Journal Article10.1016/J.INSMATHECO.2016.04.006
Valuation of guaranteed minimum maturity benefits in variable annuities with surrender options
TL;DR: A numerical approach to the pricing of guaranteed minimum maturity benefits embedded in variable annuity contracts in the case where the guarantees can be surrendered at any time prior to maturity that improves on current approaches is presented.
read more
Abstract: We present a numerical approach to the pricing of guaranteed minimum maturity benefits embedded in variable annuity contracts in the case where the guarantees can be surrendered at any time prior to maturity that improves on current approaches. Surrender charges are important in practice and are imposed as a way of discouraging early termination of variable annuity contracts. We formulate the valuation framework and focus on the surrender option as an American put option pricing problem and derive the corresponding pricing partial differential equation by using hedging arguments and Ito’s Lemma. Given the underlying stochastic evolution of the fund, we also present the associated transition density partial differential equation allowing us to develop solutions. An explicit integral expression for the pricing partial differential equation is then presented with the aid of Duhamel’s principle. Our analysis is relevant to risk management applications since we derive an expression of the delta for the sensitivity analysis of the guarantee fees with respect to changes in the underlying fund value. We provide algorithms for implementing the integral expressions for the price, the corresponding early exercise boundary and the delta of the surrender option. We quantify and assess the sensitivity of the prices, early exercise boundaries and deltas to changes in the underlying variables including an analysis of the fair insurance fees.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Optimal Surrender of Guaranteed Minimum Maturity Benefits Under Stochastic Volatility and Interest Rates
Boda Kang,Jonathan Ziveyi +1 more
TL;DR: In this article, the authors analyse how the policyholder surrender behavior is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity.
Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates
Boda Kang,Jonathan Ziveyi +1 more
TL;DR: In this article, the authors analyse how the policyholders' surrender behavior is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity.
Optimal surrender strategies and valuations of path-dependent guarantees in variable annuities
Junkee Jeon,Minsuk Kwak +1 more
TL;DR: This paper derives the optimal surrender strategies and the values of three different types of guarantees embedded in VA contracts, and applies the Mellin transform to the non-homogeneous PDE to obtain an integral equation that produces the value of the embedded guarantee as well as the optimal surrendered boundary in a variable annuity contract.
20
Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees
TL;DR: In this article , the valuation and optimal surrender of variable (equity-linked) annuities under a Lévy-driven equity market with mortality risk were studied, where a practical periodic fee structure which can vary over time and is assessed as a proportion of the fund value was proposed.
11
Pricing variable annuity with surrender guarantee
Junkee Jeon,Minsuk Kwak +1 more
TL;DR: The surrender benefit of the variable annuity contract embedded with a guaranteed minimum accumulated benefit rider provides a protection against the downside risk of financial market throughout the life of contract, and thus it can be referred to as surrender guarantee.
9
References
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
31.9K
The Analytic Valuation of American Options
TL;DR: In this article, the authors derived valuation formulas for American options and analyzed the properties associated with the optimal exercise boundary, and a numerical technique to implement the valuation formulas was presented to evaluate the performance of these formulas.
666
Optimal Stopping and the American Put
TL;DR: In this article, it was shown that the problem of pricing the American put is equivalent to solving an optimal stopping problem and that there is a unique solution to this problem which has a lower boundary.
Alternative characterizations of american put options
TL;DR: In this article, the authors derive alternative representations of the McKean equation for the value of the American put option, and demonstrate the equivalence of their results to the Mckean equation.
535
A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities
TL;DR: In this article, the authors proposed a general framework for pricing variable annuities with embedded guarantees, including guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB).