The Pricing Of Chooser Option And Equity-linked Life Insurance

In 1973, the classical Black-Scholes model of option pricing was derived by F. Black and M. Scholes under the assumptions that market interest rates are fixed and the market is frictionless. Black-Scholes model has a profound effect on pricing derivatives. The paper studied the price of the Chooser option and the price of the Equity-linked Life Insurance under the assumption that the interest rate follows the Vasicek model. The main results are as follows:(1) The pricing of chooser option under the stochastic interest rates model was studied. Firstly, the expression of chooser option is obtained by Risk-Neutral valuation when stochastic differential equations of the underlying assets, interest rates and default intensity were given. And then we derived choose option pricing formula by Girsanov theorem and risk-neutral pricing principle. Next, we give the analytical solution of the chooser option under the stochastic interest rate model when stochastic differential equations of the default intensity with jump. Finally, we analyze the effects of parameters on the chooser option value though numerical analysis.(2) The pricing of two kinds of equity-linked life insurances pricing under the stochastic interest rates were studied. Firstly, the expression of the single-premium of equity-linked life insurances are obtained by Risk-Neutral valuation when stochastic differential equations of the investment accounts, interest rates and default intensity were given. And then an equivalent probability measure is introduced by Girsanov theorem. Next, we can get the analytical solutions of equity-linked life insurances by the nature of Brownian motion and Bayesian law. Finally, we analyze the effects of parameters on equity-linked life insurances premium though numerical analysis.