scholarly journals Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 731
Author(s):  
Xiaoyu Tan ◽  
Shenghong Li ◽  
Shuyi Wang
Keyword(s):  
Interest Rate ◽  
Diffusion Model ◽  
Lévy Process ◽  
Process Model ◽  
Jump Diffusion ◽  
Levy Process ◽  
Martingale Measure ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Jump Diffusion Model

This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the uniform formalized pricing formulas under the equivalent martingale measure. This model contains not only the traditional jump-diffusion model, such as the compound Poisson model, the renewal model, the pure-birth jump-diffusion model, but also the infinite activities Lévy model.

Likelihood-based estimation of a semiparametric time-dependent jump diffusion model of the short-term interest rate

2019 ◽  
Vol 35 (2) ◽  
pp. 539-557 ◽  
Author(s):  
Tianshun Yan ◽  
Yanyong Zhao ◽  
Wentao Wang
Keyword(s):  
Interest Rate ◽  
Diffusion Model ◽  
Jump Diffusion ◽  
Time Dependent ◽  
Short Term ◽  
Jump Diffusion Model

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.

scholarly journals Pricing Participating Products under a Generalized Jump-Diffusion Model

2008 ◽  
Vol 2008 ◽  
pp. 1-30 ◽  
Author(s):  
Tak Kuen Siu ◽  
John W. Lau ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Life Insurance ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Martingale Measure ◽  
Practical Implementation ◽  
Switching Models ◽  
Jump Diffusion Model ◽  
Equivalent Martingale ◽  
Markovian Regime Switching

We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.

scholarly journals Optimal Investment for Insurers with the Extended CIR Interest Rate Model

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mei Choi Chiu ◽  
Hoi Ying Wong
Keyword(s):  
Interest Rate ◽  
Closed Form Solution ◽  
Critical Factor ◽  
Compound Poisson Process ◽  
Optimal Investment ◽  
Form Solution ◽  
Insurance Companies ◽  
Stochastic Interest Rate ◽  
Stochastic Interest ◽  
Jump Diffusion Model

A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

scholarly journals A jump-diffusion model for pricing electricity under price-cap regulation

2019 ◽  
Vol 13 (4) ◽  
pp. 395-405
Author(s):  
M. Kegnenlezom ◽  
P. Takam Soh ◽  
M. L. D. Mbele Bidima ◽  
Y. Emvudu Wono
Keyword(s):  
Diffusion Model ◽  
Jump Diffusion ◽  
Exact Formula ◽  
Martingale Measure ◽  
Spot Price ◽  
Price Cap Regulation ◽  
Price Cap ◽  
Electricity Spot Price ◽  
Jump Diffusion Model ◽  
Equivalent Martingale

Abstract In this paper, we derive a new jump-diffusion model for electricity spot price from the “Price-Cap” principle. Next, we show that the model has a non-classical mean-reverting linear drift. Moreover, using this model, we compute a new exact formula for the price of forward contract under an equivalent martingale measure and we compare it to Cartea et al. (Appl Math Finance 12(4):313–335, 2005) formula.

Valuation of Equity-indexed Annuities with Stochastic Interest Rate and Jump Diffusion

2014 ◽  
Vol 43 (14) ◽  
pp. 2870-2885
Author(s):  
Linyi Qian ◽  
Rongming Wang ◽  
Qian Zhao
Keyword(s):  
Interest Rate ◽  
Jump Diffusion ◽  
Stochastic Interest Rate ◽  
Stochastic Interest
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