Selected Topics in Valuation of Financial and Insurance Contracts

Abstract

In this thesis, selected topics on valuation and hedging of financial and insurance contracts are studied. First of all, we study the most common in mathematical finance Black-Scholes market and provide an alternative derivation of the famous Black-Scholes formula from the binomial option pricing model. Secondly, we develop a method for pricing and hedging the equity-linked life insurance contracts without switching to a new probability measure, using quadratic risk-minimization criterion. Thirdly, we consider a quantile hedging problem for the Black-Scholes and jump-diffusion markets and extend existing results in this subarea by introducing dividends. Application to pricing and hedging the equity-linked life insurance contracts is demonstrated. Fourthly, we study a market with defaultable securities and develop a quantile hedging methodology for this market, providing insurance applications. Finally, we revisit the Bachelier model – the first model of the financial market in mathematical finance history. We study the modification of the classical Bachelier model by absorbing the stock price at zero and give alternative proofs for the option pricing formulas on this market. Using these results, we develop a quantile hedging methodology and provide insurance applications for both classical and modified Bachelier markets.