The use of economic scenarios generators in unstable economic periods

In the current politico-economic context made unstable by the coming up of several different conflicts, it is interesting to deal with the use and the development of models. Indeed, it is necessary to pay special attention to projections obtained with current models because parameters are often estimated with data which no longer reflect the economic context they have to describe. Moreover, a model is valid in a precise frame and for a given time horizon: universal models do not exist. It is necessary to keep in mind that a model, by definition, allows to produce simplified representations of unpredictable and very complex systems. That is why, the model presented in this paper is not meant to be adapted to all situations: for instance, the model is not adapted to a day to day dynamic management in a stable economic situation. This study deals with the development of economic scenarios generators (ESG) and their use in asset management. We propose a tool or more globally a process allowing to take into account, during the optimization of an equity portfolio, the drastic increase of the major crises probability faced since the beginning of the 21st century. At first, we present a brief analysis describing the world politico-economic context. Besides, we give some fundamental principles to be adopted to build or use an ESG. Then, we present the basic ESG structure retained and the method chosen to integrate external elements stemming from a fundamental market analysis. Finally, we present a simple illustration among a large number of possible applications: the optimization of an equity portfolio by following the created process. The use of economic scenarios generators in unstable economic periods By Hervé Fraysse January 2015 N°31 Texts appearing in SCOR Papers are the responsibility of their authors alone. In publishing such articles, SCOR takes no position on the opinions expressed by the authors in their texts and disclaims all responsibility for any opinions, incorrect information or legal errors found therein. Winner of the French Actuarial Prize, 2013 Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background 1 Unstable economic context and combined approaches 1.1 A drastic increase of major crises risks In the French actuarial magazine L’actuariel nb.6, Jean-Paul Delevoye said th t Future is not the projection f past anymore, but the calling into question of the latt . This thinking illus rates t e breaking noticed since the beginning of the 21st century with the apparition of several crises (financial, geopolitical. . . ) at a high and unprecedented frequency. Below, we propose a brief review of the major crises having occurred since the beginning of the century. They will be classified according to their natures: • Financial crises: they provoke a strong volatility on markets and participate in the collapse of stock exchanges. Firstly, let us remind the three speculative bubbles bursting: the technology stocks bubble in 2000 following the development of the Internet; and the real estate bubble and the credit one coming from the United States in 2007. Secondly, let us remind the crisis of the sovereign debts and the European crisis which have disturbed financial markets since 2010. • Military conflicts, persistent or starting, national or international: these conflicts unsettle the world stability and badly affect the investor’s confidence. Some most known examples are: the Israeli-Palestinian conflict, wars in Iraq and Afghanistan, the Arab Spring riots in 2010, the revolts in Senegal as well as in Syria. . . The movements of revolt in Russia and the economic situation of China also participate in this instability. We would lik to underline an element on this last point: an analysis of the budget of China shows that this country plans an important annual increase of its defence budget until 2015 to reach a 240 billion dollar total budget. This i f ur times more than the defence budget of Japan (which is the second one in Asia). This element tends to prove that the Asian situation is not peaceful. Is it a cold war with important economic consequences? We can also add crisis scenarios which can burst out because of the unbalanced economic situation existing between BRIC and developing countries, for two main reasons: • There is no reason so that the Chinese GDP per capita stays lower than the Japanese’s one. This implies a fourfold increase of the Chinese GDP in the next years. • Because of BRIC, Europe is inevitably going to continue to lose mark t s ares for the benefit of emerging countries and to pursue its process of deind strializat on. Consequently, adaptation crises will be inevitable. That is why multiple and varied scenarios are to be taken into account. Olivier Blanchard, head economist of the International Monetary Fund and Christine Lagarde’s adviser even evoked the possibility of a big depression. To conclude, we would like to mention an economic argument corroborating the fact that crises are to be planned. The demographic power of the Asian countries creates a modification of the world economy evolution and disturbs several economic theories such as the Kondratieff one: according to this theory, the economy follows a long cycle of about fifty six years including five seasons: SCOR Paper no31 ESGs in unstable economic periods 2 Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background • Spring: inflationary boom and bullish cycle of quantities. • Summer: cruising speed, the economy goes well. • Stagflation: decreasing growth and hyperinflation. • Indian summer: period of artificial prosperity ideal for speculative bubble creation ending by a crash. • Depression: decrease of assets prices and solvency problems. According to Francois-Xavier Chevalier’s study [4], we should be at the beginning of a long cycle but yet the growth decreases. . . This implies that several long-term scenarios are possible. This brief study of the politico-economic situation shows that it is essential to adapt the traditional asset management by giving priority to careful management focusing on the research of values which fall less than the others in crises period, the resilient values. 