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In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the tail asymptotics for these option types fall into four scenarios.

Exchange traded funds (ETFs) are financial innovations that may be considered as a part of the index financial instruments category, together with stock index derivatives. The aim of this paper is to explore the trajectories and formulates predictions regarding the spread of ETFs on the financial markets in six European countries. It demonstrates ETFs&rsquo, development trajectories with regard to stock index futures and options that may be considered as their substitutes, e.g., in risk management. In this paper, we use mathematical models of the diffusion of innovation that allow unveiling the evolutionary patterns of turnover of ETFs, the time span of the analysis is 2004&ndash, 2015, i.e., the period of dynamic changes on the European ETF markets. Such an approach has so far rarely been applied in this field of research. Our findings indicate that the development of ETF markets has been strongest in Italy and France and weaker in the other countries, especially Poland and Hungary. The results highlight significant differences among European countries and prove that diffusion has not taken place in all the cases, there are also considerable differences in the predicted development paths.

In the first part of the paper, the positive and negative jumps of NASDAQ daily (log-) returns and three of its stocks are estimated based on the methodology presented by Theodosiadou et al. 2016, where jumps are assumed to be hidden random variables. For that reason, the use of stochastic state space models in discrete time is adopted. The daily return is expressed as the difference between the two-sided jumps under noise inclusion, and the recursive Kalman filter algorithm is used in order to estimate them. Since the estimated jumps have to be non-negative, the associated pdf truncation method, according to the non-negativity constraints, is applied. In order to overcome the resulting underestimation of the empirical time series, a scaling procedure follows the stage of truncation. In the second part of the paper, a nonparametric change point analysis concerning the (variance–) covariance is applied to the NASDAQ return time series, as well as to the estimated bivariate jump time series derived after the scaling procedure and to each jump component separately. A similar change point analysis is applied to the three other stocks of the NASDAQ index.

In this paper we introduce an intra-sector dynamic trading strategy that captures mean-reversion opportunities across liquid U.S. stocks. Our strategy combines the Avellaneda and Lee methodology (AL, Quant. Financ. 2010, 10, 761–782) within the Black and Litterman framework (BL, J. Fixed Income, 1991, 1, 7–18, Financ. Anal. J. 1992, 48, 28–43). In particular, we incorporate the s-scores and the conditional mean returns from the Orstein and Ulhembeck (Phys. Rev. 1930, 36, 823–841) process into BL. We find that our combined strategy ALBL has generated a 45% increase in Sharpe Ratio when compared to the uncombined AL strategy over the period from January 2, 2001 to May 27, 2010. These new indices, built to capture dynamic trading strategies, will definitely be an interesting addition to the growing hedge fund index offerings. This paper introduces our first “focused-core” strategy, namely, U.S. Equity Mean-Reversion.

In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors’ equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line.

This paper shows the effects of the COVID-19 pandemic on energy markets. We estimate daily volatilities and correlations among energy commodities relying on a mixed-frequency approach that exploits information from the number of weekly deaths related to COVID-19 in the United States. The mixed-frequency approach takes advantage of the MIxing-Data Sampling (MIDAS) methods. We compare our results to those obtained by employing two well-known models that do not account for the COVID-19 low-frequency variable, namely the Dynamic EquiCorrelation (DECO) and corrected Dynamic Conditional Correlation (cDCC). Moreover, we consider four possible specifications of the volatility: GARCH, GJR, GARCH-MIDAS, and Double-Asymmetric GARCH-MIDAS. The empirical results show that our approach is statistically superior to other models and represents a valuable methodology that can be used for risk managers, investors, and policy makers to assess the effects of the pandemic on spillovers effects in energy markets.

An increasing number of empirical studies have shown a positive relationship between lifetime income and life expectancy at retirement. One’s income during the active part of one’s career translates into the amount of retirement benefits one might receive, leading to actuarial unfairness inside cohorts of retirees. In order to discuss unfairness and sustainability issues, the Belgium pension reform committee issued a proposal for a point system designed to be both sustainable and adequate. In this paper, we use a similar defined benefit framework in order to set out a compensation mechanism linked to life expectancy heterogeneity during the active part of the career, aiming to reduce unfairness once reaching retirement. This method is based on the progressivity of pension benefit formulae. We implement these ideas in a simple demographic context in order to capture the constraints related to the model.

Fraud is one of the most harmful phenomena, because it leads to collapse of organizations, causes economic downfall of countries, and destroys faith in a country’s capital markets. The impact of fraud is complex and has varying degrees depending on political and financial institutional structures of a country. In this paper, we investigate the combined effect of economic and non-economic variables on fraud using a sample of 41 developed, in transition, and developing European countries. The data cover the period July 2014–December 2020. Panel data techniques of pooled estimation and the dynamic panel data/generalized method of moments (DPD/GMM) is used, keeping in view the endogeneity perspective. Nevertheless, two-way impacts of fixed effect model estimation—cross-sectional and time-based (panel) effects (alternatively)—are used for analyzing the relationship among the given variables, based on Hausman specification test results. Empirical results of panel data extended REM and FEM approaches with country-specific cross-sectional effects showing that political stability, economic freedom, poverty, and GDP significantly affect fraud proliferation. Political stability is appraised to be the most scoring determinant of fraud incidence in a country.

This paper examines the relative contribution of regular and e-mini futures market to price discovery of EUR/USD futures contracts on the Chicago Mercantile Exchange (CME), using intraday data in 2010.The relative contribution to price discovery is estimated using the information share approach proposed by Hasbrouck and Gonzalo-Granger. Empirical findings indicate that regular futures market contributes significantly to the price discovery, accounting for approximately 66.5% of price discovery in the EURO/USD market. This study also examines if the regular future’s information share (IS) can be explained by the positioning of commercial and non-commercial traders. We find a positive significant relationship between IS and both the speculative trade position and hedgers trade position. The results support the conclusion that the IS of regular futures can be better explained by speculators than hedgers.

Legislation imposes insurance companies to project their assets and liabilities in various financial scenarios. Within the setup of with-profit life insurance, we consider retrospective reserves and bonus, and we study projection of balances with and without policyholder behavior. The projection resides in a system of differential equations of the savings account and the surplus, and the policyholder behavior options surrender and conversion to free-policy are included. The inclusion results in a structure where the system of differential equations of the savings account and the surplus is non-trivial. We consider a case where we are able to find accurate differential equations and suggest an approximation method to project the savings account and the surplus, including policyholder behavior, in general. To highlight the practical applications of the results in this paper, we study a numerical example.

With the emergence of global digital service providers, concerns about digital oligopolies have increased, with a wide range of potentially harmful effects being discussed. One of these relates to cyber security, where it has been argued that market concentration can increase cyber risk. Such a state of affairs could have dire consequences for insurers and reinsurers, who underwrite cyber risk and are already very concerned about accumulation risk. Against this background, the paper develops some theory about how convex cyber risk affects Cournot oligopoly markets of data storage. It is demonstrated that with constant or increasing marginal production cost, the addition of increasing marginal cyber risk cost decreases the differences between the optimal numbers of records stored by the oligopolists, in effect offsetting the advantage of lower marginal production cost. Furthermore, based on the empirical literature on data breach cost, two possibilities are found: (i) that such cyber risk exhibits decreasing marginal cost in the number of records stored and (ii) the opposite possibility that such cyber risk instead exhibits increasing marginal cost in the number of records stored. The article is concluded with a discussion of the findings and some directions for future research.

This paper follows the recent literature on real estate price prediction and proposes to take advantage of machine learning techniques to better explain which variables are more important in describing the real estate market evolution. We apply the random forest algorithm on London real estate data and analyze the local variables that influence the interaction between housing demand, supply and price. The variables choice is based on an urban point of view, where the main force driving the market is the interaction between local factors like population growth, net migration, new buildings and net supply.

This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options.

This paper investigates dynamic correlations of stock&ndash, bond returns for different stock indices and bond maturities. Evidence in the US shows that stock&ndash, bond relations are time-varying and display a negative trend. The stock&ndash, bond correlations are negatively correlated with implied volatilities in stock and bond markets. Tests show that stock&ndash, bond relations are positively correlated with economic policy uncertainty, however, are negatively correlated with the monetary policy and fiscal policy uncertainties. Correlation coefficients between stock and bond returns are positively related to total policy uncertainty for returns of the Dow-Jones Industrial Average (DJIA) and the S&amp, P 500 Value stock index (VALUE), but negatively correlated with returns of S&amp, P500 (Total market), the NASDAQ Composite Index (NASDAQ), and the RUSSELL 2000 (RUSSELL).

The paper presents an alternative approach to measuring systemic illiquidity applicable to countries with frontier and emerging financial markets, where other existing methods are not applicable. We develop a novel Systemic Illiquidity Noise (SIN)-based measure, using the Nelson–Siegel–Svensson methodology in which we utilize the curve-fitting error as an indicator of financial system illiquidity. We empirically apply our method to a set of 10 divergent Central and Eastern Europe countries—Bulgaria, Croatia, Czechia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, and Slovakia—in the period of 2006–2020. The results show three periods of increased risk in the sample period: the global financial crisis, the European public debt crisis, and the COVID-19 pandemic. They also allow us to identify three divergent sets of countries with different systemic liquidity risk characteristics. The analysis also illustrates the impact of the introduction of the euro on systemic illiquidity risk. The proposed methodology may be of consequence for financial system regulators and macroprudential bodies: it allows for contemporaneous monitoring of discussed risk at a minimal cost using well-known models and easily accessible data.

This paper investigates option valuation when the underlying market suffers from illiquidity of price impact. Using option data, I infer trading activities and price impacts on the buy side and the sell side in the stock market from option prices across maturities. The finding displays that the stock market is active when the stock prices plummet, but becomes silent after the market crashes. In addition, the difference of option implied price impacts between the buy side and the sell side, which indicates asymmetric liquidity, increases with the time to maturity, especially on the day of the market crisis. Moreover, investors have different perspectives on the future liquidity after liquidity shocks when they are in a bull market or in a bear market according to the option implied price impact (or market depth) curves. I also calibrate three market indices simultaneously and reach the same conclusion that the three markets become erratic on the event date and calm down in the aftermath.

In this paper, the generalized Pareto distribution (GPD) copula approach is utilized to solve the conditional value-at-risk (CVaR) portfolio problem. Particularly, this approach used (i) copula to model the complete linear and non-linear correlation dependence structure, (ii) Pareto tails to capture the estimates of the parametric Pareto lower tail, the non-parametric kernel-smoothed interior and the parametric Pareto upper tail and (iii) Value-at-Risk (VaR) to quantify risk measure. The simulated sample covers the G7, BRICS (association of Brazil, Russia, India, China and South Africa) and 14 popular emerging stock-market returns for the period between 1997 and 2018. Our results suggest that the efficient frontier with the minimizing CVaR measure and simulated copula returns combined outperforms the risk/return of domestic portfolios, such as the US stock market. This result improves international diversification at the global level. We also show that the Gaussian and t-copula simulated returns give very similar but not identical results. Furthermore, the copula simulation provides more accurate market-risk estimates than historical simulation. Finally, the results support the notion that G7 countries can provide an important opportunity for diversification. These results are important to investors and policymakers.

