In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the...

In the paper we present the application of risk neutral measure estimation in the analysis of the index WIG20 from Polish stock market. The risk neutral measure is calculated from the process of the options on that index. We assume that risk neutral measure is the mixture of lognormal...

Bitcoin Pricing Kernels (PKs) are estimated using a novel data set from Deribit, the leading Bitcoin options exchange. The PKs, as the ratio between risk-neutral and physical density, dynamically reflect the change in investor preferences. Thus, the PKs improve the understanding of investor...

I study the effect of heterogeneous beliefs about asset prices on the long-term behavior of financial markets. Starting from the ideas of Abreu and Brunnermeier (2003), a two-dimensional system of differential equations is developed. The first dynamic variable is the asset price growth rate. The...