Бидний тухай
Багш ажилтан
Because the asset value of a private company is not observable, the structural model has not been developed for a private company. For this reason, this paper attempts to develop the Merton’s structural model for the private company by using the dividend discount model (DDM). In this paper, we obtain closed–form formulas of risk–neutral equity and liability values, default probability, optimal debt amount, and optimal portfolio, prices of bonds, prices of Margrabe options with default risk for the private company.
In this study, we introduce new estimation methods for the required rate of returns on equity of private and public companies using the stochastic dividend discount model (DDM). To estimate the required rate of return on equity, we use the maximum likelihood method, the Bayesian method, and the Kalman filtering. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data over a 32-year period. Overall, the suggested methods can be used to estimate the required rate of returns.
Abstract: The report introduces multi-period loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraint as Basel II and modelling economic condition as AR(1) process, we obtain results regarding the existence of loan interest rate equilibrium. Basel II uses a “three pillars” concept, namely, minimum capital requirements (addressing credit risk, market risk, and operational risk), supervisory review, and market discipline. Process of Basel II attracted a lot of interest in quantitative credit risk models in industry, academia, and among regulators. A sensitivity analysis for the solvency constraint model and some numerical results are presented. Keywords: Nash equilibrium model, one factor KMV/Risk metrics model, Basel II solvency constraint, credit rating, loan interest rate
This paper presents pricing and hedging methods for rainbow options and lookback options under Markov-Switching Vector Autoregressive (MS-VAR) process. Here we assumed that a regime-switching process is generated by a homogeneous Markov process. An advantage of our model is it depends on economic variables and simple as compared with previous existing papers.
This paper introduces multi–period loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraint as Basel II and modelling economic condition as AR(1) process, we obtain results regarding the existence of loan interest rate equilibrium. A sensitivity analysis for the solvency constraint model and some numerical results are presented.
In this paper, we obtain results regarding partial derivatives of risk measures. It is a wellknown fact that for a linear loss random variable, partial derivatives of the Value-at-Risk are represented by conditional expectations. We proved that the result for the Value-at-Risk still holds for any risk measures.
This paper introduces a stochastic dividend discount model with regime–switching and conditional heteroscedasticity. We obtain formulas, corresponding to a default probability and -th moment of a random stock price of a company. Next, we connect option pricing, hedging, and equity–linked life insurance products to the stochastic dividend discount model. Also, the paper provides maximum likelihood estimators of parameters of the stochastic dividend discount model. Finally, we present numerical results for the equity–linked life insurance products in the case of Walmart.
The study introduces a stochastic multi{period dividend discount model (DDM) that includes (i) a compound non homogenous Poisson{process for dividend growth and (ii) the probability of firm default. We obtain maximum likelihood (ML) estimators and confidence interval formulas of our model parameters. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data over a 42{year period. Interestingly, stock price estimations calculated with the model are close to the observable prices. Overall, we prove that the model can be a useful tool for stock pricing.
This paper introduces a stochastic multi-period dividend discount model (DDM) with dividend jump. In the paper, we derive a joint distribution of random default time and random stock price of a company with default risk. Based on the joint distribution we obtain a moment formula of the company's random stock price. Next, we connect option pricing, hedging and several life insurance products to the stochastic DDM. Finally, we obtain ML estimators of the stochastic DDM and sampling distributions of the estimators.
This paper attempts to study loan interest rate Nash game models in the banking sector under regulatory solvency constraints. By taking solvency constraints as Basel I, Basel II, and Expected Shortfall (ES), we obtain results regarding the existence of loan interest rate equilibrium. A sensitivity analysis for solvency models and some numerical results are presented. Numerical results show that the weighted loan interest rate of the Mongolian banking system is consistent with the base case of the theoretical weighted loan interest rate corresponding to the Nash equilibrium.
The Selenge basin contributes approximately 50% of the total inflow into Lake Baikal and is thus of high significance for the regional hydrological regime. Our study was conducted in the upper reaches of the basin, where the Selenge river and its tributaries flow through the Mongolian forest-steppe. Monthly and maximum runoff, precipitation, and air temperature data from 12 gauging stations collected between 1978 and 2015 were analyzed to characterize the hydrological regime response to climate change. Concomitant with rising temperatures and increased potential evaporation, river runoff in the Mongolian part of the Selenge basin has decreased from the first interval (1978–1995) of our study period compared with the consecutive interval from 1996 to 2015. The decrease in runoff throughout the study area was most likely caused by an increase in potential evapotranspiration (and not reduced precipitation or land use changes) for both summer rainfall- and snowmelt-dominated rivers. Annual maximum runoff has also strongly decreased suggesting that reduced flooding is a contemporary threat for Mongolia’s riverine ecosystems, probably causing the replacement of wetland and mesic habitats.
Энэхүү судалгааны ажлын хүрээнд бид ноогдол ашгийг нийлмэл нэгэн төрлийн бус Пуассоны процессоор загварчилснаас гадна компани дефолт болох магадлалыг тооцсон олон үет стохастик ноогдол ашгийн хямдруулалтын загварыг боловсрууллаа. Бид өөрсдийн загварын параметрүүдийн хамгийн их үнэний хувь бүхий үнэлэлтүүд болон итгэх завсрыг тооцох томъёог гарган авсан. S\&P500 индексэд багтдаг компаниудын сүүлийн 41 жилийн түүхэн өгөгдөл, зэрэглэл тогтоогч байгууллагын гаргасан зэрэглэлд үндэслэн өөрсдийн боловсруулсан загварыг туршихад бидний боловсруулсан загвараар тооцсон онолын үнэ нь бодит үнэтэй нилээн ойролцоо гарч байна.
Энэ ажлын хүрээнд бид зээлийн хүүгээрээ өрсөлддөг банкны зах зээлд төв банкны шаардах өөрийн хөрөнгийн хүрэлцээний үзүүлэлтийг хангасан байхаар банкууд Нэшийн тэнцвэрд хүргэх зээлийн хүүг хэрхэн тогтоох талаар авч үзсэн. Санамж 4-д буй зээл болон хадгаламжийн хүүний өрсөлдөөний загварыг ашиглан хадгаламжийн хүүнд дээд зааг тавих замаар зээлийн хүү буурна гэсэн маргаанд хариу өгч болно. Өөрийн хөрөнгийн хүрэлцээний зааглалтаар Basel-I, Basel-II-аас шаарддаг өөрийн хөрөнгийн зааглалт мөн Expected Shortfall зааглалтыг авч үзсэн. Загваруудын хувьд тэнцвэрт хүү оршин байхыг баталж, мэдрэмжийн шинжилгээ хийж сонгон авсан гурван банкны хувьд тоон туршилт явуулсан.
This paper deals with an extension of the one-period model in non-life insurance markets (cf. [1]) by using a transition probability matrix depending on some economic factors. We introduce a multi-period model and in each period the solvency constraints will be updated. Moreover, the model has the inactive state including some uninsured population. Similar results on the existence of premium equilibrium and sensitivity analysis for this model are presented and illustrated by numerical results.
This paper deals with some results of stochastic dividend discount model based on VAR process. We get following main results: In this paper we derived closed form formula of mult-period theoretical price of six type stocks and introduce impulse response analysis. When innovation process has multivariate normal distribution we get closed form expression for distribution of future stock price. We analytically derives a formula for the covariance between future random stock prices. We obtain closed form formula and recurrent formula for linear minimum MSE predictor of all six type stocks. Also we construct formula of maximum likelihood estimation and generalized least estimation for all six type stocks. Finally, we developed connection between stochastic dividend discount model and portfolio selection theory.
