Hedging and Cash Flows in the Presence of Taxes and Expenses in Life and Pension Insurance

Abstract

Abstract:In investment and insurance contracts, certain stipulated payments may depend on the hedging strategy. We study the problem of calculation, hedging and valuation of such cash flows, by considering a payment process in a setup with taxes and investment costs that are functions of the investment returns or the current value of the hedging strategy. We determine the market value of the combined liability and decompose the value into the tax part, the investment cost part and the benefit part, and we determine the associated hedging strategies. Moreover, we identify the expected future tax payments and investment cost cash flows. Our results show that the current Danish insurance accounting practice for taxes is in general conservative, when considered in an idealized setting with symmetric and continuously-paid taxes. Finally, we consider the special case of affine interest rates, where explicit results can be obtained, and study some numerical results.

Computation of Bonus in Multi-State Life Insurance

“…The parameters β, α, and σ may be found in Table 1. They are taken from the numerical example in Buchardt and Møller (2018) and yield a mean reversion to about 0.043.…”

Tax- and expense-modified risk-minimization for insurance payment processes

“…In this setting, we apply the criterion of riskminimization directly within this artificial after-tax and after-expense market. Second, we follow [5] and construct explicitly the payment processes associated with taxes and expenses and introduce the concept of tax-and expense-modified risk-minimization. The two approaches are conceptually different but are, as we unveil, mathematically equivalent in a specific sense which we explain later.…”

“…The necessity to take taxes and expenses into account is also reflected in the Solvency II regulation, see [12] Article 77-78 and [13] Article 28, and the forthcoming IFRS17 regulation, see [3] Paragraph 34 and Paragraph B65(j). It is our impression that a unified theory for market consistent valuation in the presence of taxes and expenses is yet to be developed, and accordingly, it is common among practitioners to take taxes and expenses into account via certain ad hoc adjustments of the forward interest rate curve, confer with [5].…”

“…In [5], valuation of insurance payment processes in the presence of continuously paid and symmetrical taxes and expenses is studied in complete markets. By identifying and explicitly constructing the inherent tax and expense payment processes and adding these to the existing insurance payment process, [5] were able to derive replicating strategies and determine the market value of the combined liability. In this paper, we essentially extend these results to incomplete markets.…”

“…Having determined the value of the combined liability, as well as the associated riskminimizing investment strategy, it is interesting, as was done for complete markets in [5], to study the decomposition into benefit, tax, and expense parts. This is, however, together with extensions of the tax-and expense setup to include discrete and assymetrical payments postponed to future research.…”