Empirical Examinations of the Black-Scholes Model and Merton Jump-Diffusion Model in the Chinese Options Market

2018 ◽  
Author(s):  
Zhiwei Zhang
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Options Market ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Jump Diffusion Model

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.

scholarly journals Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model

2011 ◽  
Vol 48 (03) ◽  
pp. 637-656 ◽  
Author(s):  
Ning Cai
Keyword(s):  
Laplace Transform ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Jump Diffusion ◽  
Option Prices ◽  
Black Scholes Model ◽  
Double Exponential ◽  
Black Scholes ◽  
Jump Diffusion Model

This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

scholarly journals Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model

2011 ◽  
Vol 48 (3) ◽  
pp. 637-656 ◽  
Author(s):  
Ning Cai
Keyword(s):  
Laplace Transform ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Jump Diffusion ◽  
Option Prices ◽  
Black Scholes Model ◽  
Double Exponential ◽  
Black Scholes ◽  
Jump Diffusion Model

This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.

scholarly journals A combined compact difference scheme for option pricing in the exponential jump-diffusion models

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rahman Akbari ◽  
Reza Mokhtari ◽  
Mohammad Taghi Jahandideh
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Asset Market ◽  
European Options ◽  
Compact Difference Scheme ◽  
High Order Method ◽  
Compact Difference ◽  
Black Scholes ◽  
Jump Diffusion Model

AbstractIn the present paper, starting with the Black–Scholes equations, whose solutions are the values of European options, we describe the exponential jump-diffusion model of Levy process type. Here, a jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general “partial integro-differential equation” (PIDE). With a combined compact difference (CCD) scheme for the spatial discretization, a high-order method is proposed for solving exponential jump-diffusion models. The method is sixth-order accurate in space and second-order accurate in time. A known analytical solution to the model is used to evaluate the performance of the numerical scheme.

scholarly journals Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Panhong Cheng ◽  
Zhihong Xu
Keyword(s):  
Firm Value ◽  
Asset Price ◽  
Jump Diffusion ◽  
Bifractional Brownian Motion ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Actuarial Approach ◽  
Jump Diffusion Model ◽  
Vulnerable Options ◽  
Klein Model

In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. By using the actuarial approach, analytic formulae for pricing the European vulnerable options are derived. The proposed pricing model contains many existing models such as Black–Scholes model (1973), Merton jump-diffusion model (1976), Klein model (1996), and Tian et al. model (2014).

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