المدربThe switch option of a Bermudan is its value minus the value of its most expensive co-terminal European: the value of being able to choose the exercise date after seeing the rates.
أمثلة
Example 9.6 (A ten-non-call-one receiver)
On chapter 2’s euro OIS curve, with Hull–White at and basis points (chapter 7’s single-volatility fit), a receiver Bermudan at the ten-year par rate of 2.585% exercisable every year from one to nine is worth 358.4 basis points of notional. Its co-terminal Europeans are worth 209.5, 245.3, 249.5, 237.8, 214.1, 184.3, 147.8, 104.3 and 54.9 basis points (tree, within 1.4 of Jamshidian’s formula; Figure 9.1); the most expensive is the three-year. The switch option is worth 109.0 basis points, 44% of the best European.
Example 9.7 (Mean reversion and the switch)
Recalibrating so that the five-into-five European keeps its price, the Bermudan and its switch option depend on (table below): stronger mean reversion decorrelates the rates of successive exercise dates and makes the choice of date more valuable, while the best European barely moves.