A Diffusion Approximation to the Markov Chains Model of the Financial Market and the Expected Riskless Profit Under Selling of Call and Put Options

Abstract: A discrete time model of financial markets is considered. It is assumed that the stock price evolution is described by a homogeneous Markov chain. In the focus of attention is the expected value of the guaranteed profit of the investor that arises when the jumps of the stock price are bounded. The suggested diffusion approximation for the Markov chain allows establishing a convenient approximate formula for the studied characteristic.;