Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
European Actuarial Journal
Erschienen in: European Actuarial Journal 1/2022

18.06.2021 | Original Research Paper

Practical partial equilibrium framework for pricing of mortality-linked instruments in continuous time

verfasst von: Petar Jevtić, Minsuk Kwak, Traian A. Pirvu

Erschienen in: European Actuarial Journal | Ausgabe 1/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This work considers a partial equilibrium approach for pricing longevity bonds in a stochastic mortality intensity setting. Thus, the pricing methodology developed in this work is based on a foundational economic principle and is realistic for the currently illiquid life market. Our model consists of economic agents who trade in risky financial security and longevity bonds to maximize the monetary utilities of their trades and income. Stochastic mortality intensity affects agents’ income, resulting in market incompleteness. The longevity bond introduced acts as a hedge against mortality risk, and we prove that it completes the market. From a practical perspective, we characterize and compute the endogenous equilibrium bond price. In a realistic setting with two agents in a transaction, numerical experiments confirm the expected intuition of price dependence of model parameters.
Vorheriger Artikel A long-term care multi-state Markov model revisited: a Markov chain Monte Carlo approach
Nächster Artikel Premium rating without losses

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
Indeed, in the more classical Von Neumann–Morgenstern risk preferences paradigm, equilibria are characterized by complex fixed point theorems, making their numerical computation difficult.
 
2
This assumption of zero risk-free rate corresponds to the case in which the money market account is the numéraire. Thus, \(\mu _t^S\) denotes the excess return of the risky asset.
 
3
There is an emerging body of empirical research exemplified in works by Ang and Maddaloni [1], Favero et al. [15], Maurer [27], and Dacorogna and Cadena [11], all of which suggest a connection between long-run demographic trends and financial markets. Therefore, it appears advisable to consider stochastic mortality intensity models that can be correlated with financial securities to some extent, and our model incorporates such case when \( \sigma ^2_\Lambda \ne 0\). Moreover, for purposes of generality of the model, in Assumption 1, we additionally allow the market price of financial risk to depend on mortality intensity.
 
4
Throughout this paper, it is assumed that all idiosyncratic mortality risks are diversified by the existence of an appropriate number of large annuity portfolios.
 
5
The inverse of the risk tolerance parameter is the absolute risk aversion coefficient of the exponential utility function that yields the same risk criterion (see bottom of page 215 in [17]).
 
6
See [17] for more on this.
 
7
In order to clearly show difference between prices and considering that face value of longevity bonds are at least in millions of monetary units (see [7]), we consider 8 decimal places for Table 1.
 
8
The choice of parameters \(S_0 = 100\), \(\mu ^S = 0.05\), \(\Lambda _0 = 0.10\) and \(\mu ^{\Lambda }= 0.09\) is stylized to reflect an older age cohort (see [25]) and the nominal conditions of the financial market.
 
9
According to [2], the absolute risk aversion range on a gamble of size 100 is [0.000401, 0.346574]. Since the risk tolerance parameter is the inverse of the absolute risk aversion coefficient, it translates into the risk tolerance range [2.885, 2493.76]. The work by [9] estimated the average absolute risk aversion, and this ranges from 0.00037 to 0.0031, yielding the following interval [322, 2702.7] for risk tolerance coefficient. We choose 50 and 300 as the values of risk tolerance, which are in the range or near the range of these studies.
 
10
This approach has already been introduced and used in [17], and it allows us to use the same equilibrium MPR with more convenient analysis.
 