The aim of this paper is to present life expectancy of both genders depending on their income and to determine the impact of a possible regularity on the state pension policy. The study was based on the income of pensioners in Poland (over 5 million people receiving old-age pension). The results obtained made it possible to formulate several important conclusions: the rich live longer, the impact of income on life expectancy is much stronger among men than women, and with age, income has less and less impact on life expectancy. Consequently, in the capital model that is in force in Poland, the state should take this fact into account in its pension policy when calculating the amount of the benefit.

Low saving rates combined with low effective retirement age herald old-age poverty. This paper examines the preferred strategies of future Polish pensioners in order to sustain the standard of living in the future. A two-step approach is used: as a first-best strategy, we explore determinants of supplementary saving with binary logistic models, as a second-best strategy, we examine alternative options with principal component analysis. Future retirees rarely accumulate long-term savings, do not use dedicated instruments, and they start to save additionally far too late. Savings are concentrated in wealthier and better educated groups. Such myopia is governed by their political stance and not by awareness of dire prospects. Second-best strategies are based on optimistic assumptions about future health (seeking for additional jobs), on the assumed generosity of acquaintances or social institutions (relying on external assistance), or on rebelling. Given the increasing political power of elder generations, balancing the interests of workers and retirees will be an increasingly difficult task for policy makers.

This paper models the gradual elements of catastrophic events on non-life insurance capital with a particular focus on the impact of pandemics, such as COVID-19. A combination of actuarial and epidemiological models are handled by the Markovian probabilistic approach, with Feynman&rsquo, s path calculation and Dirac notations, in order to observe how a pandemic risk may affect an insurer via reduced business. We also examine how the effects of a pandemic can be taken into account both during and at the end of the process. Examples are also provided showing the potential effects of a pandemic on different types of insurance product.

This paper focuses on weather derivatives as efficient risk management instruments and proposes a more advanced approach for their pricing. An &ldquo, hybrid&rdquo, contract is introduced, combining insurance properties, specifically tailored for the region under study and introducing Value-at-Risk (VaR) and Expected Shortfall (ES) as appropriate measures for the strike price. The numerical results show that VaR and ES are both efficient ways for managing the so-called Tail Risk, further, being ES more conservative than VaR and due to its subadditivity property, it can be seen that seasonal contracts are generally better off than monthly contracts in reducing global risk.

This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of volatile or turbulent regimes. We show that, in the case of the S&P 500 index, the returns from the Volatility Index (VIX) index are significant for both the volatile and the turbulent regimes, while the gold, WTI oil, and the dollar indices have some explanatory power only for the turbulent regime.

This paper examines the joint movement and tail dependence structure between the pair of foreign exchange rates (EUR, USD and GBP) against the GHS, using daily exchange rates data expressed in GHS per unit of foreign currencies (EUR, USD and GBP) between the time range of 24 February 2009 and 19 December 2019. We use different sets of both static (time-invariant) and time-varying copulas with different levels of dependence and tail dependence measures, and the study results reveal positive dependence between all exchange rates pairs, though the dependencies for EUR-USD and GBP-USD pairs are not as strong as the EUR-GBP pair. The findings also reveal symmetric tail dependence, and dependence evolves over time. Notwithstanding this, the asymmetric tail dependence copulas provide evidence of upper tail dependence. We compare the copula results to DCC(1,1)-GARCH(1,1) model result and find the copula to be more sensitive to extreme co-movement between the currency pairs. The afore-mentioned findings, therefore, offer forex market players the opportunity to relax in hoarding a particular foreign currency in anticipation of domestic currency depreciation.

The authors wish to make the following corrections to this paper (Ye and Bellotti 2019): [...]

The aim of this paper is to analyze the relation between maturity structure, sovereign bond yields and sovereign risk in the Economic and Monetary Union for the period of 1990&ndash, 2013. The results confirm the existence of an inverse relationship between sovereign bond yields, sovereign risk and the maturity structure of sovereign debt, regardless of the proxy that is used to measure sovereign risk and the time variance of the variables employed. The results indicate that risk shortens the maturity structure of sovereign debt because it reduces the stock of long-term debt. The relationship between maturity structure and sovereign bond yields differs depending on the risk of the countries analyzed (non-monotonic relationship) and the differences between peripheral and core countries are greater for higher levels of the yields. If we control for the indebtedness level of these countries, the results show that the relationship between the sovereign bond yields and maturity strengthens as the debt level increases.

