A Differential Equations Analysis of Stock Prices

2019 ◽  
pp. 361-365
Author(s):  
Georgios Katsouleas ◽  
Miltiadis Chalikias ◽  
Michalis Skordoulis ◽  
Georgios Sidiropoulos
Keyword(s):  
Differential Equations ◽  
Stock Prices

ESTIMATION IN CONTINUOUS-TIME STOCHASTIC VOLATILITY MODELS USING NONLINEAR FILTERS

2000 ◽  
Vol 03 (02) ◽  
pp. 279-308 ◽  
Author(s):  
JAN NYGAARD NIELSEN ◽  
MARTIN VESTERGAARD
Keyword(s):  
Differential Equations ◽  
Stochastic Volatility ◽  
Stock Prices ◽  
Continuous Time ◽  
Stock Price ◽  
Estimation Method ◽  
Small Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Filtering Problem

The stylized facts of stock prices, interest and exchange rates have led econometricians to propose stochastic volatility models in both discrete and continuous time. However, the volatility as a measure of economic uncertainty is not directly observable in the financial markets. The objective of the continuous-discrete filtering problem considered here is to obtain estimates of the stock price and, in particular, the volatility using discrete-time observations of the stock price. Furthermore, the nonlinear filter acts as an important part of a proposed method for maximum likelihood for estimating embedded parameters in stochastic differential equations. In general, only approximate solutions to the continuous-discrete filtering problem exist in the form of a set of ordinary differential equations for the mean and covariance of the state variables. In the present paper the small-sample properties of a second order filter is examined for some bivariate stochastic volatility models and the new combined parameter and state estimation method is applied to US stock market data.

scholarly journals Existence Theorems for Solutions to Set-Valued Stochastic Differential Equations and Applications

2012 ◽  
Vol 1 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Van Hoa Ngo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Wiener Process ◽  
Langevin Equation ◽  
Stock Prices ◽  
Hausdorff Space ◽  
Existence Theorems ◽  
Uniqueness Of Solution ◽  
Hukuhara Derivative ◽  
Interval Valued

In this paper, a class of new stochastic differential equations on semilinear Hausdorff space under Hukuhara derivative, called set-valued stochastic differential equations (SSDEs) driven by a Wiener process. Moreover, some corresponding properties of SSDEs are discussed such as existence, uniqueness of solution. Finaly, we give some applications to models of interval-valued stochastic differential equations such as stock prices model and the Langevin equation.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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