Bayesian Estimating for cox Ingersoll Ross process

the model of term structure of interest rates are consider the most significant and computationally difficult portion of the modern finance due to a relative complexity of using techniques. This article concerns the Bayesian estimation of interest rate models. Assume the short term interest rate follows the Cox Ingersoll Ross (CIR) process , this process has several feature. In particular mean reverting and the other feature is remanis non- negative , so this is what distinguishes it from previous models. It is implement in the R programing.

Maintaining AACSB international accreditation: from basics to best practices

Purpose A truly successful continuous improvement review (CIR) visit does more than merely check the boxes for a positive recommendation. It builds the story of the school and should be an opportunity for its culture to shine through. The purpose of this paper is to demonstrate how to facilitate a successful CIR visit by moving from the basics of accreditation to understanding, implementing and “living” best practices. Design/methodology/approach Short tenure and high turnover among business school deans, mean that the majority of those leading the CIR may have no previous experience with the process. Findings This study begins by providing an overview of the role of accreditation and the role of the dean in the accreditation process. With a combined experience of over 35 years in the dean role and having served on or chaired over 35 accreditation visits, the authors share their experiences and offer a seven-step process for understanding and implementing best practices in the Association to Advance Collegiate Schools of Business accreditation process. Originality/value The suggestions offered in this study should help schools enhance long-term positive outcomes and serve as a guide to those navigating the CIR process.

Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables

In this paper, we construct second-order weak split-step approximations of the CKLS and CEV processes that use generation of a three−valued random variable at each discretization step without switching to another scheme near zero, unlike other known schemes (Alfonsi, 2010; Mackevičius, 2011). To the best of our knowledge, no second-order weak approximations for the CKLS processes were constructed before. The accuracy of constructed approximations is illustrated by several simulation examples with comparison with schemes of Alfonsi in the particular case of the CIR process and our first-order approximations of the CKLS processes (Lileika– Mackevičius, 2020).

Pricing spread options under Levy jump-diffusion models

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

Pricing spread options under Levy jump-diffusion models

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

The Covid-19 Effect on Security Mortgage Valuation

The reverse mortgage market has been expanding rapidly in developed economies in recent years. Reverse mortgages provide an alternative source of funding for retirement income and health care costs. We often hear the phrase “house rich and cash poor” to refer the increasing number of elderly persons who hold a substantial proportion of their assets in home equity. Reverse mortgage contracts involve a range of risks from the insurer’s perspective. When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices, and mortality rates. In this context, Covid-19 has occurred and the insurer is faced with this additional source of risk. We analyse the combined impact of these risks on the pricing and the risk profile of reverse mortgage loans. We consider a CIR process for the evolution of the interest rate, a Black & Scholes model for the dynamics of house prices and the Gompertz model for the trend in mortality Our results show that the decrease in the mortality curve due to Covid exposes the insurer to higher risks once the shock is reabsorbed. The risk is higher the higher the age of entry. Only a significant reduction of the shock adjustment coefficient will return the situation to normality.

On The Closed Form Strategies of an Investor under the CEV and CIR Processes

In this paper, the explicit solutions of the optimal investment plans of an investor with exponential utility function exhibiting constant absolute risk aversion (CARA) under constant elasticity of variance (CEV) and stochastic interest rate is studied. A portfolio comprising of a risk-free asset modelled by the Cox-Ingersoll-Ross (CIR) process and two risky assets modelled by the CEV process is considered, where the instantaneous volatilities of the two risky assets form a 2 x 2 matrix n = {np,q}2x2 such that nnT is positive definite. Using the power transformation and change of variable approach with asymptotic expansion technique, explicit solutions of the optimal investment plans are found. Moreover, numerical simulations are used to study the effects of the interest rate, elasticity parameter, correlation coefficient and the risk averse coefficient on the optimal investment plans.