Pricing Perpetual American Option under the Fractional Black-Scholes Model

2010 ◽  
Author(s):  
Wenli Huang ◽  
Shenghong Li ◽  
Songyan Zhang
Keyword(s):  
American Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Perpetual American Option

scholarly journals Bounds for perpetual American option prices in a jump diffusion model

2006 ◽  
Vol 43 (03) ◽  
pp. 867-873 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
American Option ◽  
Option Prices ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Jump Diffusion Model ◽  
Perpetual American Option

We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.

scholarly journals Bounds for perpetual American option prices in a jump diffusion model

2006 ◽  
Vol 43 (3) ◽  
pp. 867-873 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
American Option ◽  
Option Prices ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Jump Diffusion Model ◽  
Perpetual American Option

We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.

A fractional reduced differential transform method for solving time fractional Black Scholes American option pricing equation

2021 ◽  
Vol 30 (1) ◽  
pp. 1-10
Author(s):  
MANZOOR AHMAD ◽  
RAJSHREE MISHRA ◽  
RENU JAIN
Keyword(s):  
Option Pricing ◽  
American Option ◽  
Differential Transform Method ◽  
American Option Pricing ◽  
Transform Method ◽  
Put Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Differential Transform ◽  
Reduced Differential Transform Method

In this paper, fractional reduced differential transform method (FRDTM) is operated to solve time fractional Black-Scholes American option pricing equation paying no dividends.The Black-Scholes model plays a significant role in the evaluation of European or American call and put options. The advantage of the proposed method to other existing methods is that it finds the solution without discretization or transformation. While using this method, no recommended assumptions are needed and hence the computational work reduces to a greater extent. Numerical experiments prove that the proposed method is efficient and valid for obtaining the solution of time fractional Black-Scholes equation governing American options. This method proves to be powerful for solving general fractional order partial differential equations (PDEs) existing in the field of Science, Engineering and other related fields.

An analytical approximation formula for the pricing of credit default swaps with regime switching

2021 ◽  
Vol 63 ◽  
pp. 143-162
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

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