A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Atsuyuki Kogure ◽  
Takahiro Fushimi
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate ◽  
Longevity Bonds ◽  
Carter Model

AbstractMortality-linked securities such as longevity bonds or longevity swaps usually depend on not only mortality risk but also interest rate risk. However, in the existing pricing methodologies, it is often the case that only the mortality risk is modeled to change in a stochastic manner and the interest rate is kept fixed at a pre-specified level. In order to develop large and liquid longevity markets, it is essential to incorporate the interest rate risk into pricing mortality-linked securities. In this paper we tackle the issue by considering the pricing of longevity derivatives under stochastic interest rates following the CIR model. As for the mortality modeling, we use a two-factor extension of the Lee-Carter model by noting the recent studies which point out the inconsistencies of the original Lee-Carter model with observed mortality rates due to its single factor structure. To address the issue of parameter uncertainty, we propose using a Bayesian methodology both to estimate the models and to price longevity derivatives in line with (Kogure, A., and Y. Kurachi. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.”

scholarly journals Valuing strategic investments under stochastic interest rates: A real option approach

2019 ◽  
Vol 16 (3) ◽  
pp. 89-97
Author(s):  
Luca Vincenzo Ballestra ◽  
Graziella Pacelli ◽  
Davide Radi
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Interest Rates ◽  
Real Option ◽  
Interest Rate Risk ◽  
Stochastic Interest Rates ◽  
Investment Projects ◽  
Rate Risk ◽  
Stochastic Interest ◽  
The Interest Rate

One of the most challenging issues in management is the valuation of strategic investments. In particular, when undertaking projects such as an expansion or the launch of a new brand, or an investment in R&D and intellectual capital, which are characterized by a long-term horizon, a firm has also to face the risk due to the interest rate. In this work, we propose to value investments subject to interest rate risk using a real options approach (Schulmerich, 2010). This task requires the typical technicalities of option pricing, which often rely on complex and time-consuming techniques to value investment projects. For instance, Schulmerich (2010) is, to the best of our knowledge, the first work where the interest rate risk is considered for real option analysis. Nevertheless, the valuation of investment projects is done by employing binomial trees, which are computationally very expensive. In the current paper, a different modeling framework (in continuous-time) for real option pricing is proposed which allows one to account for interest rate risk and, at the same time, to reduce computational complexity. In particular, the net present value of the cash inflows is specified by a geometric Brownian motion and the interest rate is modeled by using a process of Vasicek type, which is calibrated to real market data. Such an approach yields an explicit formula for valuing various kinds of investment strategies, such as the option to defer and the option to expand. Therefore, the one proposed is the first model in the field of real options that accounts for the interest rate risk and, at the same time, offers an easy to implement formula which makes the model itself very suitable for practitioners. An empirical analysis is presented which illustrates the proposed approach from the practical point-of-view and highlights the impact of stochastic interest rates in investment valuation.

scholarly journals Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk

2006 ◽  
Vol 36 (01) ◽  
pp. 79-120 ◽  
Author(s):  
Andrew J.G. Cairns ◽  
David Blake ◽  
Kevin Dowd
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Mortality Factors ◽  
Market Models ◽  
Force Of Mortality ◽  
Mortality Models ◽  
The Interest Rate ◽  
Risk Free Rate ◽  
Longevity Bonds

It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

scholarly journals Confederation debt management since 1970

2019 ◽  
Vol 155 (1) ◽  
Author(s):  
Basil Guggenheim ◽  
Mario Meichle ◽  
Thomas Nellen
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Debt Maturity ◽  
Debt Management ◽  
Total Debt ◽  
Rate Risk ◽  
Rate Environment ◽  
The Interest Rate ◽  
Lock In

Abstract This paper analyzes the Confederation’s debt management. The Confederation actively manages roll over and interest rate risk by increasing bond maturity with increasing marketable debt-to-GDP levels. It further engages in active but asymmetric, one-sided interest rate positioning; i.e., it uses mostly bonds to affect debt maturity and does so only when the interest rate environment is favorable to lock-in interest rates by issuing longer-term bonds. Debt management is mainly driven by marketable debt rather than total debt. Issuing behavior became more regular and demand-oriented during the early 1990s when marketable and total debt increased in tandem.

scholarly journals Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk

2006 ◽  
Vol 36 (1) ◽  
pp. 79-120 ◽  
Author(s):  
Andrew J.G. Cairns ◽  
David Blake ◽  
Kevin Dowd
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Mortality Risk ◽  
Mortality Factors ◽  
Market Models ◽  
Force Of Mortality ◽  
Mortality Models ◽  
The Interest Rate ◽  
Risk Free Rate ◽  
Longevity Bonds

It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

Research on the Interest Rate Risk Management of Commercial Bank Based on F-W Duration Convexity Model

2014 ◽  
Vol 644-650 ◽  
pp. 5825-5827
Author(s):  
Feng Liu ◽  
Ping Zou
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Commercial Banks ◽  
Interest Rate Risk ◽  
Rate Risk ◽  
Interest Rate Risk Management ◽  
The Interest Rate ◽  
Marketization Reform ◽  
Management Capabilities

With the pace of interest rate marketization reform accelerates, interest rate risk faced by commercial banks increasingly prominent, so a higher demand for its interest rate risk management capabilities is required. This article describes the type of interest rate risk, then use F-W Duration Convexity model to make an empirical analysis in five large commercial banks. The results show: the five large bank duration and convexity gap are all positive, when interest rates rise, the five bank NV will be reduced, interest rates decline, then increased. According to ΔNV/PA, ICBC CCB and ABC faced the biggest interest rate risk, BOC followed, BCM minimum.

