Furthermore, insurance rms operating within the European Union will, from the end of 2012, be subject to the Solvency II directive, which places new demands on insurance companies. For example, the valuation of assets and liabilities now needs to be market consistent. One way to accomplish a market consistent valuation is through the use of an economic scenario generator (ESG), which creates stochastic scenarios of future asset returns. In this thesis, we construct an ESG that can be used for a market consistent valuation of guarantees on insurance contracts.
Bonds, stocks and real estate are modelled, since a typical insurance company's portfolio consists of these three assets. The ESG is calibrated to option prices, wherever these are available. An Otherwise the calibration is based on an analysis of historical volatility. assessment of how well the models capture prices of instruments traded on the market is made, and nally the ESG is used to compute the value of a simple insurance contract with a minimum interest rate guarantee.
Acknowledgements We would like to thank Handelsbanken Liv for making this thesis possible.In the First, it is likely that some companies have not realised that their policies consist of several components which must be evaluated separately. Second, at the time of policy initiation, the options embedded in insurance contracts were so far outof-the-money, that the companies disregarded their value as it was considered negligible compared with the costs associated with the valuation. well as a great deal of computer power and data. In the light of current economic events and new legislations, insurance companies have realised the importance of properly managing their options and guarantees.Insurers have recently experienced signicantly lower rates of return than before, Third, the valuation of these policies sometimes requires complex analytical methods, as 1 which means that minimum interest rate guarantees have moved from being far out-of-the-money to expiring in-the-money.
As a result, companies have experienced solvency problems. Furthermore, insurance rms operating within the European Union will, from the end of 2012, be subject to the Solvency II directive. The directive is a set of regulatory requirements and is based It is a riskon economic principles for the valuation of assets and liabilities. equirements will depend directly on this. based system, as risk will be measured on consistent principles, and capital 1. 2 Valuation of Liabilities under Solvercy II Solvency II is a new legislation that aects the insurance industry.
It is scheduled to come into eect on 31 December 2012. This new set of rules creates many new demands on insurance companies regarding for example capital requirement, risk management processes, and transparency. The Solvency II framework consists of three pillars. Pillar I contains the quantitative requirements, i.
e. ow assets and liabilities should be valued and the capital that a company is required to hold. Pillar II covers the qualitative requirements, i. e.
how risks should be governed and managed, as well as supervised. Finally, Pillar III sets out the requirements for disclosure and transparency, for example reporting to supervisory authorities. Pillar I denes two levels of capital requirements: Minimum Capital Requirement (MCR) and Solvency Capital Requirement (SCR). The MCR is the absolute minimum capital that an insurance company has to hold.
If the capital falls below this level the supervisory authorities will intervene.The SCR represents the required level of capital that an insurance company should hold, and it can be calculated either through a standard formula or through the use of an internal model which must be approved by the supervisory authorities. In order to determine the capital requirements of an insurance company, one rst has to calculate the technical provisions. Technical provisions is the amount that an insurance company must hold to ensure that it can meet its expected future obligations on insurance contracts.
It consists of risks that can be hedged and risks that cannot be hedged.The value of the technical provisions for risks that cannot be hedged should be the sum of a best estimate of the expected liabilities and a risk margin. 1. 2.
1 QIS5 The insurance industry has been asked to participate in so-called Quantitative Impact Studies, where the 5th (QIS5) was undertaken in the autumn of 2010. The studies have given the European Commission an idea on how the proposed regulation will aect the industry and, in particular, the level of the required 2 capital the insurance companies need to hold. As a background document, the European Commission issued, in July 2010, the [12] and theQIS5 Technical Specications Annexes to the QIS5 Technical Specication s [13]. These documents lay out the most recent details regarding the valuation of assets and liabilities under Solvency II.
It is important to stress that QIS5 is a study for testing purposes, to ensure that the Solvency II framework is as accurately formulated as possible when it comes into eect. This means that what is written in the QIS5 Technical Specications might not be exactly what the framework will look like in a couple of years, depending on the results of the study.However, at this point in time, it is the best available description of how the required capital should be calculated, and it is generally believed that drastic changes to the methods proposed by the QIS5 Technical Specications are unlikely. 1. 2. 2 Best Estimate The QIS5 Technical Specications states that the best estimate is the probability weighted average of future cash ows, discounted to its present value [12].
The Specications suggests three dierent methods for the calculation of the best estimate; namely simulation techniques, deterministic techniques, and analytical techniques. Using an analytical technique means that the insurance company must be able to nd a closed form solution for calculating the best estimate. One analytical technique can be to value guarantees by calculating the cost for fully hedging the guarantee. Another analytical technique is to make an assumption that future claims follow a given distribution. • With a deterministic technique, the projection of the cash ows is based on a xed set of assumptions.
Examples of deterministic techniques are stress and scenario testing, and actuarial methods such as the ChainLadder method. •A simulation approach means using a stochastic model to generate future scenarios. When using this method, there is no need to generate all possible future scenarios. However, one has to make sure that enough scenarios are generated so that they are representative of all possible future scenarios. There may also be other methods that can be used to perform this calculation, but there are certain criteria that they need to full, according to the QIS5 Technical Specications.
For example, they need to be actuarial or statistical methods that take into account the risks that aect the future cash ows.The QIS5 Technical Specications state that simulation methods can lead to a more robust valuation of the best estimate of insurance contracts with embedded 3 options and guarantees. The deterministic and analytical approaches are more appropriate for the best estimate of non-life liabilities, as well as for life insurance liabilities without options or guarantees [12]. Since insurance contracts with the multi-period minimum interest rate guarantees are path dependent, i.
e. the insurance contract, the simulation approach is particularly suitable. uaranteed rate is given at the end of each period, not just at the maturity of 1. 3 Aim and Scope The valuation of insurance contracts with multi-period minimum interest rate guarantees requires complex mathematics.
