scholarly journals Pricing Warrant Bonds with Credit Risk under a Jump Diffusion Process

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiaonan Su ◽  
Wei Wang ◽  
Wensheng Wang
Keyword(s):  
Numerical Analysis ◽  
Diffusion Process ◽  
Default Risk ◽  
Stock Price ◽  
Jump Diffusion ◽  
Pricing Model ◽  
Default Intensity ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model ◽  
The Interest Rate

This article investigates the pricing of the warrant bonds with default risk under a jump diffusion process. We assume that the stock price follows a jump diffusion model while the interest rate and the default intensity have the feature of mean reversion. By the risk neutral pricing theorem, we obtain an explicit pricing formula of the warrant bond. Furthermore, numerical analysis is provided to illustrate the sensitivities of the proposed pricing model.

A TWO-FACTOR JUMP-DIFFUSION MODEL FOR PRICING CONVERTIBLE BONDS WITH DEFAULT RISK

2016 ◽  
Vol 19 (06) ◽  
pp. 1650046 ◽  
Author(s):  
RADHA KRISHN COONJOBEHARRY ◽  
DÉSIRÉ YANNICK TANGMAN ◽  
MUDDUN BHURUTH
Keyword(s):  
Interest Rate ◽  
Default Risk ◽  
Stock Price ◽  
Numerical Experiments ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Minor Effect ◽  
Jump Diffusion Model ◽  
The Interest Rate

The current literature on convertible bonds (CBs) comprises only models where the stock price and the interest rate are governed by pure-diffusion processes. This paper fills a gap by developing and implementing a two-factor model where both underlying factors follow jump-diffusion processes, and which also incorporates default risk. We derive the partial integro-differential equation satisfied by the CB price in our model, and solve it by a spectral method based on Chebyshev discretizations and Clenshaw–Curtis quadratures. The conversion, call, and put constraints give rise to a linear complementarity problem, which is solved by an operator-splitting (OS) method. Through numerical experiments, we investigate the effects that the various parameters have on the CB price. In particular, our numerical experiments show that jumps in the stock price have a significant impact on the CB price, while jumps in the interest rate tend to have a minor effect on the price. In general, the dynamics of the stock price have more impact in pricing the CB than the dynamics of the interest rate.

scholarly journals Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

2020 ◽  
Vol 2020 ◽  
pp. 1-26 ◽  
Author(s):  
Man Li ◽  
Yingchun Deng ◽  
Ya Huang ◽  
Hui Ou
Keyword(s):  
Diffusion Process ◽  
Default Risk ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Corporate Bond ◽  
Value Functions ◽  
Case Scenario ◽  
Worst Case ◽  
Special Cases ◽  
Jump Diffusion Model

In this paper, we consider a robust optimal investment-reinsurance problem with a default risk. The ambiguity-averse insurer (AAI) may carry out transactions on a risk-free asset, a stock, and a defaultable corporate bond. The stock’s price is described by a jump-diffusion process, and both the jump intensity and the distribution of jump amplitude are uncertain, i.e., the jump is ambiguous. The AAI’s surplus process is assumed to follow an approximate diffusion process. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle, and the reinsurance type has to follow a self-reinsurance function. In performing dynamic programming, both the predefault case and the postdefault case are analyzed, and the optimal strategies and the corresponding value functions are derived under the worst-case scenario. Moreover, we give a detailed proof of the verification theorem and give some special cases and numerical examples to illustrate our theoretical results.

