Table 1 Examples of the sigma approach with odd and even numbers of states
From: Weighted-indexed semi-Markov model: calibration and application to financial modeling
State 1 | State 2 | State 3 | State 4 |
|---|---|---|---|
\(\left[ min,-\sigma \right)\) | \(\left[ -\sigma ,0\right)\) | \(\left[ 0,\sigma \right)\) | \(\left[ \sigma ,max\right]\) |
State 1 | State 2 | State 3 | State 4 | State 5 |
|---|---|---|---|---|
\(\left[ min,-2\frac{\sigma }{2}\right)\) | \(\left[ -2\frac{\sigma }{2},-\frac{\sigma }{2}\right)\) | \(\left[ -\frac{\sigma }{2},\frac{\sigma }{2}\right)\) | \(\left[ \frac{\sigma }{2},2\frac{\sigma }{2}\right)\) | \(\left[ 2\frac{\sigma }{2},max\right]\) |