The Performance of Deterministic and Stochastic Interest Rate Risk Measures

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.”

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

Corporate Ownership and Control ◽

10.22495/cocv16i3art8 ◽

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.

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Risk measures and behaviors for bonds under stochastic interest rate models

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2011.11.070 ◽

2012 ◽

Vol 56 (9-10) ◽

pp. 204-217 ◽

Cited By ~ 1

Author(s):

Na Song ◽

Tak Kuen Siu ◽

Farzad Alavi Fard ◽

Wai-Ki Ching ◽

Eric S. Fung

Keyword(s):

Interest Rate ◽

Risk Measures ◽

Stochastic Interest Rate ◽

Interest Rate Models ◽

Stochastic Interest ◽

And Behaviors

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