In this work we perform a pricing exercise of different types of spread options; we particularly focus on European calendar and crack spread options. We present the expressions followed by the joint characteristic functions of the underlying log-prices for a panel of bivariate processes. The...

The capital asset pricing model (CAPM) is a widely adopted model in asset pricing theory and portfolio construction because of its intuitive nature. One of its main conclusions is that there exists a global market portfolio that each rational investor should hold in proportion with the risk-free...

This note demonstrates how a covariance matrix estimated using log-returns of multiple assets in their respective base currencies can be converted directly into a covariance matrix in a single common currency using basic matrix multiplication. This approach eliminates the need to compute returns...