amount and a series of options that the policy holder may exercise, by incurring additional fees. These defi-nitions are fairly standard but the insurance company issuing the prod-uct may add more bells and whistles to any of these.

At a conceptual level, F3 is com-prised of three distinct objects that are collectively used to perform all valuations and risk analysis on all types of financial instruments. This framework has been designed to separate the financial modeling functions so users defining payoffs will not have to be concerned with model calibration and mathemati-cal model selection, unless desired. Before we move to the specific fea-tures of GMIBs and their common pricing concerns, we begin with a higher-level overview of F3, as a valuation and risk framework. This will provide a good sense of how F3 is utilized to model and price a multitude of financial instrument types, variable annuities represent-ing just one example. Additionally, F3’s transparent modeling capabili-

Variable annuities rep-resent a widely used investment vehicle for retirees based on some of their key attributes,

such as lifetime income benefits and death benefit protection. There are several different flavors of VAs, each with different features. The first type – guaranteed minimum withdrawal benefit options – allows policy holders to participate in positive market increases and periodically take withdrawals without suffering from negative market declines. The second type eliminates downside risk and guarantees beneficiaries’ payments by paying the greater of initial investment value or a guaran-teed minimum, which is known as a guaranteed minimum death ben-efit option. The third type – known as guaranteed minimum income benefit options (GMIB) – allows for the greater of an index return and a guaranteed coupon paid periodically once the contract has been annui-tized. Each of these three insurance policies can be viewed as a principal

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models�and�valuation�specifications,�saving�financial�modeling�time�through�key�functionality.�The��

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ties allow for visibility in all risk and valuations, enabling the user to con-sider the macro risk tolerance levels of an individual trade or the largest of portfolios.

The Model object holds the parameters of the mathematical models being used for valuation, along with a snapshot of the market data set, in an arbitrage-free view of financial markets. Calibration and bootstrapping are done automati-cally, because the Model object con-tains both the parameters required for valuation and the market data from which they are derived. Any calibrated or bootstrapped model parameters are provided in the Model object in the form of curves. Examples of curves are a discount curve bootstrapped from interest rate derivatives (cash deposits, for-ward rate agreements, swaps, etc.) or a swaption volatility cube calibrated to swaption quotes, but also more basic curves such as LIBOR fixings on specific dates, the mean rever-sion parameter for an interest rate model, or a foreign exchange rate chain object which, given currencies

AAA, BBB, and CCC, can imply the AAA:CCC rate given quotes for AAA:BBB and BBB:CCC. These are just a few examples of different curves in F3 that go into building a model to value financial instruments. A multitude of curves and complete mathematical models come pre-built in F3, but the user can easily add their own curves. A Model object can contain any number of curves defining a variety of financial mod-els without compromising compu-tational efficiency, as all curves are handled by lazy evaluation, which is a key concept of F3. As we have seen, the Model object is constructed in a series of steps, starting with an

empty shell and in each step creat-ing a new Model object built on the previous Model object but with the addition of either market data sets or curve-builders. Lazy evalua-tion means that in any valuation, only the curves that are required for the valuation are constructed. This approach is highly efficient as, in a given valuation, only the required calculations (which could include computationally expen-sive calibrations) are carried out. Without affecting computation times, a single Model object can therefore contain a large variety of curves and be used for valuing any number of trades, carrying out only

the required calculations, but also retaining any curves that have been built for later re-use. Lastly, another consequence of lazy evaluation is that the order in which a Model object is built does not matter as long as all the needed curves and market data sets are present when a given curve is requested.