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 Adaptive nonparametric drift estimation of an integrated jump diffusion process

2018 ◽  
Vol 22 ◽  
pp. 236-260 ◽  
Author(s):  
Benedikt Funke ◽  
Émeline Schmisser
Keyword(s):  
Diffusion Process ◽  
High Frequency ◽  
Jump Diffusion ◽  
High Frequency Data ◽  
Compact Set ◽  
Penalized Least Squares ◽  
Adaptive Estimator ◽  
Drift Estimation ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

In the present article, we investigate nonparametric estimation of the unknown drift function b in an integrated Lévy driven jump diffusion model. Our aim will be to estimate the drift on a compact set based on a high-frequency data sample. Instead of observing the jump diffusion process V itself, we observe a discrete and high-frequent sample of the integrated process Xt := ∫0t Vsds Based on the available observations of Xt, we will construct an adaptive penalized least-squares estimate in order to compute an adaptive estimator of the corresponding drift function b. Under appropriate assumptions, we will bound the L2-risk of our proposed estimator. Moreover, we study the behavior of the proposed estimator in various Monte Carlo simulation setups.

scholarly journals Valuation of Game Options in Jump-Diffusion Model and with Applications to Convertible Bonds

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Lei Wang ◽  
Zhiming Jin
Keyword(s):  
Free Boundary ◽  
Diffusion Process ◽  
Stock Price ◽  
Free Boundary Problems ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Simple Application ◽  
Boundary Problems ◽  
Game Options ◽  
Jump Diffusion Model

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS

2021 ◽  
pp. 1-25
Author(s):  
CAIBIN ZHANG ◽  
ZHIBIN LIANG ◽  
KAM CHUEN YUEN
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

Abstract We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Optimal portfolio and consumption for a Markovian regime-switching jump-diffusion process

2021 ◽  
Vol 63 ◽  
pp. 308-332
Author(s):  
Caibin Zhang ◽  
Zhibin Liang ◽  
Kam Chuen Yuen
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Optimal Portfolio ◽  
Dynamic Programming Principle ◽  
Pure Diffusion ◽  
Special Cases ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.   doi:10.1017/S1446181121000122

Productivity Assessment Based on Jump Diffusion Model Considering the Effort Management for OSS Project

2019 ◽  
Vol 26 (05) ◽  
pp. 1950022 ◽  
Author(s):  
Yoshinobu Tamura ◽  
Hironobu Sone ◽  
Shigeru Yamada
Keyword(s):  
Project Management ◽  
Diffusion Process ◽  
Process Model ◽  
Jump Diffusion ◽  
Equation Model ◽  
Operation Performance ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model ◽  
Productivity Assessment

Various open source software (OSS) projects are in action around the world. Many OSS are developed and maintained under these OSS projects. Considering the characteristics of OSS, the operation performance of OSS development will take an irregular fluctuation in the long term of operation, because several developers and many users are closely related to the maintenance of OSS. This paper focuses on the irregular fluctuation of the operation performance of OSS. We apply the jump diffusion process model to the noisy cases in the operation of OSS. In particular, the maintenance effort is estimated by the stochastic differential equation model in terms of OSS project management. Moreover, we discuss the method of maintenance effort management based on jump diffusion process model considering the irregular fluctuation of performance for OSS projects. In particular, we propose the method of productivity assessment based on the proposed jump diffusion models. Thereby, it is helpful for the OSS development managers to understand the effort status of OSS from the standpoint of OSS project management. Also, we analyze actual data to show numerical examples of the proposed method considering the characteristics of OSS projects.

scholarly journals Jump Adapted Scheme Of a Non Mark Dependent Jump Diffusion Process with Application to the Merton Jump Diffusion Model

2017 ◽  
Vol 5 (4) ◽  
pp. 80
Author(s):  
Renaud Fadonougbo ◽  
George O. Orwa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Diffusion Process ◽  
Strong Convergence ◽  
General Result ◽  
Jump Diffusion ◽  
Discretization Scheme ◽  
Complete Proof ◽  
Jump Diffusion Process ◽  
Jump Diffusion Model

This paper provides a complete proof of the strong convergence of the Jump adapted discretization Scheme in the univariate and mark independent jump diffusion process case. We put in detail and clearly a known and general result for mark dependent jump diffusion process. A Monte-Carlo simulation is used as well to show numerical evidence.

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