In this paper, we study a stochastic control problem faced by an insurance company allowed to pay out dividends and make capital injections. As in (L&oslash, kka and Zervos (2008), Lindensj&ouml, and Lindskog (2019)), for a Brownian motion risk process, and in Zhu and Yang (2016), for diffusion processes, we will show that the so-called L&oslash, kka&ndash, Zervos alternative also holds true in the case of a Cram&eacute, r&ndash, Lundberg risk process with exponential claims. More specifically, we show that: if the cost of capital injections is low, then according to a double-barrier strategy, it is optimal to pay dividends and inject capital, meaning ruin never occurs, and if the cost of capital injections is high, then according to a single-barrier strategy, it is optimal to pay dividends and never inject capital, meaning ruin occurs at the first passage below zero.

The paper analyzes the relationship between the credit default swaps (CDS) spreads for 5-year CDS in Europe and US, and fundamental macroeconomic variables such as regional stock indices, oil prices, gold prices, and interest rates. The dataset includes consideration of multiple industry sectors in both economies, and it is split in two sections, before and after the global financial crisis. The analysis is carried out using multivariate regression of each index vs. the macroeconomic variables, and a Granger causality test. Both approaches are performed on the change of value of the variables involved. Results show that equity markets lead in price discovery, bidirectional causality between interest rate, and CDS spreads for most sectors involved. There is also bidirectional causality between stock and oil returns to CDS spreads.

The direction of price movements are analysed under an ordered probit framework, recognising the importance of accounting for discreteness in price changes. By extending the work of Hausman et al. (1972) and Yang and Parwada (2012),This paper focuses on improving the forecast performance of the model while infusing a more practical perspective by enhancing flexibility. This is achieved by extending the existing framework to generate short term multi period ahead forecasts for better decision making, whilst considering the serial dependence structure. This approach enhances the flexibility and adaptability of the model to future price changes, particularly targeting risk minimisation. Empirical evidence is provided, based on seven stocks listed on the Australian Securities Exchange (ASX). The prediction success varies between 78 and 91 per cent for in-sample and out-of-sample forecasts for both the short term and long term.

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer's payments to its policyholders and shareholders, respectively. To this end, we introduce a Gerber-Shiu-type function, which further incorporates the higher moments of these two quantities. This not only unifies the individual study of various ruin-related quantities, but also allows for new measures concerning covariances to be calculated. The integro-differential equation satisfied by the generalized Gerber-Shiu function and the boundary condition are derived. In particular, when the claim severity is distributed as a combination of exponentials, explicit expressions for this Gerber-Shiu function in some special cases are given. Numerical examples involving the covariances between any two of (i) the aggregate discounted claims until ruin, (ii) the discounted dividend payments until ruin and (iii) the time of ruin are presented along with some interpretations.

In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath-Jarrow-Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

Life insurers are exposed to deflation risk: falling prices could lead to insufficient investment returns, and inflation-indexed protections could make insurers vulnerable to deflation. In this spirit, this paper proposes a market-based methodology for measuring deflation risk based on a discrete framework: the latter accounts for the real interest rate, the inflation index level, its conditional variance, and the expected inflation rate. US inflation data are then used to estimate the model and show the importance of deflation risk. Specifically, the distribution of a fictitious life insurer’s future payments is investigated. We find that the proposed inflation model yields higher risk measures than the ones obtained using competing models, stressing the need for dynamic and market-consistent inflation modelling in the life insurance industry.

