A Hybrid Model for Pricing and Hedging of Long-dated Bonds

A Hybrid Model for Equity Indices and Stochastic Interest Rates

This paper considers a modification of the well known constant elasticity of variance model where it is used to model the growth optimal portfolio (GOP). It is shown that, for this application, there is no equivalent risk neutral pricing measure and therefore the classical risk neutral pricing methodology fails. However, a consistent pricing and hedging framework can be established by application of the benchmark approach. Perfect hedging strategies can be constructed for European style contingent claims, where the underlying risky asset is the GOP. In this framework, fair prices for contingent claims are the minimal prices that permit perfect replication of the claims. Numerical examples show that these prices may differ significantly from the corresponding ‘risk neutral’ prices.

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.

With regard to asset liability management (ALM), the future evolution of the interest rate market plays a major role. This is natural, as with a deterministic evolution of the interest rate (in fact, only in a deterministic setting we could speak of the interest rate!), interest rate risk would not play a role in ALM. However, as the main objective of ALM is to relate payments occurring at dif-ferent times in a suitable way, especially when the time horizon is large, assum-ing a deterministic interest rate evolution is absolutely inappropriate. Thus, finding a good model for the evolution of the term structure of interest rates is one of the main obstacles to overcome for successful ALM.

Benchmark Approach and Risk Neutral Pricing in a Special Hybrid Model

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

Over the past decades, financial markets have increasingly exhibited features of both randomness and uncertainty, creating challenges for interest rate models that rely solely on stochastic or uncertain processes. These models often fail to adequately capture the dual nature of indeterminacy, limiting their relevance in volatile and unpredictable market conditions. This study aims to design and assess an interest rate model for uncertain-stochastic financial markets and to derive a framework for zero-coupon bond pricing under this setting. The methodology applies uncertain stochastic differential equations, which integrate elements of both probability theory and uncertainty theory, thereby accommodating aleatory and epistemic forms of indeterminacy. The proposed model extends the classical short-rate frameworks by introducing two sources of indeterminacy and provides theoretical derivations for bond pricing. Numerical illustrations are included to demonstrate the application of the model to zero-coupon bond valuation and to highlight differences from conventional approaches. The findings indicate that interest rates and zero-coupon bond prices in uncertain stochastic financial markets can be effectively modeled through uncertain random processes, leading to improved pricing accuracy and risk management in environments characterised by incomplete information and unpredictable shocks. The key conclusion is that incorporating uncertain stochastic differential equations into the interest rate and zero-coupon bonds’ prices modelling offers a more robust and flexible framework for uncertain stochastic markets. This study contributes to the growing body of uncertain stochastic finance by underscoring the need for hybrid models capable of guiding policymakers, investors and financial institutions in ensuring stability and resilience under future market uncertainties.

In this chapter, we establish the fundamental relationships between interest rates, bond prices and forward rates. We further discuss the modelling of interest rates and analyse typical models for the spot interest rate and the forward rates. As we desire interest rates to be non-negative, we seek stochastic processes with this feature such as the Feller process. Thus we present the motivation of the Feller process and its relevance to the interest rate modelling. We also summarise the main results of Fubini’s theorem, that are very useful for modelling forward rates.

PurposeLife insurance is a kind of long-term investment; hence, the purpose of buying life insurance is to cover both current and future damages for the insured. Although insurance plays a crucial rule in fiscal and economic development, in MENA countries, insurance, especially life insurance, remains undeveloped, with a low penetration rate. Therefore, the purpose of this paper is to determine the factors that affect life insurance demand.Design/methodology/approachTo analyze the determinants of life insurance demand during 2004-2012, a panel data model was estimated with Eviews software. Data on population, gross domestic product (GDP), interest rate, inflation rate, and human development index are extracted from the World Bank, and data on life insurance premium are gathered from Sigma International reports.FindingsResults show that the price elasticity of life insurance demand is −0.77, the elasticity of life insurance subject to HDI is 1.68, the elasticity of life insurance subject to GDP is 0.92, and the elasticity of life insurance subject to interest rate is −0.33. The demand for life insurance has a positive significant relationship with population size.Research limitations/implicationsThe low elasticity of life insurance demand subject to GDP, interest rate, and inflation rate shows that the life insurance penetration rate in MENA countries is due to the dominance of compulsory insurance, and not due to voluntary purchasing of life insurance. The higher effect of HDI on the life insurance demand illustrates that, for developing the life insurance market, it is first necessary to improve the standard of life, education status, and the economic base.Originality/valueAs in the MENA region life insurance has remained undeveloped and there are no related studies in this area, it can be hypothesized that the life insurance penetration rate in MENA is due to the dominance of compulsory insurance and not due to voluntary purchasing of life insurance. The higher effect of HDI on life insurance demand illustrates that, for developing the life insurance market, it is first necessary to improve the standard of life, education status, and economic base.

