AGGREGATION OF RETURNS: HETEROSKEDASTIC MODELS, (GEOMETRIC) BROWNIAN MOTION, AND FORECASTING RETURN-AT-RISK
Aggregation of returns can be classified into two types: Type I and Type II. Type I involves summing returns over time to understand their volatility. Typically, the volatility of aggregated returns for assets is heteroscedastic, meaning it varies over time. Therefore, heteroskedastic models like...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/82996 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Aggregation of returns can be classified into two types: Type I and Type II. Type
I involves summing returns over time to understand their volatility. Typically, the
volatility of aggregated returns for assets is heteroscedastic, meaning it varies over
time. Therefore, heteroskedastic models like ARCH(1)/GARCH(1,1) are required
to handle this non-constant volatility. Furthermore, the aggregation of returns that
follows a heteroskedastic model is linked with the Brownian motion (Bm) process,
allowing Bm to model the aggregation of returns and geometric Brownian motion
(gBm) to model asset prices. Type II, on the other hand, involves aggregating returns
from multiple assets to examine the relationships among these assets. This type
represents the sum of Type I aggregations of returns for several assets, considering
dependencies (Pearson correlation). Since the results of aggregating returns from
both types can yield negative values (losses), a risk measure is needed to assess these
losses. One such method is Return-at-Risk (RaR), which measures the maximum
loss of aggregated returns that can be tolerated at a specific confidence level. |
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