11
This step demonstrates why we introduce the equivalent model with zero net supply of longevity derivatives.
 
Literatur
1.
2.
Babcock BA, Kwan CE, Eli F (1993) Risk and probability premiums for CARA utility functions. J Agric Resour Econ 18(1):17–24
3.
Bauer D, Börger M, Ruß J (2010) On the pricing of longevity-linked securities. Insurance: Math Econ 46(1):139–149
4.
Biffis E (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance: Math Econ 37(3):443–468
5.
Blackburn C, Sherris M (2013) Consistent dynamic affine mortality models for longevity risk applications. Insurance: Math Econ 53(1):64–73
6.
Blake D, Cairns AJ, Dowd K (2006) Living with mortality: longevity bonds and other mortality-linked securities. Br Actuar J 12(01):153–197CrossRef
7.
Blake D, Cairns AJ, Dowd K, Kessler AR (2019) Still living with mortality: the longevity risk transfer market after one decade. Br Actuar J 24:1–80CrossRef
8.
Cairns AJG, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73(4):687–718CrossRef
9.
Cohen A, Liran E (2007) Estimating risk preferences from deductible choice. Am Econ Rev 97:745–788CrossRef
10.
Cox SH, Lin Y, Pedersen H (2010) Mortality risk modelling: applications to insurance securitization. Insurance: Math Econ 46(1):242–253
11.
12.
Dahl M (2004) Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts. Insurance: Math Econ 35(1):113–136
13.
De Rosa C, Luciano E, Regis L (2017) Geographical diversification in annuity portfolios. Collegio Carlo Alberto Notebook, 546
14.
Delong L (2013) Backward stochastic differential equations with jumps and their actuarial and financial applications. Springer, BerlinCrossRef
15.
Favero CA, Gozluklu AE, Tamoni A (2011) Demographic trends, the dividend-price ratio, and the predictability of long-run stock market returns. J Financ Quant Anal 46(05):1493–1520CrossRef
16.
Gianin ER (2006) Risk measures via g-expectations. Insurance: Math Econ 46(39):19–34
17.
Horst U, Pirvu TA, Dos Reis G (2010) On securitization, market completion and equilibrium risk transfer. Math Financ Econ 2(4):211–252MathSciNetCrossRef
18.
Ignatieva K, Song A, Ziveyi J (2016) Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality. Insurance: Math Econ 70:286–300
19.
IMF. Global Financial Stability Report, (2012) The quest for lasting stability. IMF, Washington, DC, p 2012
20.
Jevtić P, Regis L (2019) A continuous-time stochastic model for the mortality surface of multiple populations. Insurance: Math Econ 88:181–195
21.
Jevtić P, Luciano E, Vigna E (2013) Mortality surface by means of continuous time cohort models. Insurance: Math Econ 53(1):122–133
22.
Lando D (2009) Credit risk modeling: theory and applications. Princeton University Press, PrincetonCrossRef
23.
Leung M, Fung MC, O’Hare C (2018) A comparative study of pricing approaches for longevity instruments. Insurance: Math Econ 82:95–116
24.
Li JS-H, Ng AC-Y (2011) Canonical valuation of mortality-linked securities. J Risk Insur 78:853–884CrossRef
25.
Luciano E, Vigna E (2008) Mortality risk via affine stochastic intensities: calibration and empirical relevance. Belg Actuar Bull 8(1):5–16MathSciNetMATH
26.
27.
28.
Michaelson A, Mulholland J (2014) Strategy for increasing the global capacity for longevity risk transfer: developing transactions that attract capital markets investors. J Altern Invest 17(1):18–27CrossRef
29.
Milevsky M, Promislow D (2011) Mortality derivatives and the option to annuitise. Insurance: Math Econ 29(3):299–318
30.
Pedersen J (1999) Convergence of strategies: an approach using Clark–Haussmann’s formula. Finance Stoch 3(3):323–344MathSciNetCrossRef
31.
Pitacco E, Denuit M, Haberman S, Olivieri A (2009) Modelling longevity dynamics for pensions and annuity business. Oxford University Press, OxfordMATH
32.
Schrager D (2006) Affine stochastic mortality. Insurance: Math Econ 38(1):81–97
33.
34.
35.
36.
Zeddouk F, Devolder P (2019) Pricing of longevity derivatives and cost of capital. Risks 7(41):2–29
37.
Zhou R, Li JS-H, Tan KS (2015) Economic pricing of mortality-linked securities: a Tatonnement approach. J Risk Insur 1(82):65–96CrossRef
Metadaten
Titel
Practical partial equilibrium framework for pricing of mortality-linked instruments in continuous time
verfasst von
Petar Jevtić
Minsuk Kwak
Traian A. Pirvu
Publikationsdatum
18.06.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
European Actuarial Journal / Ausgabe 1/2022
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-021-00287-w

Weitere Artikel der Ausgabe 1/2022

European Actuarial Journal 1/2022 Zur Ausgabe

Original Research Paper

An optimal reinsurance simulation model for non-life insurance in the Solvency II framework

Original Research Paper

Pricing participating longevity-linked life annuities: a Bayesian Model Ensemble approach

Correction

Correction to: Current developments in German pension schemes: What are the benefits of the new target pension?

Letter

Best upper and lower bounds on Spearman’s rho for zero-inflated continuous variables and their application to insurance

Survey Paper

Modern tontines as a pension solution: a practical overview

Original Research Paper

A long-term care multi-state Markov model revisited: a Markov chain Monte Carlo approach