An economic scenario generator A scenario in this context (ESG) can be used as a tool for this valuation. is a stochastically generated economic simulation from a Monte-Carlo driven model. According to the Solvency II directive, ESG models are a key element of market consistent valuation for life insurance businesses.The aim of this thesis is to describe and calibrate a market consistent ESG that can be used for the valuation of insurance contracts with multi-period minimum interest rate guarantees. The construction of the ESG requires a choice of assets or asset classes to be modelled, followed by a choice and calibration of a model for each asset class. When each asset has been calibrated and the correlation between them established, scenarios for each asset class can be generated.
There are many dierent assets that can be modelled in an ESG, for example, bonds, stocks, real estate, ination, exchange rates and credit risk.Since a typical insurance company's portfolio consists of bonds, stocks, and real estate, these are the three asset classes we choose to model in our ESG. The calibration will be based on data from the Swedish market. The thesis is outlined as follows.
Chapter 2 gives the theoretical background, focusing on the models for the asset classes bonds, stocks, and real estate. The analysis is presented in Chapter 3, where the results of the simulations are illustrated in various plots. In Section 3. 4 a valuation of a simplied insurance contract based on the ESG is demonstrated.Finally, Chapter 4 oers a summary of the results and some concluding remarks.
4 Chapter 2 Theoretical Background 2. 1 Economic Scenario Generators In the insurance industry there are two types of ESGs with two dierent areas of application. A real world ESG is used to generate valid real world distributions ESG, on the other hand, is used in for all the main risk factors, to support the calculation of the Solvency Capital Requirement (SCR). A market consistent the calculation of the technical provisions for insurance contracts with nancial options and guarantees [28].
Real world scenarios should be scenarios that reect the expected future evolu- tion of the economy by the insurance company, i. e. they should reect the real world, hence the name. They should include risk premium and the calibration of volatilities and correlations is usually based on analysis of historical data. Market consistent scenarios market prices. are of use during market consistent valuations in they do not include Solvency II, and the main function of these scenarios should be to reproduce Often the scenarios are risk neutral, i.
e. isk premium, since this simplies calculations without changing the valuation. Market consistent scenarios need to be arbitrage free. It is important to stress that the market consistent scenarios are not intended to reect real world expectations; for example ten-year long market consistent scenarios do not reect how the insurer expects the world to look like in ten years. Instead they can be used to value a derivative with a maturity of ten years.
Market consistent scenarios can help us calculate market prices today while real world scenarios can show us what the world might look like tomorrow. 2. 2 Calibration of a Market Consistent ESG The Solvency II directive places several requirements on a market consistent ESG. First, it must generate asset prices that are consistent with deep, liquid, and transparent nancial markets; and second, it assumes no opportunity for arbitrage.
To clarify this • • • A liquid market means that assets can be easily bought and sold without causing signicant movements in price. A deep market means that a large number of assets can be transacted without signicantly aecting the price of the nancial instruments.Transparency in the market means that current trade and price information is normally readily available to the public. The requirements that need to be considered regarding the calibration of a market consistent asset model: • It should be calibrated to instruments which in some way reect the nature and term of the liabilities. It is especially important that they reect liabilities that cause substantial guarantee cost. • • It should be calibrated to the current risk-free term structure used to discount cash ows.
It should be calibrated to an appropriate volatility measure. What constitutes an appropriate volatility measure is still debatable within the Solvency II framework. There are two possible approaches; calibration to market prices of dierent derivatives, and calibration based on analysis of historical volatilities of the assets themselves. The purpose behind a market consistent valuation of an insurance company's liabilities is to reproduce the price the liabilities would be traded at, if they were in fact traded on the market.
In order to do this it is important that the ESG can reproduce market prices of assets which have similar characteristics to the liability being valued. The liabilities stemming from insurance contracts with embedded options and guarantees have option-like features, which means that the ESG should be able to reproduce option prices on the market. prices of options. However, there are also reasons why a calibration based on analysis of historical volatilities can be appropriate. To begin with, option prices are not available for all assets, for example for the asset class real estate.
Also, a life insurance company generally has obligations stretching many years into the future, and An ESG calibrated to option prices would generally give a very good t to the market 6 option prices with long maturities are often not available on the market. Another important advantage of calibration to historical volatilities is that they are more stable than the volatility implied by option prices. When the market is stressed, implied volatilities tend to be higher than real volatility leading to an overestimation of technical provisions.This type of pro-cyclical eect would be avoided by calibrating to historical volatilities. In order to ensure market consistency, in a normal market situation, calibration to option prices seems more appropriate if these prices are available.
This is also the conclusion in the QIS5 Annex G [13] where the denition of an appropriate volatility measure is discussed. This view was also supported by the majority of the insurance companies and associations who commented on CEIOPS Consultation Paper 39 [6, 7] where the best estimate calculation under Solvency II is discussed.However, many emphasised that the Solvency II directive should not limit insurance companies to calibrating only to volatilities implied by option prices or only to historical volatilities, but that it should be up to the individual company to choose which volatility measure to use, depending on the asset class and the market situation at the time of calibration. To determine whether option prices are reliable and liquid and to establish what constitutes a stressed market is not always a straightforward task, and often requires expert judgement.
