Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2011.12753

State Space Vasicek Model of a Longevity Bond

Georgina Onuma Kalu·Chinemerem Dennis Ikpe·Benjamin Ifeanyichukwu Oruh·Samuel Asante Gyamerah
View original source ↗Read source document ↗Export metadata ↓

Abstract

Life expectancy have been increasing over the past years due to better health care, feeding and conducive environment. To manage future uncertainty related to life expectancy, various insurance institutions have resolved to come up with financial instruments that are indexed-linked to the longevity of the population. These new instrument is known as longevity bonds. In this article, we present a novel classical Vasicek one factor affine model in modelling zero coupon longevity bond price (ZCLBP) with financial and mortality risk. The interest rate r(t) and the stochastic mortality of the constructed model are dependent but with uncorrelated driving noises. The model is presented in a linear state-space representation of the contiuous-time infinite horizon and used Kalman filter for its estimation. The appropriate state equation and measurement equation derived from our model is used as a method of pricing a longevity bond in a financial market. The empirical analysis results show that the unobserved instantaneous interest rate shows a mean reverting behaviour in the U.S. term structure. The zero-coupon bonds yields are used as inputs for the estimation process. The results of the analysis are gotten from the monthly observations of U.S. Treasury zero coupon bonds from December, 1992 to January, 1993. The empirical evidence indicates that to model properly the historical mortality trends at different ages, both the survival rate and the yield data are needed to achieve a satisfactory empirical fit over the zero coupon longevity bond term structure. The dynamics of the resulting model allowed us to perform simulation on the survival rates, which enables us to model longevity risk.

Explore related subjects

q-fin.MF

Keep this discovery

BibTeXRIS

Georgina Onuma Kalu, Chinemerem Dennis Ikpe, Benjamin Ifeanyichukwu Oruh, Samuel Asante Gyamerah. 2020-11-25. State Space Vasicek Model of a Longevity Bond. https://arxiv.org/abs/2011.12753

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Variance-Optimal Hedging in the Rough Hawkes--Heston Model

We study variance-optimal stock hedging and the convergence of approximate strategies in the rough Hawkes--Heston model. Starting from the model's affine conditional transform and the affine Volterra jump framework, we obtain semi-explicit hedges for European calls and a representation of the minimum quadratic error through the Galtchouk--Kunita--Watanabe projection. Our main approximation result keeps the original stock, variance driver, and information flow fixed while regularizing the kernel used to evaluate the hedge. To handle singular memory and common marked jumps, we construct the approximate holdings from histories available before trading and preserve the conditional transform's random modulus envelope. Riccati--Volterra stability and weighted truncation then yield convergence in the original stock's trading norm on compact Fourier intervals. For calls, a joint choice of kernel regularization and Fourier cutoff gives convergence of the initial capitals and strategies, uniform-in-time square-mean convergence of continuous-time gains, and convergence of the terminal mean-square error to the variance-optimal value. A numerical experiment with shifted fractional kernels illustrates the construction on common original-market paths.

q-fin.MF↗
arXiv2026

Numeraire Invariance of Entropy-Projected Martingale Measures

Let \(P\) be a fixed physical law and let \(Q\) be an equivalent martingale measure selected from the martingale-measure set associated with a chosen numeraire. A change of numeraire maps \(Q\) to \(T_LQ\), where \(d(T_LQ)=L\,dQ\) and \(L\) is the terminal likelihood ratio. The forward relative-entropy projection minimizing \(D_{\mathrm{KL}}(P\Vert Q)\) commutes with this transform because its objective changes only by the constant \(-E_P\log L\). The minimal entropy martingale measure (MEMM) orientation \(D_{\mathrm{KL}}(Q\Vert P)\) does not have this property, and a trinomial counterexample shows that independently recomputed MEMMs need not be likelihood compatible. We make two economic consequences explicit. First, the two entropy orientations are precisely the \(Q\)-dependent terms in the classical convex-dual objectives for logarithmic and exponential utility, respectively. Second, likelihood compatibility is equivalent to equality of the pricing functionals obtained in the two numeraires. Hence the forward selectors value every integrable claim consistently across numeraires, whereas the two MEMMs in the counterexample assign different prices to a nonreplicable digital claim. We also prove a finite-state class-level characterization: uniform invariance over the elementary one-period likelihood-ratio families forces a smooth convex \(f\)-divergence to be logarithmic, up to scaling and affine equivalence. Finally, in finite-state markets, the forward projection exists under the usual strictly positive feasible-point condition; its density \(dP/dQ^*\) is attainable log-optimal terminal wealth, and the minimum forward entropy equals maximal expected log growth.

q-fin.MF↗
arXiv2026

The Delta of a Variance Swap

We define the variance swap delta as the sensitivity of the price of variance to a change in underlying price. We use Carr-Madan spanning formulas to analyze this sensitivity when the implied volatility smile curve may depend on the underlying price. We show that the variance swap total delta is zero for the class of smile curves that are pure functions of (log) moneyness, which goes against the empirical observation that variance is up when the market is down. We propose a simple modification of the smile to correct this issue.

q-fin.MF↗