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Modern Valuation Tecniques by Stuart Jarvis, Frances Southall and Elliot Varnell

By Stuart Jarvis, Frances Southall and Elliot Varnell

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Valuing a single with-profits policy in isolation is almost impossible. This is because of the role of the estate; it is very hard to separate the impact of a single policy or cohort of policies. We have followed the example of Hare et al (2001) in considering a single policy in which, somewhat artificially, the shareholders receive a share of bonuses but also explicitly underwrite the guarantees inherent in the bonus policy. This approach is consistent with some recent attempts to restructure with-profits funds making the role of shareholder capital more explicit.

A theory of the term structure of interest rates", Econometrica 53: 385-408 DUFFIE, D. (1996). , TEEGER, M. , (1999). "A Stochastic Investment Model for Asset & Liability Management" SIAS Paper FLESAKER, B. , (1995). "Positive interest", Risk, 9: 46-49 FLESAKER, B. , (1997). P. , (2001). "A market-based approach to pricing with-profits guarantees", British Actuarial Journal 6: 143-196. , (1981). D. , (2000). Y. , (1986). "Term structure movements & pricing interest rate contingent claims", Journal of Finance, 41: 1011-1029 LEIPPOLD, M.

So the implied discount rate is relatively high for tight restrictions. Relaxing the restriction increases the volatility of the earlier payments relating to reversionary bonuses, but reduces the volatility of the shortfall payment. This reduction in volatility is reflected in the decrease in the discount rate as the restriction is reduced. 5 Conclusions The basic model has illustrated a number of points: • Stochastic projections of shareholder income are required in order to model the volatility of these cashflows from a with-profits policy.

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