scholarly journals Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Peng Li ◽  
Wei Wang ◽  
Lin Xie ◽  
Zhixin Yang
Keyword(s):  
Markov Chain ◽  
Numerical Analysis ◽  
Continuous Time ◽  
Regime Switching ◽  
Pension Fund ◽  
Premature Termination ◽  
Pension Plans ◽  
Pension Benefit ◽  
Bear Market ◽  
Retirement Security

The Pension Benefit Guaranty Corporation (PBGC) provides insurance coverage for single-employer and multiemployer pension plans in private sector. It has played an important role in protecting the retirement security for over 1.5 million people since it was established about half a decade ago. PBGC collects insurance premiums from employers that sponsor insured pension plans for its coverage and receives funds from pension plans that it takes over. To address the issue of underfunded plans that the PBGC has, this work studies how to evaluate risk-based premiums for the PBGC. Inspired by a couple of existing work in which the premature termination of pension fund and distress termination of sponsor assets are analyzed separately, our work examines the two types of terminations under one framework and considers the occurrence of each termination dynamically. Given that market regime might have a big impact on the dynamics of both pension fund and sponsor’s assets, we thus formulate our model using a continuous-time two-state Markov chain in which bull market and bear market are delineated. We thus formulate our model using a continuous-time two-state Markov Chain in which bull market and bear market are delineated. In other words, the pension fund and sponsor assets are market dependent in our work. Given that this additional uncertainty described by regime switching makes the market incomplete, we therefore utilize the Esscher transform to determine an equivalent martingale measure and apply the risk neutral pricing method to obtain the closed-form expressions for premium of PBGC. In addition, we carry out numerical analysis to demonstrate our results and observe that premium increases according to the retirement benefit irrespective of the type of terminations. In comparison to the case of early distress termination of sponsor assets, the premium goes up more quickly when premature termination of pension funds occurs first due to the fact that pension fund is the first venue of retirement security. Furthermore, we look at how the premium changes with respect to other key parameters as well and make some detailed observations in the section of numerical analysis.

HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950047 ◽  
Author(s):  
TAK KUEN SIU ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Continuous Time ◽  
Regime Switching ◽  
Stochastic Flows ◽  
Finite State ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Over Time

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

scholarly journals Pricing energy contracts under regime switching time-changed Levy Processes

2021 ◽  
Author(s):  
Konrad Gajewski
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Continuous Time ◽  
Regime Switching ◽  
Switching Time ◽  
Continuous Time Markov Chain ◽  
Energy Data ◽  
Varying Parameters ◽  
Call Options ◽  
Black Scholes

The failures of the popular Black-Scholes-Merton (BSM) model led to an interest in new, robust models which could more accurately model the behavior of historical prices. We consider one such model, the regime switching time-changed Levy process, which builds upon the BSM model by incorporating jumps through a random clock, as well as randomly varying parameters according to a continuous-time Markov chain. We develop the characteristic function as well as two methods for pricing European call options. Finally, we estimate the parameters of the model by incorporating historic energy data and option quotes using a variety of methods.

scholarly journals Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Chaoqun Ma ◽  
Hui Wu ◽  
Xiang Lin
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Regime Switching ◽  
Game Problem ◽  
Comparative Statics ◽  
Optimal Portfolio ◽  
Hjb Equations ◽  
Risky Assets ◽  
Portfolio Strategies ◽  
The Impact

We consider a nonzero-sum stochastic differential portfolio game problem in a continuous-time Markov regime switching environment when the price dynamics of the risky assets are governed by a Markov-modulated geometric Brownian motion (GBM). The market parameters, including the bank interest rate and the appreciation and volatility rates of the risky assets, switch over time according to a continuous-time Markov chain. We formulate the nonzero-sum stochastic differential portfolio game problem as two utility maximization problems of the sum process between two investors’ terminal wealth. We derive a pair of regime switching Hamilton-Jacobi-Bellman (HJB) equations and two systems of coupled HJB equations at different regimes. We obtain explicit optimal portfolio strategies and Feynman-Kac representations of the two value functions. Furthermore, we solve the system of coupled HJB equations explicitly in a special case where there are only two states in the Markov chain. Finally we provide comparative statics and numerical simulation analysis of optimal portfolio strategies and investigate the impact of regime switching on optimal portfolio strategies.

scholarly journals Portfolio Selection with Jumps under Regime Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Lin Zhao
Keyword(s):  
Markov Chain ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Regime Switching ◽  
Jump Processes ◽  
Bank Account ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance

We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account and multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is employed to model the problem.

OPTION PRICING USING A REGIME SWITCHING STOCHASTIC DISCOUNT FACTOR

2014 ◽  
Vol 17 (03) ◽  
pp. 1450020
Author(s):  
ROBERT J. ELLIOTT ◽  
AHMED S. HAMADA
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Regime Switching ◽  
Stock Price ◽  
Option Price ◽  
Analytical Form ◽  
Discount Factor ◽  
Stochastic Discount Factor ◽  
Occupation Times ◽  
The Fourier Transform

The paper discusses the pricing of derivatives using a stochastic discount factor modeled as a regime switching geometric Brownian motion. The regime switching is driven by a continuous time hidden Markov chain representing changes in the economy. The stochastic discount factor enables to define a risk neutral measure. We model the stock price as discounted future dividends driven by the same continuous time Markov chain. The stochastic discount factor is used to price European style options under the historical probability measure. The introduction of occupation times of the Markov chain and the corresponding conditional characteristic function allows the evaluation of the expected value of European type claims. The option price is given as a semi-analytical form using the Fourier transform.

PARAMETER ESTIMATION FOR A REGIME-SWITCHING MEAN-REVERTING MODEL WITH JUMPS

2005 ◽  
Vol 08 (06) ◽  
pp. 791-806 ◽  
Author(s):  
PING WU ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Parameter Estimation ◽  
Markov Chain ◽  
Continuous Time ◽  
Regime Switching ◽  
Energy Markets ◽  
Finite Dimensional ◽  
The Em Algorithm ◽  
Finite State ◽  
The Mean ◽  
The Interest Rate

In this paper we propose a type of mean reverting model with jumps, where the mean reverting level changes according to a continuous time, finite state Markov chain. This model could be applied to the interest rate and energy markets. We apply filtering techniques and obtain finite dimensional filters for the unobservable state of the Markov chain based on observations of the mean reverting diffusion. Various auxiliary filters are developed that allow us to estimate the parameters of the Markov chain by the EM algorithm. A simulation study is done for a concrete example.

scholarly journals Pricing energy contracts under regime switching time-changed Levy Processes

2021 ◽  
Author(s):  
Konrad Gajewski
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Continuous Time ◽  
Regime Switching ◽  
Switching Time ◽  
Continuous Time Markov Chain ◽  
Energy Data ◽  
Varying Parameters ◽  
Call Options ◽  
Black Scholes

The failures of the popular Black-Scholes-Merton (BSM) model led to an interest in new, robust models which could more accurately model the behavior of historical prices. We consider one such model, the regime switching time-changed Levy process, which builds upon the BSM model by incorporating jumps through a random clock, as well as randomly varying parameters according to a continuous-time Markov chain. We develop the characteristic function as well as two methods for pricing European call options. Finally, we estimate the parameters of the model by incorporating historic energy data and option quotes using a variety of methods.

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