Non-Gaussian noise-enhanced stochastic rate oscillations in CO oxidation on nanometer-sized Pd particles

The effect of non-Gaussian colored noise(NGN),mainly its departure q from the Gaussian noise,on the optimal ISRO of CO oxidation on nanometer-sized Pd particles was studied.It was found that the ISRO in the absence of external noise can still be enhanced when the NGN is applied.Specifically,the ISRO varies with changing q and becomes more regular at an appropriate q value,and when q is optimal,the ISRO becomes the most regular.Because the departure q from the Gaussian noise determines the probability distribution function and hence may denote the types of noise,this result shows that different types of external noise can enhance the ISRO of CO oxidation,and non-Gaussian noise may enhance the ISRO more greatly than the Gaussian noise.Therefore,non-Gaussian noise could play more effective roles in the catalytic process of CO oxidation on nanometer-sized Pd particles.

PRICES OF ASIAN OPTIONS UNDER STOCHASTIC INTEREST RATES

Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.

Reliability-based congestion pricing model under endogenous equilibrated market penetration and compliance rate of ATIS

A reliability-based stochastic system optimum congestion pricing(SSOCP) model with endogenous market penetration and compliance rate in an advanced traveler information systems(ATIS) environment was proposed. All travelers were divided into two classes. The first guided travelers were referred to as the equipped travelers who follow ATIS advice, while the second unguided travelers were referred to as the unequipped travelers and the equipped travelers who do not follow the ATIS advice(also referred to as non-complied travelers). Travelers were assumed to take travel time, congestion pricing, and travel time reliability into account when making travel route choice decisions. In order to arrive at on time, travelers needed to allow for a safety margin to their trip.The market penetration of ATIS was determined by a continuous increasing function of the information benefit, and the ATIS compliance rate of equipped travelers was given as the probability of the actually experienced travel costs of guided travelers less than or equal to those of unguided travelers. The analysis results could enhance our understanding of the effect of travel demand level and travel time reliability confidence level on the ATIS market penetration and compliance rate; and the effect of travel time perception variation of guided and unguided travelers on the mean travel cost savings(MTCS) of the equipped travelers, the ATIS market penetration, compliance rate, and the total network effective travel time(TNETT).

Pricing Multi-Strike Quanto Call Options on Multiple Assets with Stochastic Volatility, Correlation, and Exchange Rates

Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.

An Actuarial Approach to Reload Option Valuation for a Non-tradable Risk Assets under Jump-diffusion Process and Stochastic Interest Rate

We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.

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.

The three-factor model of evaluating mining rights of coal resources based on options

Since mining rights of coal resources(for short MRCR) could be regarded as a multi-stage compound real option,the evaluation for MRCR can be better solved using op- tion theory than the NPV.In the former research,we developed a two-factor model of evaluating MRCR when the coal spot price and convenience yield are stochastic based on option theory.On the basis of this two-factor model,we set up a three-factor model of evaluating MRCR when the interest rate followed a stochastic process.Through a real example application,we found the model can get higher values than the two-factor model and the NPV.This is because considering the volatility of interest rate can improve the executive opportunity of MRCR.

Convergence and optimality of BS-type discrete hedging strategy under stochastic interest rate

We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging instruments: one is the portfolio of underlying stock, zero coupon bond, and the money market account (Strategy BSI); the other is the underlying stock, zero coupon bond (Strategy BSII). Similar to the results of the deterministic interest rate case, we show that convergence speed of the discounted hedging errors is 1/2-order of trading frequency for both strategies. Then, we prove each of the BS-type strategy is not only locally optimal, but also globally optimal under the corresponding measure. Finally, we give some numerical examples to illustrate the results. All the discussion is based on non-arbitrage condition and zero transaction cost.

Valuation of correlation options under a stochastic interest rate model with regime switching

We consider the valuation of a correlation option, a two-factor analog of a European call option, under a Hull-White interest rate model with regime switching. More specifically, the model parameters are modulated by an observable, continuous-time, finite-state Markov chain. We obtain an integral pricing formula for the correlation option by adopting the techniques of measure changes and inverse Fourier transform. Numerical analysis, via the fast Fourier transform, is provided to illustrate the practical implementation of our model.

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate(SIR),stochastic volatility(SV),and double exponential jump into the jump-diffusion settings.The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns,rare events,and an SIR.Using the model,we deduce the pricing characteristic function and pricing formula of a European option.Then,we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV.For verification purposes,we conduct time efficiency analysis,goodness of fit analysis,and jump/drift term analysis of the proposed model.In addition,we compare the pricing accuracy of the proposed model with those of the Black-Scholes and the Kou(2002)models.The empirical results show that the proposed option pricing model has high time efficiency,and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.

Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income

This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before retirement,the manager tries to optimize the mean-variance utility of the wealth in the member’s pension account at retirement.At retirement,the pension account wealth(or part of it)is used to purchase a paid-up annuity.After retirement,the manager has to pay the guaranteed annuity,continues to invest,and aims to optimize the mean-variance utility of the terminal wealth at a fix future time,to satisfy the pension member’s heritage and life needs in the next stage.Interest rate risk and income risk are introduced.Applying the game theory and the extended Bellman equation,the time-consistent investment strategies and the efficient frontiers before and after retirement are obtained explicitly.Obtained results indicate that the stochastic interest rate and the stochastic income have essential effects on the investment strategies.

Exploiting Virtual Elasticity of Production Systems to Respect OTD—Part 3: Basic Considerations for Modelling CPPS Characterized by Non-Ergodic Order Entry and Non-Deterministic Product-Mix for Fully Flexible Addressable Workstations

The recently experienced hype concerning the so-called “4th Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.

Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments

This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.

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）.

Closed-Form Formulae for European Options Under Three-Factor Models

In this paper,we derive new closed-form valuations to European options under three-factor hybrid models that include stochastic interest rates and stochastic volatility and incorporate a nonzero covariance structure between factors.We make novel use of the empirically proven 3/2 stochastic volatility model with a time-dependent drift inwhich we are free to choose the moving reversion target.Thismodel has been shown bymany authors to empirically outperform other volatility models in maximising model fit.We also improve the valuation of European options under the Heston volatility and Cox,Ingersoll,Ross interest rate model,recently published in the literature,by replacing open-form infinite series with closed-form analytic expressions.For completeness,we also add a fuller covariance structure in this setting and detail closed-form valuations for options.The inclusion of nonzero covariances amongst the factors can significantly improve option pricing by allowing for a wider variety of market behaviour.The solutions are derived by firstly formulating the price of a European call option in terms of the corresponding characteristic function of the underlying price and then determining a partial differential equation for the characteristic function.By including empirically proven models into our analysis,the options formulae could provide more realistic prices for investors and practitioners.

Extinction Effects of Multiplicative Non-Gaussian L′evy Noise in a Tumor Growth System with Immunization

The extinction phenomenon induced by multiplicative non-Gaussian L′evy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability.

Efficient Simulations of Option Pricing and Greeks Under Three-Factor Model by Conditional Monte Carlo Method

This paper proposes a hybrid Monte Carlo simulation method for pricing European options under the stochastic volatility model and three-factor model.First,the European options are expressed as a conditional expectation formula,which can be used not only for reducing variance of simulations,but also for calculating the value of Greeks easily,due to the elimination of the weak singularity for the payoff of the option.Then,in order to reduce variance further,the authors also construct a new explicit regression based control variate under Heston model and three-factor model respectively.Numerical results of experiments show that the proposed method can greatly reduce the variance of simulation for pricing European option,and is easy to complement for the calculation of Greeks.