Currently a stock market rally and at the same time extremely low interest rates can be observed. This coincides with more volatile risk premiums for interest baring assets like government bonds. The mixture makes life harder for investment managers of (especially life) insurances. They have to continuously find profitable investments with good returns for the customers’ money, in case of the life insurers, in order to be able to pay at least the promised returns of the contracts. After the stock market burst around the turn of the century the levels of stock investments by German insurers have declined significantly, therefore also missing out on the rises leading up to the Lehman crash and also not participating in recent developments. With insurance asset managers avoiding stocks in the past years the questions can be raised, if they are forfeiting a good opportunity for their portfolio and if there is still time to participate in possible future gains. On the other hand the upcoming regulatory environment, namely Solvency II, will play an important role in the future and likely already has an impact on the investment decisions of the companies. Higher capital requirements for stock investments make it even harder to earn the so-called “Garantiezins”. Without ignoring the risks related to stock investments, effectively banning equities from asset managers’ buy lists might lead to missing out on desperately needed returns for the life insurance industry. So policy makers probably should reconsider their directives. This paper evaluates the attractiveness of stock investments from a long term as well as a risk adjusted perspective using e.g. different indicators and commonly used measurements for stocks with a rather conservative focus, in order to possibly get some insight into the future performance of stocks. Looking back to a decade of boom and bust cycles in the equity markets does not necessary rule out stocks as an important source for returns. The results are discussed comprehensively also in face of the regulatory changes to come. In the end timing plays a major role and due to that the current valuation of stocks as well as the look ahead are of vital importance. Assessing the reliability of professional forecasts for financial market time series—in this context especially for stocks as well as interest rates—plays an important role for asset managers.

Out-of-Sample Performance of Spot Interest Rate Models

Insurance companies are facing major challenges that point to the need for control process and risk management. Risk management in insurance has a direct impact on solvency, economic security, and overall financial stability of insurance companies. It is very important for insurance companies to adequately calculate risks to which they are exposed. Asset liability management (ALM), as an integrated approach to financial management, requires simultaneous decision-making about categories and values of assets and liabilities in order to establish the optimum volume and the ratio of assets and liabilities, with the understanding of complexity of the financial market in which financial institutions operate. ALM focuses on a significant number of risks, whereby the emphasis in this paper will be on interest rate risk which indicates potential losses that may reflect in a lower interest margin, a lower value of assets or both, in terms of changes in interest rates. In the above context, the aim of this paper is to show how to protect from interest rate changes and how these changes influence the insurance market in Montenegro, both from the theoretical and the practical point of view. The authors consider this to be an interesting and very important topic, especially because the life insurance market in Montenegro is underdeveloped and subject to fluctuations. Also, taking into account the fact that Montenegro is a country that has been making serious efforts to join the EU, it is expected that insurance companies in Montenegro will strengthen their financial position in the market even using the ALM traditional techniques, which is shown in this paper.

This study examines the analysis of factors affecting the value of bonds in the registered banking sub-sector in IDX. In this study the data used is secondary data that is data directly obtained from the Indonesia stock Exchange. Bond prices are usually influenced by many factors such as coupons, bond rating, Bond liquidity, due period and external factors such as JCI, interest rates, exchange rate and inflation. Independent variables in this study used coupons, interest rates, liquidity and leverage, while for the dependent variable used was the value (price) of the bonds. The number of population in this research is 43 companies engaged in banking, where the number of sample there are 38 bonds of 7 companies of banking sub-sector period of 2013-2017. In this study samples were taken in purposive sampling, namely the selection of samples based on the criteria that had been determined by the study. The analysis in this study used multiple linear regression analyses. Regression analysis serves to test the influence of independent variables (coupons, interest rates, liquidity, and leverage) on dependent variables (bond values). The results of the partial test of the study showed that coupons affect significantly and positively against the value of bonds, interest rates did not affect the value of bonds, liquidity has no effect on bond prices, and independent variables Leverage affects significantly and negatively against the value (price) of bonds. Simultaneously coupons, interest rates, liquidity and leverage affect the value (price) of bonds.

Hedging Derivatives Risks - A Simulation Study