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The paper is devoted to quantile hedging in a market with defaultable securities. Both perfect and quantile hedging strategies are given for a European call option on a vulnerable equity. Applicati...

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.

The paper demonstrates the effect of the dividends on pricing and hedging the European contingent claims under a budget constraint and presents insurance applications. Explicit formulae for the quantile pricing and hedging of the European call option are derived assuming the jump-diffusion model of the financial market. These results are used to determine the premium of the pure endowment with fixed guarantee equity-linked life insurance contract as well as the survival probability of the insured. A numerical example is given to illustrate the role of dividends in valuation and risk management of such insurance contracts.

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.