PRICING EUROPEAN OPTION IN A DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL WITH TWO MARKET STRUCTURE RISKS AND ITS COMPARISONS

Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.

Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model

This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.

On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options under Regime-Switching Kou’s Jump-Diffusion Models

In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.

Reweighted Nadaraya-Watson estimation of jump-diffusion models

In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.

Threshold reweighted Nadaraya-Watson estimation of jump-diffusion models

In this paper,we propose a new method to estimate the diffusion function in the jump-diffusion model.First,a threshold reweighted Nadaraya-Watson-type estimator is introduced.Then,we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties.Finally,our estimator is demonstrated through the actual data of the Shanghai Interbank Offered Rate in China.

A revised jump-diffusion and rotation-diffusion model

Quasi-elastic neutron scattering(QENS) has many applications that are directly related to the development of highperformance functional materials and biological macromolecules, especially those containing some water. The analysis method of QENS spectra data is important to obtain parameters that can explain the structure of materials and the dynamics of water. In this paper, we present a revised jump-diffusion and rotation-diffusion model(rJRM) used for QENS spectra data analysis. By the rJRM, the QENS spectra from a pure magnesium-silicate-hydrate(MSH) sample are fitted well for the Q range from 0.3 ^(-1) to 1.9 ^(-1) and temperatures from 210 K up to 280 K. The fitted parameters can be divided into two kinds. The first kind describes the structure of the MSH sample, including the ratio of immobile water(or bound water) C and the confining radius of mobile water a_0. The second kind describes the dynamics of confined water in pores contained in the MSH sample, including the translational diffusion coefficient Dt, the average translational residence timeτ0, the rotational diffusion coefficient D_r, and the mean squared displacement(MSD) u^2. The r JRM is a new practical method suitable to fit QENS spectra from porous materials, where hydrogen atoms appear in both solid and liquid phases.

Dividend Maximization when Cash Reserves Follow a Jump-diffusion Process

This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman （HJB） equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.

The Stochastic Maximum Principle for a Jump-Diffusion Mean-Field Model Involving Impulse Controls and Applications in Finance

This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control.The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control.As for its application,a mean-variance portfolio selection problem has been solved.

Bias Free Threshold Estimation for Jump Intensity Function

In this paper,combining the threshold technique,we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps.Under mild conditions,we obtain the asymptotic normality for the proposed estimator.Moreover,we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.

A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.

A POISSON-GAUSSIAN MODEL TO PRICE EUROPEAN OPTIONS ON THE EXTREMUM OF SEVERAL RISKY ASSETS WITHIN THE HJM FRAMEWORK

This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The stochastic interest rate is assumed to follow an extended multi-factor HJM model with jumps. The authors provide explicitly the closed-form solutions of these options through the change of numeralre technique and examine the effects of both jump risks and stochastic interest rate on the option price with numerical experiment. The model can be seen as an extension of Stulz （1982）, Johnson （1987） and Lindset （2006）.

Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies

In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.

UPPER BOUND FOR FINITE-TIME RUIN PROBABILITY IN A MARKOV-MODULATED MARKET

This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.

CVaR-hedging and its applications to equity-linked life insurance contracts with transaction costs

This paper analyzes Conditional Value-at-Risk(CVaR)based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs.A nonlinear partial differential equation(PDE)that an option value process inclusive of transaction costs should satisfy is provided.In particular,the closed-form expression of a European call option price is given.Meanwhile,the CVaR-based partial hedging strategy for a call option is derived explicitly.Both the CVaR hedging price and the weights of the hedging portfolio are based on an adjusted volatility.We obtain estimated values of expected total hedging errors and total transaction costs by a simulation method.Furthermore,our results are implemented to derive target clients’survival probabilities and age of equity-linked life insurance contracts.

Empirical likelihood inference for diffusion processes with jumps

In this paper, we consider the empirical likelihood inference for the jump-diffusion model. We construct the confidence intervals based on the empirical likelihood for the infinitesimal moments in the jump-diffusion models. They are better than the confidence intervals which are based on the asymptotic normality of point estimates.

Pricing vulnerable European options with dynamic correlation between market risk and credit risk

In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.

PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

A parameter estimation method,called PMCMC in this paper,is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to term structure of interest rates under Markov regime.However,the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM)in the case of adding jumps.Although the difficulty of parameter estimation greatly prevents from researching models,we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility.The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR.Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.