Reset and withdrawal rights in dynamic fund protection

Abstract

We analyze the nature of the dynamic fund protection which provides an investment fund with a floor level of protection against a reference stock index (or stock price). The dynamic protection feature entitles the investor the right to reset the value of his investment fund to that of the reference stock index. The reset may occur automatically whenever the investment fund value falls below that of the reference stock index, or only allowed at pre-determined time instants. The protected funds may allow a finite number of resets throughout the life of the fund, where the reset times are chosen optimally by the investor. We examine the relation between the finite-reset funds and automatic-reset funds. We also analyze the premium and the associated exercise policy of the embedded withdrawal right in protected funds, where the investor has the right to withdraw the fund prematurely. The impact of proportional fees on the optimal withdrawal policies is also analyzed. The holder should optimally withdraw at a lower critical fund value when the rate of proportional fees increases. Under the assumption that the fund value and index value follow the Geometric Brownian processes, we compute the grant-date and mid-contract valuation of these protected funds. Pricing properties of the protected fund value and the cost to the sponsor are also discussed.

Lookback options and dynamic fund protection under multiscale stochastic volatility

“…This formula agrees with those obtained by Gerber and Shiu (2003) and Chu and Kwok (2004). For a multiscale volatility economy, we propose to directly model the evaluation of I F under the foreign risk-neutral measure as (5).…”

“…Under the BS dynamics, this problem has been studied by Gerber and Shiu (2003) and Chu and Kwok (2004). Here, we use an alternative view to carry out the analysis.…”

“…Gerber and Shiu (2003) considered perpetual EIA with dynamic protection, where the guarantee level is another stock index. By assuming that both the naked fund and stock index follow lognormal processes, Chu and Kwok (2004) investigated the reset and withdrawal rights in DFP. They showed that the proposed scheme of Gerber and Shiu (2003) is related to a lookback payoff.…”

Indifference fee rate for variable annuities

“…Milvesky and Posner (see [18]) are, up to our knowledge, the first to apply risk neutral option pricing theory to value GMDB in variable annuities. Withdrawal options are studied in [10] and [21], and a general framework to define variable annuities is presented in [2]. Milevsky and Salisbury (see [19]) focus on the links between American put options and dynamic optimal withdrawal policies.…”

Max–min Optimization Problem for Variable Annuities Pricing

“…Then, Milevsky and Posner [12] applied risk neutral option pricing theory to value GMDB variable annuities. The case of withdrawal options is studied by Chu and Kwok in [8] and by Siu in [15], and a general framework to define variable annuities is presented by Bauer et al in [2]. Milevsky and Salisbury studied in [13] the links between American put options and dynamic optimal withdrawal policies.…”