Pricing the American Options: A Closed-Form, Simple Formula

2019 ◽  
Author(s):  
Moawia Alghalith
Keyword(s):  
Closed Form ◽  
Simple Formula ◽  
American Options

scholarly journals Predictive mathematical models for the number of individuals infected with COVID-19

2020 ◽  
Author(s):  
A.S. Fokas ◽  
N. Dikaios ◽  
G.A. Kastis
Keyword(s):  
Lower Bound ◽  
Mathematical Models ◽  
Closed Form ◽  
Upper Bound ◽  
Logistic Model ◽  
Simple Formula ◽  
Time Dependent ◽  
Sigmoidal Curve ◽  
Specific Virus ◽  
Number Of Individuals

AbstractWe model the time-evolution of the number N(t) of individuals reported to be infected in a given country with a specific virus, in terms of a Riccati equation. Although this equation is nonlinear and it contains time-dependent coefficients, it can be solved in closed form, yielding an expression for N(t) that depends on a function α(t). For the particular case that α(t) is constant, this expression reduces to the well-known logistic formula, giving rise to a sigmoidal curve suitable for modelling usual epidemics. However, for the case of the COVID-19 pandemic, the long series of available data shows that the use of this simple formula for predictions underestimates N(t); thus, the logistic formula only provides a lower bound of N(t). After experimenting with more than 50 different forms of α(t), we introduce two novel models that will be referred to as “rational” and “birational”. The parameters specifying these models (as well as those of the logistic model), are determined from the available data using an error-minimizing algorithm. The analysis of the applicability of the above models to the cases of China and South Korea suggest that they yield more accurate predictions, and importantly that they may provide an upper bound of the actual N(t). Results are presented for Italy, Spain, and France.

Optimal Isolation of a Single-Degree-of-Freedom System With Quadratic-Velocity Damping

1981 ◽  
Vol 48 (3) ◽  
pp. 676-678 ◽  
Author(s):  
T. L. Alley
Keyword(s):  
Closed Form ◽  
Simple Formula ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Spring ◽  
Velocity Input

The response of a mass isolated by a linear spring and a quadratic-velocity damper subjected to a step-and-decay velocity input at the base is found in closed form. This solution leads immediately to the optimal isolation system for this input. The parameters of the optimal isolation system are given by a simple formula.

scholarly journals Near Exact Calculation of American Options

2020 ◽  
Vol 7 (3) ◽  
pp. 55
Author(s):  
Saied Simozar
Keyword(s):  
Closed Form ◽  
Term Structure ◽  
American Options ◽  
Lattice Models ◽  
Practical Approach ◽  
Exact Calculation ◽  
Closed Form Solutions ◽  
Bond Options ◽  
Bond Option ◽  
Binomial Lattice

A new practical approach for the analysis of American (bond) options is developed which is a combination of the closed form solutions and binomial lattice models. The model is calibrated to the observed term structure of rates and traded volatilities and is arbitrage free. The convergence is very fast, but numerically intensive. By extrapolation the near exact premium of an American (bond) option can be calculated.

Closed-form approximation of American options

1993 ◽  
Vol 9 ◽  
pp. S87-S99 ◽  
Author(s):  
Petter Bjerksund ◽  
Gunnar Stensland
Keyword(s):  
Closed Form ◽  
American Options ◽  
Closed Form Approximation
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