Least-squares Monte Carlo Simulation Research Articles

Optimal annuitisation, housing and reverse mortgage in retirement in the presence of a means-tested public pension

AbstractIn this paper we develop a model to find optimal decisions in retirement with respect to the consumption, risky asset allocation, access to annuities, reverse mortgage and the option to scale housing in the presence of a means-tested public pension. To solve the corresponding high-dimensional optimal stochastic control problem, we use the Least-Squares Monte Carlo simulation method. The model is applied in the context of the Australian retirement system. Few retirees in Australia utilise financial products in retirement, such as annuities or reverse mortgages. Since the government-provided means-tested Age Pension in Australia is an indirect annuity stream which is typically higher than the consumption floor, it can be argued that this could be the reason why many Australians do not annuitise. In addition, in Australia where assets allocated to the family home are not included in the means tests of Age Pension, the incentive to over-allocate wealth into housing assets is high. This raises the question whether a retiree is really better off over-allocating into the family home, while accessing home equity later on either via downsizing housing or by taking out a reverse mortgage. Our findings confirm that means-tested pension crowds out voluntary annuitisation in retirement, and that annuitisation is optimal sooner rather than later once retired. We find that it is never optimal to downscale housing when the means-tested pension and a reverse mortgage are available; only when there is no other way to access equity then downsizing is the only option.

Investment Decision for Long-Term Battery Energy Storage System Using Least Squares Monte Carlo

The use of renewable energy sources to achieve carbon neutrality is increasing. However, the uncertainty and volatility of renewable resources are causing problems in power systems. Flexible and low-carbon resources such as Energy Storage Systems (ESSs) are essential for solving the problems of power systems and achieving greenhouse gas reduction goals. However, ESSs are not being installed because of Korea’s fuel-based electricity market. To address this issue, this paper presents a method for determining the optimal investment timing of Battery Energy Storage Systems (BESSs) using the Least Squares Monte Carlo (LSMC) method. A case study is conducted considering the System Marginal Price (SMP) and Capacity Payment (CP), which are electricity rates in Korea. Revenue is calculated through the arbitrage of a 10 MW/40 MWh lithium-ion BESS, and linear programming optimization is performed for ESS scheduling to maximize revenue. The ESS revenue with uncertainty is modeled as a stochastic process using Geometric Brownian Motion (GBM), and the optimal time to invest in an ESS is determined using an LSMC simulation considering investment costs. The proposed method can be used as a decision-making tool for ESS investors to provide information on facility investments in arbitrage situations.

Inland port and waterway capacity expansion model under demand uncertainty

We address the inland port and waterway capacity expansion (IPWCE) problem under demand uncertainty, the purpose of which is to determine the capacity expansion scales and timings for inland ports and waterways. To achieve this goal, we first build an inland waterway multimodal network (IWMN) that consists of physical and operational multimodal networks. Second, by viewing the IPWCE problem under deterministic demand as a subproblem of the IPWCE problem under uncertain demand, we develop a model for IPWCE under deterministic demand (IPWCEDD) based on bilevel programming and a model for IPWCE under uncertain demand (IPWCEUD) based on network real options theory. Third, we propose a sensitivity analysis-based descent search (SADS) algorithm to solve the IPWCEDD model. Moreover, in accordance with the optimal solutions of the IPWCEDD model, we then develop a least squares Monte Carlo simulation (LSM) method to solve the IPWCEUD model. Finally, we verify the effectiveness, efficiency, and applicability of the proposed models as well as the solution algorithm and methods through experiments of two different scales. The results of the small-scale experiment indicate that the proposed SADS algorithm and LSM method can solve the models optimally within the time limit. The large-scale experiment, which is conducted on the Yangtze River IWMN of mainland China, shows that capacity expansions at Chongqing Port, Nanjing Port, and Wuhan Port and on the waterway links connecting these ports can yield the maximum increased option values for the IPWCE problem under demand uncertainty. Moreover, the corresponding optimal expansion timing for implementing the capacity expansion plan is in the second year. Our research outcomes can help to guide IPWCE under demand uncertainty and further establish a high-quality inland river transport system.

