| Περίληψη : | Εδώ θα εστιάσουμε στην μέθοδο της ιστορικής προσομοίωσης και θα εξέτάσουμε δυο σημαντικές επεκτάσεις της. Την ζυγισμένη ως προς τον χρόνο ιστορική προσομοιώση και την ζυγισμένη ως προς την μεταβλητότητα ιστορική προσομοίωση. Τις οποίες στο κεφάλαιο της ανάλυσης θα τις εφαρμόσουμε σε πραγματικά δεδομένα και πιο συγκεκριμένα σε 4 μεγάλους χρηματιστηριακούς δείκτες των ευρωπαϊκών αγορών. Τέλος, η αξιοπιστία κάθε μιας απο της παραπάνω μεθόδους θα αξιολογηθεί με την βοήθεια εξειδικευμένων στατιστικών ελέγχων, μια προσέγγιση που είναι γνωστή και ως Ανάστροφος έλεγχος
The concept of risk applies to every aspect of our daily lives. The word “risk”, without a trace of exaggeration, is evident in all activities of all organizations and economic entities, regardless of their purpose and the structure of their daily operations. Businesses constantly face various types of risks that may primarily stem from their activities, actions, and decisions. Consequently, effective and careful management is required to minimize their impacts. Risks arise either as direct threats that can lead to failure in achieving a business’s goals or as opportunities that can offer an improved way to achieve those goals. If someone were to ask us to define risk, it would be quite difficult because it is primarily defined by the context in which it is used. For example, a doctor defines risk differently than a military pilot or a financier. Generally, however, we can say that risk expresses our exposure to adversity and uncertainty (see, e.g., [12]). It is thus clear that there are many types of risks we face in our daily lives. In this paper, we will focus on a very specific type of risk, known as financial risk. Financial risk partly arises from investors’ exposure to fluctuations in financial markets and is directly related to the potential losses that may result from various financial and investment activities (see, e.g., [13]). Therefore, it is clear and entirely logical that effectively managing financial risk is a process of great importance for the viability of any economic unit within a developed economy. Within the framework of modern risk management strategy, measuring risk (i.e., quantifying our exposure to this specific risk) is a step of utmost importance. Among the many tools used to measure risk, this paper will employ the Value at Risk (VaR) methodology, which estimates the potential loss that an asset may incur over a specific time horizon. Several methods have been proposed for calculating Value at Risk (VaR) to date, including both parametric and non-parametric approaches. Each of these methods makes its own assumptions and has its own advantages and disadvantages. In this paper, we will focus on a very fundamental method that is widely used in the market, namely the historical simulation method. After presenting this method and demonstrating how it can be directly applied in practice, we will introduce two equally important extensions: the time-weighted historical simulation and the volatility-weighted historical simulation. All these methods will be applied to real data, specifically to four major European stock market indices. Finally, the reliability of each of these methods will be evaluated with the help of specialized statistical tests, a procedure also known as back testing.
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