suggest important modifications of current design practice for belt tensioning and life appraisal.

Reynolds Equations for Common Generalized Newtonian Models and an Approximate Reynolds-Carreau Equation

2005 ◽  
Author(s):  
Scott Bair ◽  
M. M. Khonsari
Keyword(s):  
Closed Form ◽  
Flow Rate ◽  
Numerical Solutions ◽  
Reynolds Equations ◽  
One Dimensional ◽  
Ellis Model

Exact, closed form one-dimensional Reynolds equations are presented for the Ostwald-DeWaele model, Ellis model, Spriggs model and the double-Newtonian Rabinowitsch and Ferry models. From numerical solutions for flow rate, an approximate Reynolds-Carreau equation is obtained.

Three-dimensional stress state in inclined backfilled stopes obtained from numerical simulations and new closed-form solution

2018 ◽  
Vol 55 (6) ◽  
pp. 810-828 ◽  
Author(s):  
Abtin Jahanbakhshzadeh ◽  
Michel Aubertin ◽  
Li Li
Keyword(s):  
Stress State ◽  
Closed Form ◽  
Numerical Solutions ◽  
Hanging Wall ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Solid Waste Disposal ◽  
Inclination Angles ◽  
Backfilled Stopes

Backfill is commonly used world-wide in underground mines to improve ground stability and reduce solid waste disposal on the surface. Practical solutions are required to assess the stress state in the backfilled stopes, as the stress state is influenced by the fill settlement that produces a stress transfer to the adjacent rock walls. The majority of existing analytical and numerical solutions for the stresses in backfilled openings were developed for two-dimensional (plane strain) conditions. In reality, mine stopes have a limited extension in the horizontal plane so the stresses are influenced by the four walls. This paper presents recent three-dimensional (3D) simulations results and a new 3D closed-form solution for the vertical and horizontal stresses in inclined backfilled stopes with parallel walls. This solution takes into account the variation of the stresses along the opening width and height, for various inclination angles and fills properties. The numerical results are used to validate the analytical solution and illustrate how the stress state varies along the opening height, length, and width, for different opening sizes and inclination angles of the footwall and hanging wall. Experimental results are also used to assess the validity of the proposed solution.

scholarly journals Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Wei-Guo Zhang ◽  
Ping-Kang Liao
Keyword(s):  
Credit Risk ◽  
Regime Switching ◽  
Numerical Solutions ◽  
Dilution Effect ◽  
Convertible Bonds ◽  
Bond Pricing ◽  
Convertible Bond ◽  
Pricing Model ◽  
Black Scholes ◽  
The Impact

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

Squeeze Film Characteristics of Circular Contacts at Constant Squeeze Velocity Motion with Non-Newtonian Lubricants

2011 ◽  
Vol 63-64 ◽  
pp. 147-151
Author(s):  
Li Ming Chu ◽  
Wang Long Li ◽  
Hsiang Chen Hsu
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Closed Form Solution ◽  
Elastohydrodynamic Lubrication ◽  
Form Solution ◽  
Squeeze Film ◽  
High Pressure Stage ◽  
Time Calculation ◽  
Film Characteristics

In this paper, the numerical solutions in pure squeeze motion are explored by using hydrodynamic lubrication (HL) and elastohydrodynamic lubrication (EHL) models at constant squeeze velocity with power law lubricants. This paper also proposes a closed form solution to calculate the relationship between central pressure and central film thickness under HL condition. In order to save time calculation, the present closed form solution can be used as the initial condition for analysis of EHL at the high-pressure stage. In addition, this paper also discussed the HL and EHL squeeze film characteristics.

Sign in / Sign up

Export Citation Format

Share Document