Real options valuation of photovoltaic investments: A case from Turkey

Investments in renewable energy resources have become inevitable due to increasing energy demand and energy prices, diminishing non-renewable energy resources, and the outgrowth of carbon footprints. Photovoltaic (PV) systems offer high solar energy potential in sustainable energy production whereas their high initial costs necessitate critical strategic valuation of investments. Valuation with conventional methods has been challenging due to existence of uncertainties such as fluctuating PV panel prices, changing meteorological conditions with certain effects on power generation, and governmental policies on energy market regulations. This study aims to propose a real options approach to valuation of residential rooftop PV system investments considering these uncertainties and demonstrate benefits of this approach with an application on the residential PV investment decisions in Turkey. The proposed method, Real Options Valuation (ROV) with Least-Squares Monte Carlo Simulation (LSMC) considers the deferral option of the investor by utilizing stochastic simulations, the discounted cash flow method, linear regression, and backward dynamic programming and thus evaluates the effects of uncertainties on financial attractiveness of residential PV investments. The case study findings proved that ROV with LSMC having a 7-years deferral option supported the investment decision with realizable cost-effective options while “NPV method” resulted in an infeasible investment. Scenario analysis was also conducted to explore policy options that can be used to promote solar energy investments in Turkey. This study has a potential to have practical contributions for investors as well as implications for policy-makers.

Pricing Multi-Asset Bermudan Commodity Options with Stochastic Volatility Using Neural Networks

It has been recognized that volatility in commodity markets fluctuates significantly depending on the demand–supply relationship and geopolitical risk, and that risk and financial management using multivariate derivatives are becoming more important. This study illustrates an application of multi-layered neural networks for multi-dimensional Bermudan option pricing problems assuming a multi-asset stochastic volatility model in commodity markets. In addition, we aim to identify continuation value functions for these option pricing problems by implementing smooth activation functions in the neural networks and evaluating their accuracy compared with other activation functions or regression techniques. First, we express the underlying asset dynamics using the multi-asset stochastic volatility model with mean reversion properties in the commodity market and formulate the multivariate Bermudan commodity option pricing problem. Subsequently, we apply multi-layer perceptrons in the neural network to represent the continuation value functions of Bermudan commodity options, wherein the entire neural network is trained using the least-squares Monte Carlo simulation method. Finally, we perform numerical experiments and demonstrate that applications of neural networks for Bermudan options in a multi-dimensional commodity market achieve sufficient accuracy with regard to various aspects, including changing the exercise dates, the number of layers/neurons, and the dimension of the problem.

Dynamic initial margin estimation based on quantiles of Johnson distributions

The estimation of dynamic initial margin (DIM) is a challenging problem. We describe an accurate new approach using Johnson-type distributions, which are fitted to conditional moments, estimated using a least-squares Monte Carlo simulation (the Johnson least-squares Monte Carlo (JLSMC) algorithm). We compare the JLSMC DIM estimates with those computed using an accurate nested Monte Carlo simulation as a benchmark, and with another method that assumes portfolio changes are Gaussian. The comparisons reveal that the JLSMC algorithm is accurate and efficient, producing results that are comparable with nested Monte Carlo with an order of magnitude less computational effort. We provide illustrative examples using the Hull–White and Heston models for different derivatives and portfolios. A further advantage of our new approach is that it relies only on the readily available data that is needed for any exposure or value adjustment calculation.

Analysis and Calculation of Prospective Reserves - Where Payments Depend on the Reserve and a Reserve-Dependent Markov Process

Life insurance companies have a great interest in the calculation of prospective reserve since it is an item on the balance sheet of the company. In this thesis, we de ne the prospective reserve such that we can incorporate reserve-dependent payments and such that company made decisions like investment strategies and costs are allowed to depend on the reserve. We study in depth how to calculate the prospective reserve using both analytical and simulation method. We deduce a partial differential equation for the reserve and introduce the two simulation methods: nested simulation and least-squares Monte Carlo simulation, and investigate how to use these methods to calculate the reserve. Furthermore, we calculate the prospective reserve in various examples to illustrate the methods in practice.

A Real Options Model to Value Offshore Wind Power Project under Market Linkage Mechanism

This study puts forward a real options model and uses it to evaluate the investment value of offshore wind power project under market co-movement effect. The main purpose is to check investment benefit of offshore wind power project, as an investor. Several uncertainties are taken into account, including investment costs, feed-in tariffs, carbon prices and policy subsidy. Moreover, an additional uncertain factor, i.e. the market linkage of investment costs, is considered. As a case study, Jiangsu Xiangshui offshore wind park is used to illustrate the model in scenario analysis. Using a least-squares Monte Carlo simulation method, we obtain that the project value is negative. Therefore investors should abandon or postpone investment until better conditions prevail. Furthermore, this paper shows sensitivity analysis of the impact of uncertain factors on the project value. Especially sensitivity analysis of variable costs, it shows a certain impact on project value in here, which has been ignored in previous real options studies. The research results would be helpful for renewable energy project assessment and the decision-making process associated with it.

Valuation of Guaranteed Unitized Participating Life Insurance under MEGB2 Distribution

Crisis events have significantly changed the view that extreme events in financial markets have negligible probability. Especially in the life insurance market, the price of guaranteed participating life insurance contract will be affected by a change in asset volatility which leads to the fluctuations in embedded option value. Considering the correlation of different asset prices, MEGB2 (multivariate exponential generalized beta of the second kind) distribution is proposed to price guaranteed participating life insurance contract which can effectively describe the dependence structure of assets under some extreme risks. Assuming the returns of two different assets follow the MEGB2 distribution, a multifactor fair valuation pricing model of insurance contract is split into four components: the basic contract, the annual dividend option, the terminal dividend option, and the surrender option. This paper studies the effect of death rate, minimum guaranteed yield rate, annual dividend ratio, terminal dividend ratio, and surrender on the embedded option values and calculates the single premium of the insurance contract under different influence factors. The Least-Squares Monte Carlo simulation method is used to simulate the pricing model. This article makes a comparison in the sensitivity of the pricing parameters under the MEGB2 distribution and Multivariate Normal distribution asset returns. Finally, an optimal hedging strategy is designed to cover the possible risks of the underlying assets, which can effectively hedge the risks of portfolio.

Dynamic Initial Margin Estimation Based on Quantiles of Johnson Distributions

The estimation of dynamic initial margin (DIM) for general portfolios is a challenging problem. The present paper describes an accurate new approach, based on regression, that uses Johnson-type distributions, which are fitted to conditional moments estimated using least-squares Monte Carlo simulation (the JLSMC approach). This approach is compared to DIM estimates computed using nested Monte Carlo as a benchmark. Under a number of test cases, the two approaches are shown to be coherent. Furthermore, we show that estimates of DIM produced under the standard regression approach, which assumes portfolio changes are Gaussian, diverges significantly from the better estimates using the JLSMC and nested Monte Carlo approaches. The standard approach performs particularly poorly if the portfolio changes are far from Gaussian (e.g. for options). To further demonstrate the efficacy of the JLSMC approach we provide illustrative examples using Hull-White and Heston models for different derivatives and portfolios. A further advantage of the new approach is that it only relies on the quantities required for any exposure or XVA calculation.

Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis

This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing. The standard approach in the option pricing literature is to choose the basis arbitrarily. By comparing four different polynomial basis we show that the choice of basis interferes in the option's price. We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis: Power, Laguerre, Legendre and Hermite A. To every American Asian Option priced, three sets of parameters are used in order to evaluate it properly. We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths. In the case of an Amerasian call option, for example, we find that the preferable polynomial basis is Hermite A. For an Amerasian put option, the Power polynomial basis is recommended. Such empirical outcome is theoretically unpredictable, since in principle all basis can be indistinctly used when pricing the derivative. In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters. Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option. Theoretically all basis can be indistinctly used when pricing the derivative. However, our results does not confirm these. We find that when pricing an American Asian put option, Power A is better than the other basis we have studied here whereas when pricing an American Asian call, Hermite A is better.

Oil and Gas Exploration Valuation and the Value of Waiting

The timing flexibility of investments in oil and gas assets can potentially add value. In this article, we examine the value of waiting in exploration projects and propose a real option–based valuation method using least-squares Monte Carlo simulation. We show that the dynamics of the oil and gas prices have a large impact on the value of the option to wait, especially for projects with long lead times and durations. The uncertainty in the forward price curve is modeled using a two-factor stochastic price process. The article also presents the valuation method in the form of MATLAB functions and routines that can be used as an efficient test and analysis platform using the industry-standard input formats.

Cross-hedging minimum return guarantees: Basis and liquidity risks

We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risks. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.

