TY - JOUR
T1 - Dynamic Fund Protection
AU - Imai, Junichi
AU - Boyle, Phelim P.
N1 - Funding Information:
Junichi Imai thanks the Japan Society for the Promotion of Science for research support, and Phelim Boyle acknowledges research support from the Social Sciences and Humanities Research Council of Canada. The authors are grateful to Elias Shiu for many helpful suggestions. They also wish to thank Wulin Suo and an anonymous referee for comments on an earlier version of this paper.
PY - 2001/7/1
Y1 - 2001/7/1
N2 - Dynamic fund protection provides an investor with a floor level of protection during the investment period. This feature generalizes the concept of a put option, which provides only a floor value at a particular time. The dynamic protection feature ensures that the fund value is upgraded if it ever falls below a certain threshold level. Gerber and Pafumi (2000) have recently derived a closed-form expression for the price of this protection when the basic portfolio follows geometric Brownian motion. In this paper we examine the pricing of this feature under the constant elasticity of variance process. Two approaches are used to obtain numerical results. First, we show how to extend the basic Monte Carlo approach to handle the particular features of dynamic protection. When a discrete-time simulation approach is used to value a derivative that is subject to continuous monitoring, there is a bias. We show how to remove this bias. Second, a partial differential equation approach is used to price dynamic protection. We demonstrate that the price of the dynamic protection is sensitive to the investment assumptions. We also discuss a discrete time modification of the dynamic protection feature that is suitable for practical implementation. The paper deals just with pricing and does not consider the important question of reserving for these contracts.
AB - Dynamic fund protection provides an investor with a floor level of protection during the investment period. This feature generalizes the concept of a put option, which provides only a floor value at a particular time. The dynamic protection feature ensures that the fund value is upgraded if it ever falls below a certain threshold level. Gerber and Pafumi (2000) have recently derived a closed-form expression for the price of this protection when the basic portfolio follows geometric Brownian motion. In this paper we examine the pricing of this feature under the constant elasticity of variance process. Two approaches are used to obtain numerical results. First, we show how to extend the basic Monte Carlo approach to handle the particular features of dynamic protection. When a discrete-time simulation approach is used to value a derivative that is subject to continuous monitoring, there is a bias. We show how to remove this bias. Second, a partial differential equation approach is used to price dynamic protection. We demonstrate that the price of the dynamic protection is sensitive to the investment assumptions. We also discuss a discrete time modification of the dynamic protection feature that is suitable for practical implementation. The paper deals just with pricing and does not consider the important question of reserving for these contracts.
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U2 - 10.1080/10920277.2001.10595996
DO - 10.1080/10920277.2001.10595996
M3 - Article
AN - SCOPUS:85011139827
SN - 1092-0277
VL - 5
SP - 31
EP - 47
JO - North American Actuarial Journal
JF - North American Actuarial Journal
IS - 3
ER -