The Valuation Specification con-tains the practical details of how a valuation is to proceed as a numeri-cal calculation. Therefore, it is here that we define details of analytical calculations or approximation methods, any valuation param-eters (for example, the tolerance to use in a root-finder, as opposed to

This framework has been designed to separate the financial modeling functions so users defining payoffs will not have to be concerned with model calibration and mathematical model selection, unless desired

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model parameters calibrated from market data which are in the Model object), and the overall calculation approach, such as Monte Carlo simu-lation or closed-form. For Monte Carlo simulations, we may have several state variables (each repre-senting an index), and each one simu-lated according to a different math-ematical model. It is in the Valuation Specification that the selection of the specific mathematical model needed for valuation is made. F3 offers a large variety of financial

models for simulating processes in all asset classes. These processes may be combined into multi-factor simu-lations within an asset class and across asset classes using F3’s hybrid modeling framework. Any valuation carried out in F3 is capable of not only returning the value of a finan-cial instrument, but also first-order sensitivities to every market data parameter that was used to build the financial model. In addition, the user has access to intermediate results, such as implied cash flows, the simulated Monte Carlo paths, or even the calculation tree that was generated to price the given finan-cial instrument.

The Product object is the repre-sentation of the legal terms stated on the financial contract. These terms are the binding responsibilities for both parties in a financial transac-tion. The flexibility of F3 is apparent in each of the three main building blocks, but it is immediately evident in the Product object through the ability to construct any conceivable financial instrument. In F3, the payoff of a financial instrument is described as a single or as multiple cash flows that depend on one or

more indices. An index represents an observable quantity, such as the level of a stock, an equity market index, or a credit survival index. Any index can be composed of other indices through F3’s intuitive index expres-sion language. It is this index expres-sion language that provides the user with the flexibility to structure any trade, thereby allowing the user to examine the valuation and risk of any instrument that can be valued using F3’s mathematical models.

Lastly, given the Model, Valuation Specification, and Product, a finan-cial modeler can specify Output Requests from an incredibly broad range. A few examples of these

requests are the product’s value, a comprehensive risk report that includes first-order risk to every market data quote that entered into the valuation, profit and loss attribu-tion, collateralized CVA, PFE, or MC VaR.

The independent construction of the Model, Valuation Specification, and Product provides a great amount of flexibility – the Model can be used not only to price various types of variable annuities, but also other financial instruments such as exotic

structured products, swaptions, credit default swaps, or even a large and diverse portfolio with thousands of financial instruments. Conversely, the Valuation Specification can eas-ily be replaced with another to price the same variable annuity assum-ing LIBOR market model dynamics instead of a Hull–White process, for example. Lastly, the Model object can be replaced for scenario analy-sis. Flexibility also comes through choosing various market data sourc-es, constructing volatility cubes or surfaces to the user’s specifications, or choosing a specific interpolation method for curve building.

Using F3’s flexibility as the focal

point in this example, we now look at guaranteed minimum income benefit options on a variable annu-ity contract. The policy holder in this contract typically invests a lump sum payment at the beginning of their accumulation phase, referenc-ing a market index or mutual fund. Throughout the accumulation phase this initial lump sum is invested in the market index, allowing for par-ticipation in positive market index returns but not penalizing policy holders for annual declines by guar-anteeing a minimum rate of return. This is referred to as a lock-in fea-ture, where annual return gains are locked in as the base level for the fol-lowing year. At the end of this accu-mulation phase investors will typi-cally begin receiving either annual distribution payments throughout their retirement based on the total amount amassed over the accumula-tion phase, or a guaranteed income amount.

In our example, we assume the policy holder is 55 years old, with an accumulation phase of 10 years, a guaranteed annual benefit of 5 per-cent per annum, and market perfor-mance linked to an equity index.

For clarity we again start with the Model object, even though the order of objects built is of no con-sequence to the user. Firstly, a base model is set up that includes cash rates, FRA rates, and swap rates which are used to bootstrap the discount curve. Next, we extend this discounting model to include the forward equity curve and add the equity volatility surface based on option market quotes. After extend-ing this model to include the surviv-al probabilities of the policy holder, we finally add the hybrid correlation between the equity and interest rate processes.

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f3’s new Hybrid modeling allows the user to price complex financial instruments like vari-able annuities, and the differentiating flexibility allows for pricing almost any insurance product in the marketplace while fincad’s patent pending Universal Risk Technology can isolate all market risk and credit exposures

12� Wilmott�magazine

With the completed Model object we can focus on building the Product. The first step is to build a survival index based on the policy holder and insurance contract as well as the payment currency and market conventions. Next, we define specific roll dates of the annuity payments as well as appropriate day count conventions, maturity, and contract tenor. Now that we have established our deal-specific data, we define the option payoff. The final payoff of the GMIB is the maximum of the following components:

1. The maximum component. A coupon payment based on the highest market index value during the accumulation phase.

2. The guaranteed return compo-nent. A coupon payment based on the guaranteed minimum annual percentage return of the annuity.

