scholarly journals Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jun Liu ◽  
Zhian Liang
Keyword(s):  
Diffusion Model ◽  
Differential Inequality ◽  
Sharp Increase ◽  
Numerical Experiments ◽  
Jump Diffusion ◽  
Underlying Asset ◽  
Put Options ◽  
Insurance Product ◽  
Jump Diffusion Model ◽  
The Impact

The insurance product with shout options which permit the holders to modify the contract rules is one of the most popular products in European and American markets today. Therefore, it is of great significance to price more precisely. A new mathematical model consisting of a partial differential inequality and constraint conditions is derived for the price of insurance products in a jump-diffusion model. The numerical experiments are performed to analyze the impact of parameters on the insurance product with shout put options, especially for the jump times and the quantities of shout opportunities. The experiment results show that the value of the product is strongly affected by the quantities of shouting opportunities, especially for high values of the underlying asset, while it is only weakly affected for low values. Meanwhile, another meaningful discovery is that the valuation has changed little as the jump times are less than five, while it has shown a sharp increase once the jump times are more than five. Furthermore, the indicator results of course grid errors show that the values of shout put options in the jump-diffusion model are more accurate than those in a Brownian motion.

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 A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jian Huang ◽  
Zhongdi Cen ◽  
Anbo Le
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Diffusion Model ◽  
Finite Difference Scheme ◽  
Jump Diffusion ◽  
Uniform Mesh ◽  
Put Options ◽  
American Put Options ◽  
Jump Diffusion Model ◽  
American Put

We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. This leads to the solution of problems with a tridiagonal M-matrix. It is proved that the difference scheme satisfies the early exercise constraint. Furthermore, it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. The numerical results support the theoretical results.

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.

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