On the Optimal Type and Level of Guarantees for Prospect Theory Investors

Ebert, Sebastian; Koos, Birgit; Schneider, Judith C.

doi:10.2139/ssrn.2081665

Cited by 16 publications

(15 citation statements)

References 28 publications

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“…We then use Monte Carlo simulations to evaluate these products under EUT, CPT, and MCPT. We are able to replicate the results of Ebert, Koos, and Schneider () under EUT and CPT, particularly the fact that CPT can explain the demand for guarantees but not for the more complex forms of guarantees. However, under our new MCPT approach, the complex products typically dominate the simple products: for investors who evaluate utility considering possible future interim changes, the subjective utility is higher for the complex than for the simple guaranteed products.…”

Section: Introductionsupporting

confidence: 53%

“…In this section, we apply MCPT to three guaranteed products ( roll‐up, ratch‐up , and cliquet ) and a product without guarantee. If not stated otherwise, we follow Ebert, Koos, and Schneider () in this section.…”

Section: Application Of Mcpt: Explaining the Demand For Cliquet‐type mentioning

confidence: 99%

“…The third and final guaranteed product is referred to as cliquet product with payoff:

A_{T}^{cli} : = \prod_{i = 1}^{n} max ((), e^{g Δ t}, α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}}) = \prod_{i = 1}^{n} (α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}} + {[e^{g Δ t} - α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}}]}^{+}) .

In each period, this product locks in the higher of a guaranteed rate g and the performance of the underlying portfolio V (the latter only with respect to a portion

α^{\frac{1}{n}}

of the investment premium). This representation of a cliquet product from Ebert, Koos, and Schneider () is rather unusual. However, for

\overset{g}{true} = g - log false(α false)

, this representation coincides with the more common representation

A_{T}^{\overset{cli}{true}} : = α \prod_{i = 1}^{n} max ((), e^{\overset{g}{true} Δ t}, \frac{V_{t_{i}}}{V_{t_{i - 1}}}) = α \prod_{i = 1}^{n} (\frac{V_{t_{i}}}{V_{t_{i - 1}}} + [e^{\overset{true˜}{g} Δ t} - \frac{V_{t_{i}}}{V_{}}])

…”

Section: Application Of Mcpt: Explaining the Demand For Cliquet‐type mentioning

confidence: 99%

“…Historical and Monte Carlo simulations are used by Dichtl and Drobetz () to analyze portfolio insurance strategies based on simple Constant Proportional Portfolio Insurance (CPPI) strategies. Ebert, Koos, and Schneider () determine the “optimal” specification of different guarantee types, where optimality is defined as creating the maximum subjective utility for a CPT investor. A main result of these articles is that, in contrast to EUT, CPT can explain the demand for guarantees .…”

Section: Introductionmentioning

confidence: 99%

“…As a first application example of MCPT, we investigate the demand for different guaranteed products. For the sake of comparability, we apply this approach to the guaranteed contracts presented by Ebert, Koos, and Schneider (); that is, we consider three different types of guarantees ( roll‐up, ratch‐up , and cliquet ) and a product without guarantee. The roll‐up guarantee provides a minimal terminal payoff, which is based on some guaranteed rate of interest.…”

Section: Introductionmentioning

confidence: 99%

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Multi Cumulative Prospect Theory and the Demand for Cliquet‐Style Guarantees

Ruß¹,

Schelling²

2017

J of Risk & Insurance

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Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT) face problems explaining preferences of long‐term investors. Previous research motivates that the subjective utility of a long‐term investment also depends on interim value changes. Therefore, we propose an approach that we call Multi Cumulative Prospect Theory. It is based on CPT and considers annual changes in the contract values. As a first application, we can show that in contrast to EUT and CPT, this approach is able to explain the demand for guaranteed products with lock‐in features, which in this framework generate a higher subjective utility than products without or with simpler guarantees.

show abstract

Section: Introductionsupporting

confidence: 53%

Section: Application Of Mcpt: Explaining the Demand For Cliquet‐type mentioning

confidence: 99%

“…The third and final guaranteed product is referred to as cliquet product with payoff:

A_{T}^{cli} : = \prod_{i = 1}^{n} max ((), e^{g Δ t}, α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}}) = \prod_{i = 1}^{n} (α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}} + {[e^{g Δ t} - α^{\frac{1}{n}} \frac{V_{t_{i}}}{V_{t_{i - 1}}}]}^{+}) .

In each period, this product locks in the higher of a guaranteed rate g and the performance of the underlying portfolio V (the latter only with respect to a portion

α^{\frac{1}{n}}

of the investment premium). This representation of a cliquet product from Ebert, Koos, and Schneider () is rather unusual. However, for

\overset{g}{true} = g - log false(α false)

, this representation coincides with the more common representation

A_{T}^{\overset{cli}{true}} : = α \prod_{i = 1}^{n} max ((), e^{\overset{g}{true} Δ t}, \frac{V_{t_{i}}}{V_{t_{i - 1}}}) = α \prod_{i = 1}^{n} (\frac{V_{t_{i}}}{V_{t_{i - 1}}} + [e^{\overset{true˜}{g} Δ t} - \frac{V_{t_{i}}}{V_{}}])

…”

Section: Application Of Mcpt: Explaining the Demand For Cliquet‐type mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi Cumulative Prospect Theory and the Demand for Cliquet‐Style Guarantees

Ruß¹,

Schelling²

2017

J of Risk & Insurance

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Moderne Verhaltensökonomie in der Ruhestandsplanung

Richter

Ruß

Schelling

2020

Ruhestandsplanung - Beratungsansatz Für Die Zielgruppe 50plus

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Minimum return rate guarantees under default risk: optimal design of quantile guarantees

2020

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The paper analyzes the design of participating life insurance contracts with minimum return rate guarantees. Without default risk, the insured receives the maximum of a guaranteed rate and a participation in the investment returns. With default risk, the payoff is modified by a default put implying a compound option. We represent the yearly returns of the liabilities by a portfolio of plain vanilla options. In a Black and Scholes model, the optimal payoff constrained by a maximal shortfall probability can be stated in closed form. Due to the completeness of the market, it can be implemented for any equity to debt ratio. Keywords Guarantee scheme • Derivatives • Life insurance • Return rate guarantees • Default risk • Regulatory requirements • Utility to the insured JEL Classification G 31 • G 22 The authors gratefully acknowledge financial support by the German Insurance Science Association (DVfVW). In addition the authors would like to thank the two anonymous referees for their valuable and helpful suggestions and comments.

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On the Optimal Type and Level of Guarantees for Prospect Theory Investors

Cited by 16 publications

References 28 publications

Multi Cumulative Prospect Theory and the Demand for Cliquet‐Style Guarantees

Multi Cumulative Prospect Theory and the Demand for Cliquet‐Style Guarantees

Moderne Verhaltensökonomie in der Ruhestandsplanung

Minimum return rate guarantees under default risk: optimal design of quantile guarantees

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