×

Pricing ratchet equity-indexed annuities with early surrender risk in a CIR\(++\) model. (English) Zbl 1412.91058

Summary: In this article we propose a lattice algorithm for pricing simple ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR\(++\) stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
PDF BibTeX XML Cite
Full Text: DOI Link

References:

[1] Alfonsi, A., High Order Discretization Schemes for the CIR Process: Application to Affine Term Structure and Heston Models, Mathematics of Computation, 79, 209-237, (2010) · Zbl 1198.60030
[2] Amin, K.; Khanna, A., Convergence of American Option Values from Discrete-to Continuous-Time Financial Models, Mathematical Finance, 4, 289-304, (1994) · Zbl 0884.90012
[3] Appolloni, E.; Caramellino, L.; Zanette, A., A Robust Tree Method for Pricing American Options with CIR Stochastic Interest Rate, (2013)
[4] Brigo, D.; Mercurio, F., Interest Rate Models—Theory and Practice, (2006), Berlin: Springer, Berlin
[5] Costabile, M.; Gaudenzi, M.; Massabï¿, I.; Zanette, A., Evaluating Fair Premiums of Equity-Linked Policies with Surrender Option in a Bivariate Model, Insurance: Mathematics and Economics, 41, 317-338, (2009)
[6] Cox, J.; Ross, S. A.; Rubinstein, M., Option Pricing: A Simplified Appoach, Journal of Financial Economics, 7, 229-264, (1979)
[7] Cox, J. C.; Ingersoll, J.; Ross, S., A Theory of the Term Structure of Interest Rates, Econometrica, 53, 385-407, (1985) · Zbl 1274.91447
[8] Ethier, S. N.; Kurtz, T., Markov Processes: Characterization and Convergence, (1986), New York: John Wiley & Sons, New York · Zbl 0592.60049
[9] Gaudenzi, M.; Lepellere, M. A.; Zanette, A., The Singular Point Method for Pricing Path-Dependent Options, Journal of Computational Finance, 14, 29-56, (2010) · Zbl 1284.91571
[10] Gerber, H.; Shiu, E., Pricing Lookback Options and Dynamic Guarantees, North American Actuarial Journal, 7, 48-67, (2003) · Zbl 1084.91507
[11] Hardy, M. R., Investment Guarantees: Modelling and Risk Management for Equity-Linked Life Insurance, (2003), New York: Wiley, New York · Zbl 1092.91042
[12] Hull, J.; White, A., Numerical Procedures for Implementing Term Structure Models. I., Journal of Derivatives, 2, 7-16, (1994)
[13] Annuity Fact Book: A Guide to Information, Trends, and Data in the Annuity Industry, (2009), Washington, DC: Insured Retirement Institute., Washington, DC
[14] Kijima, M.; Wong, T., Pricing of Ratchet Equity-Indexed Annuities Under Stochastic Interest Rate, Insurance: Mathematics and Economics, 41, 317-338, (2007) · Zbl 1141.91457
[15] Kim, Y.; Kunitomo, N., Pricing options under Stochastic Interest Rates: A New Approach, Asia-pacific Financial Markets, 6, 49-70, (1999) · Zbl 1157.91363
[16] Kunitomo, N.; Takahashi, A., On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis, Annals of Applied Probability, 13, 914-952, (2003) · Zbl 1091.91037
[17] Kushner, H.; Dupuis, P. G., Numerical Methods for Stochastic Control Problems in Continous Time, (1992), Berlin: Springer Verlag, Berlin
[18] Lin, X. D.; Tan, K. S., Valuation of Equity-Indexed Annuities under Stochastic Interest Rates, North American Auctuarial Journal, 6, 72-91, (2003) · Zbl 1084.60530
[19] Nelson, D. B.; Ramaswamy, K., Simple Binomial Processes as Diffusion Approximations in Financial Models, Review of Financial Studies, 3, 393-430, (1990)
[20] Palmer, B. A., Equity-Indexed Annuities: Fundamental Concepts and Issues, Report of Insurance Information Institute, (2006)
[21] Wei, J., Valuing American Equity Options with a Stochastic Interest Rate: A Note, Journal of Financial Engineering, 2, 195-206, (1996)
[22] Wilmott, P., Cliquet Options and Volatility Models, Wilmott Magazine, 3, 78-83, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.