1.2 Asset management in crises period One of the objectives of this paper is to describe a tool adapted to asset management in crises period. That is why it is necessary to define some fundamental principles. There were established from an a posteriori crises study allowing to understand some manager’s irrational behavior and to avoid some stumbling. First of all, we would like to quote this sentence stemming from the book of Arnaud ClémentGrandcourt [3], economist specialist of the crises periods management: anticipating a crisis is really difficult and it is very dangerous to delude o eself about the subject. This idea perfectly introduces the two main qualities of a good crisis manager : cautiousness and modesty. The study of crises leads us to define what is a careful asset manager : it is a manager who limits the number and the importance of his errors by taking measured risks and by taking into account all the important parameters to make decisions; moreover it is a person who does not overestimate his capacity of forecasting and understanding the events. To bring a real surplus value, the manager has to realize accurate market analysis and has to invest in r silient values, while k eping in mind that being careful sometimes requires being offensive: a good offense is sometimes prudent. To reach an effective assets allocation, this paper proposes: • The use of an economic scenarios generator allowing to take into account several crises scenarios, • The consideration of leading economic indicators which help to give probability to each central scenario. Before describing the economic scenario generator created, we would like to say some words about the use of models and to specify the favorite approaches to be adopted in crises periods, the combined approaches. 3 SCOR Paper no31 ESGs in unstable economic periods Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background 1.3 Combined approaches At present, it seems coherent to believe that the evolution of past risks does not augur the evolution of the 21st century risks anymore. That is why, it is necessary to use exogenous information in addition to historical data to get reliable projections. The main part of actual quantitative market models are only calibrat with past data and do not integrate the increase of the crises probability noticed since the beginning of the 21st century. Consequently, these models do not seem adapted to the current economic environment. Besides, some approaches consist in selecting values by a fundamental study only. This sort of study do not allow an optimal assets allocation for several reasons: • They are relatively subjective: the manager establishes his own vision of several firms which can be very different from an other manager’s one. • It is not possible to realize a specific analysis for many companies because it is time consuming. Consequently, it is possible to miss performing stocks. The remarks formulated above explain the reasons why it is advisable to set up mixed approaches. This paper proposes a combined approach adapted to the management of a shares fund: • Quantitative Part: realization of projections by the use of an economic scenarios generator and definition of utility function allowing the interpretation of the projections. • Qualitative Part: definition of central scenarios integrated during the realization of the projections through a jumps function. These scenarios must be determined before hand. SCOR Paper no31 ESGs in unstable economic periods 4 Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background 2 The economic scenarios generator retained Economic scenarios generators (ESG) have several advantages, particularly in period of crises: • They facilitate the decision-making by giving additional indicators. • They do not suffer from the lack of rationality. • They are tools allowing to make decisions based on the past and the future. In the following paragraphs, we justify the choice of the Wilkie’s generator structure and we describe the modifications we brought to adapt the model to the current economic context. 2.1 The Wilkie’s ESG, an efficient and simple cascading struct re The aim of this paper is not to draw a panorama of all the existing ESG. However, we would lik to briefly remind the two possible ESG structures: • Cascading structure: definition of a central value allowing to find the whole state of the market. For instance, as far as the Wilkie’s model is concerned, the inflation is the central value. • Correlation structure: based on the idea of allowing the available data (historical data) to determine a simultaneous correlation structure between variables and then to model and calibrate them according to this structure. The choice of the Wilkie’s ESG structure (1985) [1] results from several elements: • In crises periods, it is better to choose cascading structures because th y re more stable than the correlation ones. Besides, a major advantage of these structures is that they are more flexible: it is possible to adapt the ESG while keeping the same structure. • Simple to use: the equations of the model are simple no mathematical complexity. • This ESG have fewer parameters than the Wilkie’s 1995 one [2]: a retrospective study was realized on the Wilkie’s model to test its robustness. It concluded that the Wilkie’s is more successful in its first version (1985) than in its second (1995). • This ESG is a good balance between statistical complexity and speed of simulation. Let us remind that the complexity of the statistical extensions improves the adequacy to the past without improving inevitably the quality of the forecast. • Allowing projections over 1 or 5 years. 