Empirical study for uncertain finance

2021 ◽  
pp. 1-8
Author(s):  
Han Tang ◽  
Wenfei Li
Keyword(s):  
Differential Equation ◽  
Interest Rate ◽  
Empirical Study ◽  
Method Of Moments ◽  
Stock Price ◽  
Uncertain Differential Equation ◽  
European Options ◽  
Financial Model ◽  
Uncertain Finance

Interest rate, stock and option are all important parts of finance. This paper introduces uncertain differential equation to study the evolution of interest rate and stock price separately. Based on actual observations, we estimate the parameters in uncertain differential equation with the method of moments. Using the introduced interest rate and stock models, we price European options and compare the results pricing with actual observations. Finally, a paradox of the stochastic financial model is stated.

scholarly journals European Spread Option Pricing with the Floating Interest Rate for Uncertain Financial Market

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lidong Zhang ◽  
Yanmei Sun ◽  
Xiangbo Meng
Keyword(s):  
Differential Equation ◽  
Interest Rate ◽  
Financial Market ◽  
Stock Price ◽  
Numerical Algorithms ◽  
Uncertain Differential Equation ◽  
Spread Options ◽  
Put Option ◽  
Pricing Problems ◽  
Spread Option

In this paper, we investigate the pricing problems of European spread options with the floating interest rate. In this model, uncertain differential equation and stochastic differential equation are used to describe the fluctuation of stock price and the floating interest rate, respectively. We derive the pricing formulas for spread options including the European spread call option and the European spread put option. Finally, numerical algorithms are provided to illustrate our results.

THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

2005 ◽  
Vol 08 (02) ◽  
pp. 239-253 ◽  
Author(s):  
PETER CARR ◽  
ALIREZA JAVAHERI
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Stock Price ◽  
Arrival Rate ◽  
European Options ◽  
Standard Assumption ◽  
Integro Differential Equation ◽  
Local Variance ◽  
Calendar Dates

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

scholarly journals Modeling RL Electrical Circuit by Multifactor Uncertain Differential Equation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2103
Author(s):  
Yang Liu ◽  
Lujun Zhou
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Complex Structure ◽  
Internal Noise ◽  
External Noise ◽  
Electrical Circuit ◽  
Uncertain Differential Equation ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Symmetry Principle

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.

scholarly journals An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
A. S. Deakin ◽  
Matt Davison
Keyword(s):  
Differential Equation ◽  
Interest Rate ◽  
Stock Price ◽  
Analytic Solution ◽  
Integral Transforms ◽  
Convertible Bond ◽  
Motion Model ◽  
Bond Model ◽  
Brownian Motion Model ◽  
The Interest Rate

This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.

Uniqueness of the Solution to a Difference-Partial Differential Equation for Finance

2003 ◽  
Vol 13 (07) ◽  
pp. 919-943
Author(s):  
C. Mancini
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rate ◽  
Jump Diffusion ◽  
Market Model ◽  
Contingent Claim ◽  
Partial Differential ◽  
Financial Model ◽  
Diffusion Modelling ◽  
Uniqueness Of The Solution

In this paper we study a difference partial differential equation, arising from a financial model, whose solution represents the price of a security linked to a dividend-paying stock. The market model consists of a jump-diffusion process modelling the stock evolution and an independent diffusion modelling the stochastic spot interest rate. We establish the desirable property of the uniqueness of solution to the equation and, since the specialized model is complete, we can consistently price any contingent claim.

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