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Valuation of capital protection options

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  • Xiaolin Luo
  • Pavel V. Shevchenko

Abstract

This paper presents numerical algorithm and results for pricing a capital protection option offered by many asset managers for investment portfolios to take advantage of market growth and protect savings. Under optimal withdrawal policyholder behaviour the pricing of such a product is an optimal stochastic control problem that cannot be solved using Monte Carlo method. In low dimension case, it can be solved using PDE based methods such as finite difference. In this paper, we develop a much more efficient Gauss-Hermite quadrature method with a one-dimensional cubic spline for calculation of the expectation between withdrawal/reset dates, and a bi-cubic spline interpolation for applying the jump conditions across withdrawal/reset dates. We show results for both static and dynamic withdrawals and for both the asset accumulation and the pension phases (different penalties for any excessive withdrawal) in the retirement investment cycle. To evaluate products with capital protection option, it is common industry practice to assume static withdrawals and use Monte Carlo method. As a result, the fair fee is underpriced if policyholder behaves optimally. We found that extra fee that has to be charged to counter the optimal policyholder behaviour is most significant at smaller interest rate and higher volatility levels, and it is sensitive to the penalty threshold. At low interest rate and a moderate penalty threshold level (15% of the portfolio value per annum) typically set in practice, the extra fee due to optimal withdrawal can be as high as 40% and more on top of the base case of no withdrawal or the case of fixed withdrawals at the penalty threshold.

Suggested Citation

  • Xiaolin Luo & Pavel V. Shevchenko, 2015. "Valuation of capital protection options," Papers 1508.00668, arXiv.org, revised May 2017.
    • Handle: RePEc:arx:papers:1508.00668
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    References listed on IDEAS

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    1. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    2. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    5. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    6. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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