Optimal stopping behavior of equity-linked investment products with regime switching

Cheung, Ka Chun; Yang, Hailiang

doi:10.1016/j.insmatheco.2005.06.005

Cited by 8 publications

(10 citation statements)

References 31 publications

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“…This early cancellation feature is similar to the surrender right that arises in many common insurance products such as equityindexed annuities (see e.g. [8], [21], [22]). Due to the timing flexibility, the investor may stop the premium payment if he/she finds that a drawdown is unlikely to occur (e.g.…”

Section: Introductionmentioning

confidence: 54%

Stochastic modeling and fair valuation of drawdown insurance

Zhang

Leung

Hadjiliadis

2013

Insurance: Mathematics and Economics

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This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the asset value. We first consider a vanilla insurance contract whereby the protection buyer pays a constant premium over time to insure against a drawdown of a pre-specified level. This leads to the analysis of the conditional Laplace transform of the drawdown time, which will serve as the building block for drawdown insurance with early cancellation or drawup contingency. For the cancellable drawdown insurance, we derive the investor's optimal cancellation timing in terms of a two-sided first passage time of the underlying drawdown process. Our model can also be applied to insure against a drawdown by a defaultable stock. We provide analytic formulas for the fair premium and illustrate the impact of default risk.

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Section: Introductionmentioning

confidence: 54%

Stochastic modeling and fair valuation of drawdown insurance

Zhang

Leung

Hadjiliadis

2013

Insurance: Mathematics and Economics

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“…Note that a finite right-hand surrender boundary appears by time t = 4. (In fact, it happens some time in (2,3).) This is our second experiment in which the right-hand free boundary vanishes.…”

Section: Experiments 44 Impact Of Changing the Surrender Charge Periomentioning

confidence: 84%

“…We incorporate a more realistic, time-dependent hazard rate in our model and examine the impact of the mortality assumption on the optimal strategies. Our work complements the recent work of Cheung and Yang (2005) because, in order to focus on the effect of regime-swtiching, they ignore the effect of mortality and product features, such as the embedded guarantees. We focus on these assumptions and features.…”

Section: Introductionmentioning

confidence: 91%

“…This is because the left surrender boundary w l is smaller than the minimum guaranteed amount. When the investor surrenders at w = w l , she receives the minimum guaranteed amount, but the surrender charge does not apply to this amount; see equation (3). However, the right-hand surrender boundary w u is affected by the change in surrender charge during the surrender charge period.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…We, on the other hand, are not pricing EIAs but rather are determining the optimal time for an individual to surrender a given EIA. Cheung and Yang (2005) study the optimal EIA surrender strategy in a discrete-time model with regime-switching.…”

Section: Introductionmentioning

confidence: 99%

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Optimal surrender strategies for equity-indexed annuity investors

Moore

2009

Insurance: Mathematics and Economics

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An equity-indexed annuity (EIA) is a hybrid between a variable and a fixed annuity that allows the investor to participate in the stock market and earn at least a minimum interest rate. The investor sacrifices some of the upside potential for the downside protection of the minimum guarantee. Because EIAs allow investors to participate in equity growth without the downside risk, their popularity has grown rapidly.An optimistic EIA owner might consider surrendering an EIA contract, paying a surrender charge, and investing the proceeds directly in the index to earn the full (versus reduced) index growth, while using a risk-free account for downside protection. Because of the popularity of these products, it is important for individuals and insurers to understand the optimal policyholder behavior.We consider an EIA investor who seeks the surrender strategy and post-surrender asset allocation strategy that maximize the expected discounted utility of bequest. We formulate a variational inequality and a Hamilton-Jacobi-Bellman equation that govern the optimal surrender strategy and post-surrender asset allocation strategy, respectively. We examine the optimal strategies and how they are affected by the product features, model parameters, and mortality assumptions. We observe that in many cases, the "no-surrender" region is an interval (w l , w u ); i.e., that there are two free boundaries. In these cases, the investor surrenders the EIA contract if the fund value becomes too high or too low. In other cases, there is only one free boundary; the lower (or upper) surrender threshold vanishes. In these cases, the investor holds the EIA, regardless of how low (or high) the fund value goes. For a special case, we prove a succinct and intuitive condition on the model parameters that dictates whether one or two free boundaries exist.

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Insurance Derivatives

Cheung¹

2010

Encyclopedia of Quantitative Finance

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Optimal stopping behavior of equity-linked investment products with regime switching

Cited by 8 publications

References 31 publications

Stochastic modeling and fair valuation of drawdown insurance

Stochastic modeling and fair valuation of drawdown insurance

Optimal surrender strategies for equity-indexed annuity investors

Insurance Derivatives

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