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Financial markets and financial instruments and derivatives have experienced significant changes recently. Although this transition, the gold and crude oil are still leading the market and determine the main market conditions, so their importance could not be neglected. Looking back in history, there are milestone events that have drastically changed the economic, social and political circumstances, which have immediately affected the financial markets. In the recent study we calibrate jump-diffusion process to historical prices of gold (XAU) and crude brent oil futures (LCOc1), and derive piecewise approximations of the trend, volatility and jump intensity and distribution parameters. In the framework of jump-diffusion, we interpret the results as well as describe the possible future states of their prices and their impact on the global economy and quantify the respective outcomes probabilities. Based on the analysis, essential remarks for the economic environment are made in the conclusion of the paper. [ABSTRACT FROM AUTHOR]

In this work we report the development of an algorithm to solve inverse problems of determining the right boundary condition according to a measurement inside a truncated domain for the Black-Scholes equation. The difference schemes for the direct and inverse problems are derived on non-uniform Tavella-Randall grids. We propose and discuss results of computational experiments for several European options. [ABSTRACT FROM AUTHOR]