Annuities providers become more and more exposed to longevity risk due to the increase in life expectancy. To hedge this risk, new longevity derivatives have been proposed (longevity bonds, q-forwards, S-swaps&hellip, ). Although academic researchers, policy makers and practitioners have talked about it for years, longevity-linked securities are not widely traded in financial markets, due in particular to the pricing difficulty. In this paper, we compare different existing pricing methods and propose a Cost of Capital approach. Our method is designed to be more consistent with Solvency II requirement (longevity risk assessment is based on a one year time horizon). The price of longevity risk is determined for a S-forward and a S-swap but can be used to price other longevity-linked securities. We also compare this Cost of capital method with some classical pricing approaches. The Hull and White and CIR extended models are used to represent the evolution of mortality over time. We use data for Belgian population to derive prices for the proposed longevity linked securities based on the different methods.

In this paper we introduce a new coherent cumulative risk measure on a subclass in the space of cadlag processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Levy process. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed.

We present a stochastic simulation forecasting model for stress testing that is aimed at assessing banks’ capital adequacy, financial fragility, and probability of default. The paper provides a theoretical presentation of the methodology and the essential features of the forecasting model on which it is based. Also, for illustrative purposes and to show in practical terms how to apply the methodology and the types of outcomes and analysis that can be obtained, we report the results of an empirical application of the methodology proposed to the Global Systemically Important Banks (G-SIB) banks. The results of the stress test exercise are compared with the results of the supervisory stress tests performed in 2014 by the Federal Reserve and EBA/ECB.

In this paper, we analyse and construct a lifetime utility maximisation model with hyperbolic discounting. Within the model, a number of assumptions are made: complete markets, actuarially fair life insurance/annuity is available, and investors have time-dependent preferences. Time dependent preferences are in contrast to the usual case of constant preferences (exponential discounting). We find: (1) investors (realistically) demand more life insurance after retirement (in contrast to the standard model, which showed strong demand for life annuities), and annuities are rarely purchased; (2) optimal consumption paths exhibit a humped shape (which is usually only found in incomplete markets under the assumptions of the standard model).

Energy commodities and their futures naturally show cointegrated price movements. However, there is empirical evidence that the prices of futures with different maturities might have, e.g., different jump behaviours in different market situations. Observing commodity futures over time, there is also evidence for different states of the underlying volatility of the futures. In this paper, we therefore allow for cointegration of the term structure within a multi-factor model, which includes seasonality, as well as joint and individual jumps in the price processes of futures with different maturities. The seasonality in this model is realized via a deterministic function, and the jumps are represented with thinned-out compound Poisson processes. The model also includes a regime-switching approach that is modelled through a Markov chain and extends the class of geometric models. We show how the model can be calibrated to empirical data and give some practical applications.

This paper proposes a model-free approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies with a wide family of risk measures and pricing rules, and study the conditions under which the hedging problem admits a solution and pricing is possible. The practical implications of our proposed theoretical approach are illustrated with an application on hedging economic risk.

Much of the debate around a potential British exit (Brexit) from the European Union has centred on the potential macroeconomic impact. In this paper, we instead focus on understanding market expectations for price action around the Brexit referendum date. Extracting implied distributions from the GBPUSD option volatility surface, we originally estimated, based on our visual observation of implied probability densities available up to 13 June 2016, that the market expected that a vote to leave could result in a move in the GBPUSD exchange rate from 1.4390 (spot reference on 10 June 2016) down to a range in 1.10 to 1.30, i.e., a 10-25% decline-very probably with highly volatile price action. To quantify this more objectively, we construct a mixture model corresponding to two scenarios for the GBPUSD exchange rate after the referendum vote, one scenario for 'remain' and one for 'leave'. Calibrating this model to four months of market data, from 24 February to 22 June 2016, we find that a 'leave' vote was associated with a predicted devaluation of the British pound to approximately 1.37 USD per GBP, a 4.5% devaluation, and quite consistent with the observed post-referendum exchange rate move down from 1.4877 to 1.3622. We contrast the behaviour of the GBPUSD option market in the run-up to the Brexit vote with that during the 2014 Scottish Independence referendum, finding the potential impact of Brexit to be considerably higher.