scholarly journals Risk of Interest Rates at the Level of Commercial Banks in Romania

2017 ◽  
Vol 22 (4) ◽  
pp. 281-288
Author(s):  
Ioana Raluca Sbârcea
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Commercial Banks ◽  
Asset Price ◽  
Banking System ◽  
Interest Rate Risk ◽  
Point Of View ◽  
Risk Indicators ◽  
Rate Risk ◽  
The Interest Rate

Abstract The banking system in Romania is a banking system under development, subject to fluctuations that exist on the market more than on more developed banking systems, fluctuations that can generate losses for banks if they are not properly managed. The losses that may be generated by these fluctuations, known as market risk, refer to the significant fluctuations in three indicators, namely the interest rate, the exchange rate and the asset price. In this article, I will analyse the interest rate risk from a conceptual point of view and the indicators that mitigate this risk. The analysis also contains a study of this risk among commercial banks in the system to highlight the level of risk and possible effects of its manifestation. I calculated and analysed the interest rate risk indicators, individually for the first three banks in the system, but also to comparatively, in order to highlight the existing differences.

scholarly journals Interest Rate Sensitivity of Non-banking Financial Sector in India

2018 ◽  
Vol 43 (3) ◽  
pp. 152-170
Author(s):  
Renu Ghosh ◽  
K. Latha ◽  
Sunita Gupta
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Stock Returns ◽  
Financial Institutions ◽  
Rate Sensitivity ◽  
Interest Rate Risk ◽  
Cross Sectional ◽  
Rate Risk ◽  
The Interest Rate ◽  
The Impact

Executive Summary Before financial liberalization, interest rates were administered and exhibited near-zero volatility. The easing of financial repression in the 1990s generated experiences with interest rate volatility in India. Administrative restrictions on interest rates in India have been steadily eased since 1993. This has led to increased interest rate risk for financial firms. Most research studies have almost exclusively focused on the developed countries especially the banking sector of the United States. The present study attempts to examine the interest rate risk of non-banking financial institutions in India by using the methodology of panel regression and generalized autoregressive conditional heteroscedasticity (GARCH) (1, 1) model for the period from 1 April 1996 to 30 August 2014. The sample used in the study consists of all non-banking financial companies (NBFCs) listed in the S&P CNX 500 index which has continuous availability of share prices over the study period. The study also examines the impact of unanticipated changes in interest rate on stock returns of NBFCs. The Box–Jenkins methodology is applied to calculate unanticipated changes in interest rate variable, autoregressive integrated moving average (ARIMA) (24, 1, 0) model. The time series used in the present study is found to be stationary at the first logarithmic difference. Stock returns exhibit significant exposure with both market returns and interest rate changes. The interest rate sensitivity of large, medium, and small financial institutions is also found to be different. Estimation results for the variance equation in GARCH (1, 1) model suggest that the volatility for individual firm stock returns is time-variant. The ARCH and GARCH coefficients are found to be significant, providing evidence against using traditional model (ordinary least square (OLS)) that assumes time-invariant volatility. This implies that the market has a memory longer than one period and volatility is more sensitive to its own lagged values than it is to new surprises in the market. This study also investigates the possible determinants that account for cross-sectional variation in the interest rate sensitivity of NBFCs. It is found that the size of the firm is the preferred determinant that accounts for cross-sectional variation in the interest rate sensitivity of finance companies. When unanticipated changes in interest rate are used in lieu of actual interest rate changes, not much difference is observed in the significance coefficients. The only significant difference observed is in the magnitude. The impact of actual interest rate changes is more than the impact of unanticipated interest rate changes in absolute terms. This difference in the magnitude of impact arises because actual data incorporate movement in both anticipated and unanticipated components of interest rate. Hence, NBFCs managers and regulators should adopt policies and strategies to avoid the transmission of interest rate risk in their stock returns.

scholarly journals The Relationship Between Large Banks Investment In Available-For-Sale Securities And The Interest Rate Risk Of Their Securities

2010 ◽  
Vol 26 (3) ◽  
Author(s):  
Shilo Lifschutz
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Financial Risk ◽  
Fair Value ◽  
Interest Rate Risk ◽  
Empirical Examination ◽  
Rate Risk ◽  
The Interest Rate ◽  
The Relationship

This study presents an empirical examination of the relationship between large banks’ investment in available-for-sale securities (AFS) and the interest rate risk of their securities. It concentrates on the years, 1997-2000, when interest rates were relatively stable and regulatory capital was not affected by the unrealized holding gains and losses on AFS securities under Statement of Financial Accounting Standards No. 115. The two main findings of the study, having controlled for the interest risk position of the bank (exclusive of securities effect) and other risk management and economic considerations, are: (1) AFS securities’ ratio (to securities or to total assets) is positively related to the interest rate risk of securities; (2)a change in the AFS securities ratio is positively related to the change in the interest rate risk of securities.  These findings may well prove to be significant to supervisors of banks considering they are in charge of monitoring the effect of fair value accounting regulations on the financial risk management in banks.

scholarly journals Risk Management for Bonds with Embedded Options

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 790
Author(s):  
Antonio Díaz ◽  
Marta Tolentino
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Interest Rate Models ◽  
Management Measures ◽  
Interest Rate Risk Management ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Rate Change

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

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