Relating Volatility and Jumps between two markets under Directional Change

Directional change (DC) is a new concept in sampling financial market data. Instead of recording the transaction prices at fixed time intervals, as is done in time series, DC lets the data alone decide when to record a transaction. In DC, a data point is recorded when the price has risen or dropped against the current trend by a significant percentage, which is known as the threshold. The magnitude of the threshold is determined by the analyst. Previous studies on DC mainly focus on analysing single price sequences of one market. This thesis focuses on a new path; working on the DC comparative analysis between two markets. We propose a novel data-driven approach to combine the observed DC series of two markets into a single data sequence, which we call the DC combined sequence. This allows us to conduct a comparative analysis between two markets under DC. Based on this approach, we propose a novel indicator that measures the relative volatility between two markets. In addition, we define jumps under DC. Under this measure, we can pinpoint the size, direction, and quantity of DC jumps in a market. Lastly, under the DC comparative analysis, we build a new DC approach to identify co-jumps between two markets.