Transaction costs are a major factor affecting portfolio returns in asset management. We propose an enhanced target volatility strategy to reduce the deleterious effect of transaction costs by adding rebalancing boundaries to the target volatility asset allocation mechanism. We formulate a constrained optimization problem to determine the optimal rebalancing boundary level. Based on simulations using an overlapping block bootstrap approach, we find that the extended target volatility portfolio with rebalancing boundary levels can provide better investment outcomes (higher portfolio returns and reduced transaction costs) without losing the ability to control portfolio risk under a pre-determined threshold. Further computational analysis on different real market scenarios confirms these findings and allows us to summarize insights on the appropriate boundaries to use under different market conditions and transaction cost magnitudes. Our findings have important practical implications given the popularity of the target volatility investment strategy as well as other asset management concepts with a dynamic asset allocation mechanism.

Motivated by the recent market turbulence triggered by the COVID-19 pandemic and the changing interest rate environment, we propose an improved investment strategy for extending retirement coverage in the pension decumulation stage. The newly proposed strategy with interest rate dependent volatility targets can significantly improve the durability of conventional retirement portfolios with constant risky and risk-free asset allocations. This conclusion follows from our analysis in the simulated financial market with stochastic interest rate and stochastic volatility, based on the Hybrid Heston-Vasicek model. Consequently, the proposed target volatility strategy could be a suitable option for more reliable retirement coverage after retirement.

We present a hybrid method for computing volatility forecasts that can be used to implement a risk-controlled strategy for a multi-asset portfolio consisting of both US and international equities. Recent years have been characterized by extremely low yields, with 2022 marked by rising interest rates and an increasing inflation rate. These factors produced new challenges for both private and institutional investors, including the need for robust forecast methods for financial assets’ volatilities. Addressing such task, our research focuses on a hybrid solution that combines classical statistical models with specific classes of Recurrent Neural Networks (RNNs). In particular, we first use the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) approach within the preprocessing phase to capture volatility clustering, striking an efficient balance between computational effort and accuracy, to then apply RNN architectures, namely GRU, LSTM, and a mixed model with both units, as to maximize performances of volatility forecasts later used as input factors for risk-controlled investment strategies. In terms of portfolio allocation, we focus on a simplified version of the Risk Parity method that was first proposed by the Research division of S&P Global. This version ignores the contribution of cross-correlations among assets, nevertheless providing encouraging results. Indeed, we show the effectiveness of the chosen approach by providing forward-looking risk parity portfolio strategies that outperform standard risk/return portfolio structures.

We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option-based structure with a dynamic allocation logic as underlying. We provide an in-depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek-type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time-invariant portfolio protection strategies, meanwhile being also afraid to experience a cash-lock event triggered by market turmoils.

Under the impact of both increasing credit pressure and low economic returns characterizing developed countries, investment levels have decreased over recent years. Moreover, the recent turbulence caused by the COVID-19 crisis has accelerated the latter process. Within this scenario, we consider the so-called Volatility Target (VolTarget) strategy. In particular, we focus our attention on estimating volatility levels of a risky asset to perform a VolTarget simulation over two different time horizons. We first consider a 20 year period, from January 2000 to January 2020, then we analyse the last 12 months to emphasize the effects related to the COVID-19 virus’s diffusion. We propose a hybrid algorithm based on the composition of a GARCH model with a Neural Network (NN) approach. Let us underline that, as an alternative to standard allocation methods based on realized and backward oriented volatilities, we exploited an innovative forward-looking estimation process exploiting a Machine Learning (ML) solution. Our solution provides a more accurate volatility estimation, allowing us to derive an effective investor risk-return profile during market crisis periods. Moreover, we show that, via a forward-looking VolTarget strategy while using an ML-based prediction as the input, the average outcome for an investment in a drawdown plan is more sustainable while representing an efficient risk-control solution for long time period investments.

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well-knownConstant Proportion Portfolio Insurance(CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, calledguaranteed minimum equity exposure(GMEE). In particular, our proposal ensures to overcome the so-calledcash-inrisk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI-GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston-Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE.

As a response to unforeseeable market turbulence—such as the 2008 financial crisis and the most recent market drawdown triggered by the COVID-19 pandemic—we propose a new pension investment strategy that could better protect a long-term pension plan in volatile market conditions. Over a hypothetical 20-year pension scheme and various target volatility scenarios, we show that our newly proposed strategy, which attaches a target volatility mechanism to a lifecycle strategy, could provide more effective capital protection and risk control for pension investment vehicles. Our results are robust with a consideration of transaction costs.

Volatility Target (VolTarget) strategies as underlying assets for options embedded in investment-linked products have been widely used by practitioners in recent years. Available research mainly focuses on European-type options linked to VolTarget strategies. In this paper, VolTarget-linked options of American type are investigated. Within the Heston stochastic volatility model, a numerical study of American put options, as well as American lookback options linked to VolTarget strategies, is performed. These are compared with traditional American-type derivatives linked to an equity index. The authors demonstrate that using a Volatility Target strategy as a basis for an embedded American-type derivative may make any protection fees significantly less dependent of changing market volatilities. Replacing an equity index with the VolTarget strategy may also result in reducing guarantee fees of the corresponding protection features in a highly volatile market environment.

Recent years have seen an emerging class of structured financial products based on options linked to dynamic asset allocation strategies. One of the most chosen approach is the so-called target volatility mechanism. It shifts between risky and riskless assets to control the volatility of the overall portfolio. Even if a series of articles have been already devoted to the analysis of options linked to the target volatility mechanism, this paper is the first, to the best of our knowledge, that tries to develop closed-end formulas for VolTarget options. In particular, we develop closed-end formulas for option prices and some key hedging parameters within a Black and Scholes setting, assuming the underlying follows a target volatility mechanism.

Designing a structured investment product with capital protection which would be characterized by high capital protection level as well as high equity participation rate is a challenging task in the current market environment. Low interest rates and high volatility levels negatively affect the above key parameters of such investment products. One way to increase the participation rate of a structured investment product with a fixed capital protection level is to use a volatility target (VolTarget) strategy as an underlying asset for a financial option embedded in such a product. We introduce an extended VolTarget mechanism with interest rate dependent volatility target levels and provide a detailed comparative numerical study of European options linked to VolTarget strategies within a hybrid Heston–Vasičec model with stochastic volatility and stochastic interest rate.

Click to increase image sizeClick to decrease image size Acknowledgments We wish to thank the anonymous Referees for a number of very helpful suggestions that helped improve presentation of this paper. Notes Supported by the Hausdorff Institute of Mathematics (Bonn) and by the Summer Research Grant (Bentley University). The limitation is applied in order to ensure that in extreme market scenarios with very low volatility the VolTarget mechanism will not lead to a very aggressive allocation where a big portion of the risky asset investment is solely financed by loans. The limitation is also in line with certain regulatory requirements for mutual funds, see e.g. UCITS-compliant funds. In today's market, a more restrictive limitation occurs in so-called VolCap portfolios.

We study equity-linked life insurance contracts with minimum guarantees, where an underlying index is based on the set of stocks whose prices are described by the multidimensional model with interacting assets. We apply numerical techniques developed for pricing index options (path-dependent as well as plain index options) to valuation of such insurance contracts in the case of single and periodic premiums. We also numerically determine and discuss an implied guarantee rate of an insurance contract.

An extension with noise given by Poisson processes of a model of financial market with several assets that are interacting, i.e., influencing each other (even in the absence of noise) is given. We present explicit formulae for the stock price process as well as for the prices of European multi-asset contingent claims based on a residual risk minimization approach. We also provide an explicit hedging formula.