A unified pricing of variable annuity guarantees under the optimal stochastic control framework

In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the existing numerical methods. For numerical valuation of these contracts, we develop a direct integration method based on Gauss-Hermite quadrature with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is very efficient when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We also present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a benchmark for practitioners and researchers developing pricing of variable annuity guarantees.Comment: Keywords: variable annuity, guaranteed living and death benefits, guaranteed minimum accumulation benefit, optimal stochastic control, direct integration metho

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A market-consistent framework for the fair evaluation of insurance contracts under Solvency II

The entry into force of the Solvency II regulatory regime is pushing insurance companies in engaging into market consistence evaluation of their balance sheet, mainly with reference to financial options and guarantees embedded in life with-profit funds. The robustness of these valuations is crucial for insurance companies in order to produce sound estimates and good risk management strategies, in particular, for liability-driven products such as with-profit saving and pension funds. This paper introduces a Monte Carlo simulation approach for evaluation of insurance assets and liabilities, which is more suitable for risk management of liability-driven products than common approaches generally adopted by insurance companies, in particular, with respect to the assessment of valuation risk

Still living with mortality: The longevity risk transfer market after one decade

This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions – buy-outs, buy-ins and longevity insurance – have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions – longevity-spread bonds, longevity swaps, q-forwards, and tail-risk protection – have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customized solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral, and liquidity, the former perform on balance less favourably despite a lower potential cost.We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g., determining the longevity risk premiumand estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognize that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined – such as longevity-linked securities and reinsurance sidecars

Equity-Linked Pension Schemes with Guarantees

This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investor's contribution needed to finance this guarantee. Three types of schemes are considered: investment guarantee, contribution guarantee and participation surplus. The evaluation of each scheme involves pricing an Asian option, for which relatively tight upper and lower bounds can be calculated in a numerically efficient manner. We find a negative (and for two contracts pecifications also concave) relationship between the participation in the surplus return of the investment strategy and the guarantee level in terms of a minimum rate of return. Furthermore, the introduction of a possibility of early termination of the contract (e.g. due to the death of the investor) has no qualitative and very little quantitative impact on this relationship.pension funds; forward risk adjusted measure; Asian option

Theories of loan commitments: a literature review

A loan commitment is an agreement by which a bank promises to lend to a customer at prespecified terms while retaining the right to renege on its promise if the borrower's creditworthiness deteriorates. The contract also specifies the various fees that must be paid over the life of the commitment. Loan commitments are widely used in the economy. As their use has spread, a rich literature has evolved to explain why they exist, how they are priced, and how they affect the risk of the bank and the deposit insurer. This article summarizes what we have learned on these issues. Its main insight is that loan commitments are an optimal tool for risk sharing and for resolving informational problems. The author also points out some issues that the current literature leaves unexplained.Bank loans