3. The value of the policy holder’s investment account at the end of the accumulation phase.

In F3, these components are defined as indices and their values are easily implemented using the index expression language.

The final step in the Product pay-off is the creation of a choice prod-uct that takes the greater of the two coupon payment streams and the value of the underlying index perfor-mance at the end of the accumula-tion phase. In the valuation, the for-mer two take into consideration the policy holder’s survival probabilities throughout the coupon payment period. The latter represents an investment in the market index and the choice between these payment streams is the final Product object representing the GMIB. Note that choice products may be built on top of choice products to allow for the

definition of highly complex payoffs. Additionally, for institutions with large portfolios comprised of many different financial instruments, this methodology can easily be extended to value the individual products or the entire portfolio. In F3, a portfolio of Products is just another Product.

The Model, Valuation Specification, and Product are finally combined in the single func-tion called ValueProduct to value the GMIB and obtain a comprehensive risk report. In the table below, we see that the RiskReport output request automatically generated over 300 specific and fine-grained risk expo-sures after filtering out all zero exposures. This information enables financial professionals to execute hedging transactions after isolating key exposures to the market instru-ments that entered into the model calibration and valuation.

In this article, we have seen a lot of the benefits associated with F3 with regard to pricing and analyzing the risk of complex financial instru-ments, reflecting market feedback on compliance with new industry regulations. F3’s new Hybrid model-ing allows the user to price complex financial instruments like variable annuities, and the differentiating flexibility allows for pricing almost any insurance product in the mar-ketplace while FINCAD’s patent pending Universal Risk Technology can isolate all market risk and credit exposures. F3 provides the most com-prehensive set of analytics required to more effectively meet solvency and UCITS requirements, especially for the capital requirements pil-lar, where F3 can provide accurate measurements of credit and market risk. Additionally, F3 aids in the disclosure requirement because of the comprehensive and transparent

documentation, providing detailed information on assumptions and how objects have been constructed.

about the authorMatthew Streeter is the F3 Product Manager at FINCAD and has previ-ously worked at sell-side banks and buy-side asset management institutions in both structuring and trading roles. For further questions related to this article, or F3, please email: m.streeter@fincad.com. W

��BiBliogRapHyhttp://www.actuaries.org.uk/research-and-resources/documents/mortality-rates-and-complete-expectations-life-pfa92c2010-and-pma92http://www.rotman.utoronto.ca/finance/seminars/030117_boyle.pdfMarshall,�C.,�Hardy,�M.,�and�Saunders,�D.�2010.�Valuation�of�a�guaranteed�minimum�income�benefit.�North American Actuarial Journal�14(1):�38–58.

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An Introduction to Islamic FinanceTheory and Practice, 2nd EditionZamir Iqbal & Abbas MirakhorIslamic finance has experienced remarkable growth over the last three decades and the global demand for financial products and services that comply with economic and financial principles of Islam is increasing day by day. For newcomers to this burgeoning market, An Introduction to Islamic Finance offers an excellent overview of the principal concepts from two leading scholars in Islamic finance.

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Islamic Finance in a NutshellA Guide for Non-SpecialistsBrian KettellIslamic Finance in a Nutshell is a quick and easy guide to understanding the fundamentals of Islamic finance and how the Islamic financial markets work. Designed as a quick read for practitioners needing to pick up the basics of the industry, it will enable readers to understand the differences between Islamic and Western finance.

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Islamic Capital MarketsProducts and StrategiesKabir Hassan & Michael MahlknechtProducts created according to Islamic principles have shown a low correlation to other market segments and are relatively independent even from market turbulences like the subprime crisis. Therefore, they have become increasingly popular with secular Muslims and non-Muslim investors, as highly useful alternative investments for the diversification of portfolios.

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