5 SCOR Paper no31 ESGs in unstable economic periods Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background The scheme below illustrates the ESG structure: Figure 1: Wilkie’s model (1985) 2.2 Critics of Wilkie’s model The plentiful literature on this model allows avoiding some stumbling blocks and enables this model to evolve. The critics essentially concern the specification and the quality of the model adequacy. We shall limit us to remind the main problems, the reader can find precise details in [5]. Several English actuaries strongly criticized the model: in particular Kitts (1990), Huber (1995) and Geoghegan and al. (1992). The critics mainly concerned two elements: • The model specification and the initial parameters dependency: Huber (1995) has underlined that the over parametrization of the model implies a strong dependency of the results on the initial parameters. The equations, containing a mean verting process, and the choice of the mean condition the future results and the projectio s. Consequently, specifications choic s must be made with caution. • The biases linked to the estimation: Kitts (1990) ha shown that the series of inflation, initially used by Wilkie, is not a stationary one. Therefore, he has criticized the modeling of the inflation by an auto-regressive one order process. Geoghegan and al. (1992) have demonstrated that the model residuals do not respect the normality, independence and constant variance hypotheses. The residuals distribution is asymmetric and leptokurtic and residuals have strong volatility periods alternating with low volatility ones. Finally, Huber (1995) has proved that the Wilkie’s model is biased by some data corresponding in the years of strong inflationary shocks in Great Britain (on 1920, 1940 and 1974). If these years are excluded from the regression, the correlation coefficient between dividend yields and inflation is not significant anymore. There are also theoretical critics again Wilkie’s model. Indeed, two central economic theory assumptions are not respected: the financial markets efficiency and the absence of arbitrage opportunity. However, it turns out that these two critics are challenged in crisis period and that most of SCOR Paper no31 ESGs in unstable economic periods 6 Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background the asset management models do not respect these two principles. The improvements brought to the initial ESG are described in the following paragraph. Some of them consist in an wering the various critics presented above. 2.3 Adjustments on Wilkie’s model To create an ESG adapted to t e current context, several modifications have been brought t the basic Wilkie’ structure: • Modification of data, • Modification of the modeling of inflation, • Modification of the residuals distribution, • Integration of a jumps function. The fourth element being an important point of this paper, we shall dedicate it the third paragraph. 2.3.1 Modification of used data To take into account Kitts’s critics and to obtain parameters reflecting the current economic context, monthly data over the period [2000; 2011] are considered. This peri d se ms appropriate o take into account the politico-economic context changes that was discussed in the first paragraph. Besides, aving defined this period, the consideration of annual or quarterly data would not be appropriate to obtain reliable modeling. To illustrate our work, calculations were realized for three countries: France, Germany and the United States. 2.3.2 Modification of the modeling of inflation In a first approach, we have considered the inflation over a large period, including oil crises, the world wars... We quickly realized that modeling such a series by an auto-regressive order one process was not adapted. Furthermore, a brief study led to the choice to consider the core inflation because during the last ten years, the prices of foodstuffs and oil price were very volatile. Then, a temporal series study for every country, by following the Box and Jenkins algorithm and by considering all the SARIMA processes, allows to get stationary series and to identify the optimal number of delays to be considered. The ACF and PACF let appear an annual seasonality, validated by the plot of Fourier’s spectrogram. 7 SCOR Paper no31 ESGs in unstable economic periods Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background Figure 2: ACF-PACF Inflation France From a macroeconomic point of view, it is clear that the inflation ind x is sensitive to the seasonality. Indeed, prices undergo different season variations: in December for example, Christmas has a cyclical effect on prices. Finally, the modeling retained to model the inflation is the following seasonal auto-regressive integrated moving average process: SARIMA(1,1,1)(0,0,1)12. To validate the use of this modeling, we have to make sure that the obtained residuals are white noises with the Breusch-Godfrey’s test: the latter concludes the rejection of the normality hypothesis. To r solve this problem, it is possible to model the residuals volatility by a GARCH process: Wilkie proposed this modeling in the 1995 version. Studies proved that the use of this method was less effective than the initial one. In this paper, we propose to model the residuals by a Pareto Hybride distribution introduced in [6] as we developed in the following paragraphs. 