Global Optimization for Automatic Model Points Selection in Life Insurance Portfolios

Starting from an original portfolio of life insurance policies, in this article we propose a methodology to select model points portfolios that reproduce the original one, preserving its market risk under a certain measure. In order to achieve this goal, we first define an appropriate risk functional that measures the market risk associated to the interest rates evolution. Although other alternative interest rate models could be considered, we have chosen the LIBOR (London Interbank Offered Rate) market model. Once we have selected the proper risk functional, the problem of finding the model points of the replicating portfolio is formulated as a problem of minimizing the distance between the original and the target model points portfolios, under the measure given by the proposed risk functional. In this way, a high-dimensional global optimization problem arises and a suitable hybrid global optimization algorithm is proposed for the efficient solution of this problem. Some examples illustrate the performance of a parallel multi-CPU implementation for the evaluation of the risk functional, as well as the efficiency of the hybrid Basin Hopping optimization algorithm to obtain the model points portfolio.

Optimal statistical arbitrage trading of Berkshire Hathaway stock and its replicating portfolio

In this paper, we make use of the replicating asset for statistical arbitrage trading, where the replicating asset is constructed by a portfolio that mimics the returns from a factor model. Using the replicating asset in the context of statistical arbitrage has never been done before in the literature. A novel optimal statistical arbitrage trading model is applied, and we derive the average transaction length and return for the Berkshire A stock and its replicating asset. The results show that the statistical arbitrage method proposed by Bertram (2010) is profitable by using the replicating asset. We also compute the average returns under different transaction costs. For the statistical arbitrage using the replicating asset of the factor model, average annual returns were at least 33%. Robustness is examined with the S&P500. Our results can provide hedge fund managers with a new technique for conducting statistical arbitrage.

The modified binomial options pricing model and the revised replicating portfolio approach with the concept of sustainability options

This paper discusses whether the project investment can develop the decision-making for the concept of sustainability options. The conventional net present value (NPV) approach assesses whether the project investment should be implemented, and develops the evaluation criteria of implementing sustainability costs from the modified binomial options pricing model (BOPM) and the revised replicating portfolio approach. It treats options premium value and the replicating portfolio approach (RPA) value as the objective functions, and the options premium of the BOPM and the initial values of the RPA as the decision variables.

Strategic Option Pricing

In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.

The value of a liability cash flow in discrete time subject to capital requirements

The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the presented approach is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity, whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner’s perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.

How to mine gold without digging

This paper examines the main drivers of the returns of gold miner stocks and ETFs during 2006–2017. We solve a combined optimal control and stopping problem to demonstrate that gold miner equities behave like real options on gold. Inspired by our proposed model, we construct a method to dynamically replicate gold miner stocks using two factors: the spot gold ETF and market equity portfolio. Furthermore, through each firm’s factor loadings on the replicating portfolio, we dynamically infer the firm’s implied leverage parameters of our model using the Kalman Filter. We find that our approach can explain a significant portion of the drivers of firm implied gold leverage. We posit that gold miner companies hold additional real options which help mitigate firm downside volatility, but these real options contribute to lower returns relative to the replicating portfolio when gold returns are positive.