Dynamic Fund Protection

Junichi Imai, Phelim P. Boyle

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)31-47
Number of pages17
JournalNorth American Actuarial Journal
Volume5
Issue number3
DOIs
Publication statusPublished - 2001 Jul 1
Externally publishedYes

Fingerprint

Pricing
Discrete-time
Geometric Brownian Motion
Elasticity
Closed-form
Partial differential equation
Monitoring
Derivative
Numerical Results
Generalise
Demonstrate
Simulation
Concepts
Derivatives
Price dynamics
Investors
Put option
Partial differential equations
Geometric Brownian motion
Continuous monitoring

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

Dynamic Fund Protection. / Imai, Junichi; Boyle, Phelim P.

In: North American Actuarial Journal, Vol. 5, No. 3, 01.07.2001, p. 31-47.

Research output: Contribution to journalArticle

Imai, Junichi ; Boyle, Phelim P. / Dynamic Fund Protection. In: North American Actuarial Journal. 2001 ; Vol. 5, No. 3. pp. 31-47.
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