2.3.3 Modification of the residuals distribution To reach a statistically coherent model, it is interesting to look for distribution, easily implementable, and allowing to adapt itself better to the residuals of the equations. In our study, we have chosen to model residuals by an hybrid Pareto distribution. This distribution is built in the following way: the center is modeled by a normal law and the distribution tails by a generalized Pareto distribution. By fixing continuity, differentiability and density conditions, a statistical law depending on four parameters (average, variance and parameters of tail) is obtained. Schematically, below the density of an hybrid Pareto distribution: SCOR Paper no31 ESGs in unstable economic periods 8 Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background Figure 3: Hybrid-Pareto distribution It is possible to adjust an hybrid Pareto distribution to a set of data by applying classical methods such as the moments method or the maximum likelihood. Other more specific methods exist as the Zhang’s estimator. The reader will find more precise information on various methods of adjustment by consulting [6]. The modeling by an hybrid Pareto distribution is effective mainly in period of crises. Indeed, for these periods, the normal law leads to an under-estimate of extreme values. 9 SCOR Paper no31 ESGs in unstable economic periods Fair Valuation of risks Under Solvency II, the Market Value Margin (MVM) is meant to bring technical provisions to a fair value, and is to be computed using the Cost of Capital approach. In the background lies the Market Consistent economic balance sheet which reflects what Solvency II seeks to achieve: a fair valuation of risks. Limiting ourselves to the reserve risk only – as will be done in the rest of this note – the following graph shows that the Capital should be sufficient to restore the balance sheet to a fair value of liabilities after a 1 in 200 event: 2 For Solvency II, the Solvency Capital Requirement (SCR) is meant to cover one year of deterioration, meaning that only “shocks” applied to the following year are considered. The graph depicts, on the liability side of the economic balance sheet, how the capital funded at time t=0 is adequate to restore the balance sheet to a fair value of liabilities at the end of a distressed first year, where both the Best Estimate of Liabilities (BEL) and the MVM are subject to a distressed scenario. Cost of Capital approach The CoC approach takes the perspective that sufficient capital is needed to be able to run-off the business. Here, the risk margin is estimated by the present value of the expected cost of current and future SCRs for non-hedgeable risks to support the complete run-off of all liabilities. Schematically, the MVM calculation can be carried out in 4 steps: First, project the expected SCR until all liabilities run-off. This puts into the equations the fact that an undertaking taking over the portfolio has to put up future regulatory capital SCR(1), SCR(2), ... , SCR(n‐1) until the portfolio has run-off completely at time t=n; Second, multiply all current and future SCR by the Cost of Capital rate (c or CoC). This captures the fact that the insurer selling the portfolio has to compensate the insurer taking over the portfolio for immobilizing future capital requirements; Third, discount everything to time 0; The sum then gives the CoC risk margin. SCOR Paper n°18 Calculations under the SII CoC approach 1. Background 3 Integrate exogenous elements into the ESG structure The aim of this paper is to be adapted to the current economic context. Naturally, the modified Wilkie’s ESG presented in the previous paragraph is not reasonable and it is advisable to add a jumps function allowing to integrate crises scenarios duri g the pr jections. At first, a study to compar the perform nce of various leading indicators and to select one is realized. It is based on [10] and [11]. These indicators turn out to be a precious tool on whom the assets managers can lean to realize the scenarios. Secondly, various methods allowing to integrate jumps re pr ented and the c oice of one of them justified. 3.1 Composite leading indicators The composite leading indicators are descriptive chronological series which provide early signals of turning points (peaks and troughs) between economic activity expansions and slowdowns. The underlying principle is simple: the delay registered to provide the main economic statistics given, we try to identify a set of variables (called leading indicators) available faster and which evolve before the reference series. We would like to underline that he use of leading indicators faces the risk of false signals and missing signals. It is thus essential to test their reliability and their f recasting power. The study carried out consist in considering successively two reference series (the gross domestic product and the consumer price index) to test the reliability of four leading indicators (the CLI, the comp site eading indicator of OECD; the SP500 index; the ECRI; and the conference Board). The consideration f t e one or other one of these series is equivalent to plan the crises or the recessions. The study shows that, over the period [2000;2011], the Composi e Leading Indicator (CLI) is the most successful to forecast peaks and troughs, in particular for the United States. However, it is advisable to remain watchful because this indicator tends to plan too many peaks. Besides, the study has allowed to define the average lead for the studied countries: