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).

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

2020 ◽  
Vol 8 (4) ◽  
pp. 346-355
Author(s):  
Feng Xu
Keyword(s):  
Empirical Studies ◽  
Asset Price ◽  
European Options ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Bifractional Brownian Motion ◽  
Compound Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging

AbstractRecent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

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 Pricing vulnerable options under a Markov-modulated jump-diffusion model with fire sales

2019 ◽  
Vol 15 (1) ◽  
pp. 293-318 ◽  
Author(s):  
Qing-Qing Yang ◽  
◽  
Wai-Ki Ching ◽  
Wanhua He ◽  
Tak-Kuen Siu ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Fire Sales ◽  
Jump Diffusion Model ◽  
Markov Modulated ◽  
Vulnerable Options

scholarly journals The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chao Wang ◽  
Shengwu Zhou ◽  
Jingyuan Yang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Default Intensity ◽  
Stochastic Interest ◽  
Jump Diffusion Model ◽  
Vulnerable Option ◽  
Vulnerable Options

Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being.

Sign in / Sign up

Export Citation Format

Share Document