Analyses of retirement benefits with options

This study applies the contingent claim approach to evaluate retirement benefits with the options of choosing the maximum defined benefit and defined contribution pension plans. A least-squares Monte Carlo simulation values complex retirement benefits that feature the properties of multiple variables, early exercise, stochastic interest rates, and several embedded options. Furthermore, this study examines the impacts of different forms of early decrements of the value of retirement benefits with options.

The evaluation of American compound option prices under stochastic volatility and stochastic interest rates

A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate driven by Cox–Ingersoll–Ross processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free-boundary PDE problem, which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the projected successive over-relaxation method.

Sell Spot or Sell Forward? Analysis of Oil-Trading Decisions With the Two-Factor Price Model and Simulation

Summary In oil and gas markets, the relationships between the spot and futures prices reveal important opportunities for value creation. When oil prices are in contango (i.e., when futures prices are higher than the expected future spot prices), it may be profitable for a trader to hold oil in storage and enter into a futures contract instead of selling oil in the spot market. The decision to either sell oil in the spot market or use the storage to sell oil in the future is usually challenging because the future spot prices and futures prices are uncertain. In this paper, we discuss the storage trading decisions by use of a realistic example, and we propose an analysis methodology on the basis of a two-factor price process for modeling spot and futures oil prices. The dynamic decision problem, sell spot or sell forward, is analyzed with a forward dynamic optimization algorithm and the least-squares Monte Carlo simulation.

Cross-Hedging Minimum Return Guarantees: Basis and Liquidity Risk

We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risk. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.

Two-Factor Oil-Price Model and Real Option Valuation: An Example of Oilfield Abandonment

We discuss the two-factor oil-price model in valuation and analysis of flexible investment decisions. In particular, we will discuss the real options formulation of a typical oilfield-abandonment problem and will apply the least-squares Monte Carlo (LSM) simulation approach for calculation of project value. In this framework, the two-factor oil-price model will go a long way in the analysis of decisions and value creation. We also propose an implied method for estimation of parameters and state variables of the two-factor price process. The method is based on implied volatility of option on futures, the shape of the forward curve, and the implicit relationship between model parameters.

Valuation of Swing Contracts by Least-Squares Monte Carlo Simulation

Summary Natural gas and electricity are commonly traded through swing contracts that enable the buyer to exploit changes in market price or market demand by varying the quantity they receive from the producer (seller). The producer is assured of selling a minimum quantity at a fixed price, but must be able to meet the variable demand from the buyer. The flexibility of such contracts enables both parties to mitigate the risks and exploit the opportunities that arise from uncertainty in production, demand, price, and so on. But how valuable are they? Traditional net present value (NPV), based on expected values, cannot value this flexibility, and the traditional options/valuation techniques could not model the complexity of the terms of such contracts. Taking gas contracts as an example, this paper seeks to (a) raise awareness of how flexibility creates value for both parties and (b) show how least-squares Monte Carlo (LSM) simulation can be used to quantify its value in dollar terms, from the perspective of both producer and buyer. Because the value of flexibility arises from the ability it gives to respond to fluctuations (e.g., in commodity prices), a useful model of swing contracts needs to reflect the nature of these fluctuations.

Valuing Oil and Gas Options by Least-Squares Monte Carlo Simulation

Summary Least-squares Monte Carlo (LSM) simulation is a promising new technique for valuing real options that has received little or no attention in the oil and gas industry. In this paper, we will demonstrate how LSM simulation can handle more-realistic valuation situations including the ability to (1) handle more-realistic (probabilistic) price models and (2) deal with multiple, possibly correlated, uncertain variables. The LSM method is applied here to an economics problem faced by many operators: What is the value of a gas field given the decision to trade the gas on the spot market as opposed to selling the gas through a long-term supply contract? A company that chooses to trade gas can decide when and how much to produce and can profit from changing market conditions, such as by increasing production during a high-price environment. Three uncertainties have been modeled: the gas price, the operational costs, and the rate of production decline. Increasing profitability associated with rising hydrocarbon prices typically is offset partially by increasing expenditures. Hence, the costs have been correlated with the gas price. The expectation of the remaining reserves is adjusted continuously on the basis of the performance of the field. The latter is simulated by stochastically modeling the rate of production decline. The paper shows that a gas field that can be produced and abandoned at will has a large value of flexibility. The net present value (NPV) of such an asset will underestimate the true economic value. A further benefit of using the real-option-valuation (ROV) approach discussed here is that the valuation procedure produces a strategy map showing actions within the project, not just numbers.