Building a social security system to ensure Singapore residents have peace of mind in funding for retirement has been at the top of Singapore government's policy agenda over the last decade. Implementation of the Lifelong Income For the Elderly (LIFE) scheme in 2009 clearly shows that the government spares no effort in improving its pension scheme to boost its residents' income after retirement. Despite the recent modifications to the LIFE scheme, Singapore residents must still choose between two plans: the Standard and Basic plans. To enhance the flexibility of the LIFE scheme with further streamlining of its fund management, we propose some plan modifications such that scheme members do not face a dichotomy of plan choices. Instead, they select two age parameters: the Payout Age and the Life-annuity Age. This paper discusses the actuarial analysis for determining members' payouts and bequests based on the proposed age parameters. We analyze the net cash receipts and Internal Rate of Return (IRR) for various plan-parameter configurations. This information helps members make their plan choices. To address cost-of-living increases we propose to extend the plan to accommodate an annual step-up of monthly payouts. By deferring the Payout Age from 65 to 68, members can enjoy an annual increase of about 2% of the payouts for the same first-year monthly benefits.

Designing post retirement benefits requires access to appropriate investment instruments to manage the interest rate and longevity risks. Post retirement benefits are increasingly taken as a form of income benefit, either as a pension or an annuity. Pension funds and life insurers offer annuities generating long term liabilities linked to longevity. Risk management of life annuity portfolios for interest rate risks is well developed but the incorporation of longevity risk has received limited attention. We develop an immunization approach and a delta-gamma based hedging approach to manage the risks of adverse portfolio surplus using stochastic models for mortality and interest rates. We compare and assess the immunization and hedge effectiveness of fixed-income coupon bonds, annuity bonds, as well as longevity bonds, using simulations of the portfolio surplus for an annuity portfolio and a range of risk measures including value-at-risk. We show how fixed-income annuity bonds can more effectively match cash flows and provide additional hedge effectiveness over coupon bonds. Longevity bonds, including deferred longevity bonds, reduce risk significantly compared to coupon and annuity bonds, reflecting the long duration of the typical life annuity and the exposure to longevity risk. Longevity bonds are shown to be effective in immunizing surplus over short and long horizons. Delta gamma hedging is generally only effective over short horizons. The results of the paper have implications for how providers of post retirement income benefit streams can manage risks in demanding conditions where innovation in investment markets can support new products and increase the product range.

Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities with guaranteed minimum repayments at maturity and in case of the insured’s death. If the contract is prematurely surrendered, the policyholder is entitled to the current value of the fund account reduced by the prevailing surrender fee. The financial market and the mortality model are affine linear. For the surrender model, a Cox process is deployed whose intensity is given by a deterministic function (s-curve) with stochastic inputs from the financial market. So, the policyholders’ surrender behavior depends on the performance of the financial market and is stochastic. The presented pricing scheme incorporates the stochastic surrender behavior of the policyholders and is only based on suitable closed-form approximations.

Because of the profitable nature of risk businesses in the long term, de Finetti suggested that surplus models should allow for cash leakages, as otherwise the surplus would unrealistically grow (on average) to infinity. These leakages were interpreted as 'dividends'. Subsequent literature on actuarial surplus models with dividend distribution has mainly focussed on dividend strategies that either maximise the expected present value of dividends until ruin or lead to a probability of ruin that is less than one (see Albrecher and Thonhauser, Avanzi for reviews). An increasing number of papers are directly interested in modelling dividend policies that are consistent with actual practice in financial markets. In this short note, we review the corporate finance literature with the specific aim of fleshing out properties that dividend strategies should ideally satisfy, if one wants to model behaviour that is consistent with practice.