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A modification of a classical Bachelier model by letting a stock price absorb at zero is revisited. Alternative proofs are given to derive option pricing formulas under the modified Bachelier model and numerical comparison with the Black–Scholes formula is provided. Quantile hedging methodology is developed for both classical and modified Bachelier models and application to pricing the pure endowment with fixed guarantee life insurance contracts is demonstrated, both theoretically and by means of a numerical example.

In this paper we show how the results of Bernstein (1943) and recent results of Zubkov and Serov (2012) on the normal approximation to the binomial distribution lead to an alternative derivation of the Black–Scholes formula from a binomial option pricing model.

This paper analyzes the early/initial effect of change in social policy, namely passing the Federal Law of the RF No. 256-FZ from 12.29.2006 titled, “On Additional Measures of State Support of Families with Children,” on total fertility rate in Russia. Using fixed effects econometric model we confirm that introduction of the Federal Law positively influenced Russian total fertility rate. The policy impact is small in size and unlikely to induce the population to fully reproduce itself. Several other socio-economic and demographic variables have been included in the model as the control variables. Our results indicate that the large impact of unemployment, both urban and rural, emigration, and death rates on fertility rates suggests that economic policies directed at creating more jobs in Russia care would be more likely to have a larger positive impact, via increasing income per capita and lowering emigration rates of young people at the peak of their reproductive age, on total fertility rate than the current policy. Similarly, major health reform is in order to lower very high death rates among population of the reproductive age.