arXiv subjects
Publications and source records attributed to Battulga Gankhuu.
Conditional matrix variate student $t$ distribution was introduced by Battulga (2024a). In this paper, we propose a new version of the conditional matrix variate student $t$ distribution. The paper provides EM algorithms, which estimate parameters of the conditional matrix variate student $t$ distributions, including general cases and special cases with Minnesota prior.
This study introduces marginal density functions of the general Bayesian Markov-Switching Vector Autoregressive (MS-VAR) process. In the case of the Bayesian MS-VAR process, we provide closed-form density functions and Monte-Carlo simulation algorithms, including the importance sampling method. The Monte-Carlo simulation method departs from the previous simulation methods because it removes the duplication in a regime vector.
In this paper, we have studied option pricing methods that are based on a Bayesian Markov-Switching Vector Autoregressive (MS-BVAR) process using a risk-neutral valuation approach. A BVAR process, which is a special case of the Bayesian MS-VAR process is widely used to model interdependencies of economic variables and forecast economic variables. Here we assumed that a regime-switching process is generated by a homogeneous Markov process and a residual process follows a conditional heteroscedastic model. With a direct calculation and change of probability measure, for some frequently used options, we derived pricing formulas. An advantage of our model is it depends on economic variables and is easy to use compared to previous option pricing papers, which depend on regime-switching.
Economic variables play important roles in any economic model, and sudden and dramatic changes exist in the financial market and economy. For this reason, to price and hedge equity-linked life insurance products, including segregated funds and unit-linked life insurance products on maximum price of several assets, this paper introduces Bayesian Markov-Switching Vector Autoregressive (MS-VAR) process. By assuming that a regime-switching process is generated by a homogeneous Markov process and a residual process follows a heteroscedastic model, we obtain joint distribution of endogenous variables and insured's future lifetime random variable under risk-neutral probability probability measure. Using the distribution function, we obtain net single premiums and hedging formulas of the equity-linked life insurance products. An advantage of our model is it depends on economic variables and is not complicated as compared to previous papers.
In this paper, we introduce a dynamic Gordon growth model, which is augmented by a time--varying spot interest rate and the Gordon growth model for dividends. Using the risk--neutral valuation method and locally risk--minimizing strategy, we obtain pricing and hedging formulas for the dividend--paying European call and put options and equity--linked life insurance products. Also, we provide ML estimator of the model.
For a public company, pricing and hedging models of options and equity--linked life insurance products have been sufficiently developed. However, for a private company, because of unobserved prices, pricing and hedging models of the European options and life insurance products are in their early stages of development. For this reason, this paper introduces a log private company valuation model, which is based on the dynamic Gordon growth model. In this paper, we obtain closed--form pricing and hedging formulas of the European options and equity--linked life insurance products for private companies. Also, the paper provides Maximum Likelihood (ML) estimators of our model, Expectation Maximization (EM) algorithm, and valuation formula for private companies.
In this paper, we developed the Merton's structural model for public companies under an assumption that liabilities of the companies are observed. Using Campbell and Shiller's approximation method, we obtain formulas of risk-neutral equity and liability values and default probabilities for the public companies. Also, the paper provides ML estimators of suggested model's parameters.
This paper provides the first and second order derivatives of any risk measures, including VaR and ES for continuous and discrete portfolio loss random variable variables. Also, we give asymptotic results of the first and second order conditional moments for heavy-tailed portfolio loss random variable.
In this paper, we consider conditions that a higher order derivative preserve in conditional expectation operator for a generic nonlinear random variable. Also, the paper introduces higher order derivatives of the Expected Shortfall for a generic nonlinear portfolio loss random variable.
In this study, we introduce a Gordon's dividend discount model, based on Vector Autoregressive Process (VAR). We provide two Propositions, which are related to generic Gordon growth model and Gordon growth model, which is based on the VAR process.
In this study, we introduce new estimation methods for the required rate of returns on equity and liabilities 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 also provide a method that evaluates the market values of liabilities. 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.
This paper presents pricing and hedging methods for rainbow options and lookback options under Bayesian 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.
Because the asset value of a private company does not observable except in quarterly reports, the structural model has not been developed for a private company. For this reason, this paper attempt 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 and default probability for the private company. Also, the paper provides ML estimators and the EM algorithm of our model's parameters.
In this study, we introduce new estimation methods for the required rate of return of the stochastic dividend discount model (DDM) and the private company valuation model, which will appear below. To estimate the required rate of return, 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, suggested methods can be used to estimate the required rate of return.