Cox risk model with variable premium rate and stochastic return on investment

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International Asset Allocation: A New Perspective

We consider an international economy where purchasing power parity (PPP) is violated and financial asset returns and exchange rates follow, in real terms, general diffusion processes driven by K state variables. A country-specific representative individual trades on available assets to maximize the expected utility of her final consumption. Her optimal strategy is shown to contain, in addition to the usual speculative component, only two hedging components, however large is K. The first one is associated with domestic interest rate risk and the second one with the risk brought about by the co-movements of the interest rates and the market prices of risk. The implementation of the optimal strategy is thus much easier, as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous (a priori unknown) state variables. Thus, as to the necessity for rational investors to account for predictability in their optimal portfolio strategy, our results make it much easier than the traditional decomposition à la Merton. Since one hedging term depends on interest rate differentials across countries and encompasses hedging against PPP deviations, our decomposition turns to be also an elegant way to achieve optimal (indirect) currency risk hedging as opposed to usual ad hoc route to achieve such a hedging component followed by previous studies. Therefore, our decomposition gives new insights as to the pricing of foreign exchange risk at equilibrium.International Portfolio Theory; Interest rate risk; Currency risk premium; Market price of risk; Asset return predictability.

Surplus analysis for variable annuities with a GMDB option

In this paper, we analyze the insurance surplus for a Variable Annuity contract with a Guaranteed Minimum Death Benefit (GMDB) option. Initially, we derive the first two moments of the distribution of the surplus; and subsequently, we develop the whole distribution using a stochastic model which involves an integrated analysis of financial and mortality risk for a portfolio of annuities with GMDB embedded options. We offer a model according which the premium can be modified as per the forecasts of mortality probabilities, interest rate and fund evolution. Moreover, the study enables us to determine the premium that leads to a required probability of insolvency, and so it can be used for an evaluation of the adequacy of solvency. Numerical examples illustrate the results

Mortality risk and the valuation of annuities with guaranteed minimum death benefit options: application to the Italian population

In this note, we describe the payoff of Guaranteed Minimum Death Benefit options (GMDB) embedded in annuity contracts and discuss their valuation using data for the Italian male population as a case study. These put options have stochastic maturity dates due to the involuntary exercise at the moment of death. We value the GMDB as a weighted average price of a set of deterministic put options with different maturity dates, where the weights are the probability of death at every date. We take into account the mortality risk and investigate the sensitivity of the price of the option to changes in mortality probability using both deterministic and stochastic approaches

Foreign Exchange Risk Premium Determinants: Case of Armenia

This paper studies foreign exchange risk premium using the uncovered interest rate parity framework in a single country context. The analysis is performed using weekly data on foreign and domestic currency deposits in Armenian banking system. The paper provides the results of the simple tests of uncovered interest parity condition, which indicate that contrary to established view dominating in empirical literature there is a positive correspondence between exchange rate depreciation and interest rate differentials in Armenian deposit market. Furthermore, the paper presents and discusses a systematic positive risk premium required by the economic agents for foreign exchange transactions, which increases over the investment horizon. The two currency affine term structure framework is applied to identify the factors driving the systematic exchange rate risk premium in Armenia. At the end, possible directions for further research are outlined.http://deepblue.lib.umich.edu/bitstream/2027.42/40197/3/wp811.pd

Assessing Investment and Longevity Risks within Immediate Annuities

Life annuities provide a guaranteed income for the remainder of the recipient’s lifetime, and therefore, annuitization presents an important option when choosing an adequate investment strategy for the retirement ages. While there are numerous research articles studying annuities from a pensioner’s point of view, thus far there have been few contributions considering annuities from the provider’s perspective. In particular, to date there are no surveys of the general risks within annuity books. The present paper aims at filling this gap: Using a simulation framework, it provides a long-term analysis of the risks within annuity books. In particular, the joint impact of mortality risks and investment risks as well as their respective influences on the insurer’s financial situation are studied. The key finding is that, under the model specifications and using annuity data from the United Kingdom, the risk premium charged for aggregate mortality risk seems to be very large relative to its characteristics. Possible reasons as well as economic implications are provided, and potential caveats are discussed

Term Default, Balloon Risk, and Credit Risk in Commercial Mortgages

Term default and balloon risk play an interactive role in the pricing of credit risk in commercial mortgages. Most commercial mortgage pricing studies assume a borrower\u27s default decision is based solely on the property value; the mortgage valuation model here also incorporates a property income trigger. The model considers both the risk of default during the term of the loan and the risk of loss at maturity (balloon risk). Monte Carlo simulation analyses reveal that pricing models based solely on property value overestimate the probability of term default and the resulting credit risk premium. Adding a property income default trigger without considering balloon risk, however, underestimates the overall credit risk premium. In essence, a double-trigger default model that incorporates balloon risk is critical for accurate assessment of the credit risk in commercial mortgages

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors

We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds.