LO 11.7: Describe the rationale behind the use o f recombining trees in option

LO 11.7: Describe the rationale behind the use o f recombining trees in option pricing.
In the previous example, the interest rate in the middle node of period two was the same (i.e., 6.34%) regardless of the path being up then down or down then up. This is known as a recombining tree. It may be the case, in a practical setting, that the up then down scenario produces a different rate than the down then up scenario. An example of this type of tree may result when any interest rate above a certain level (e.g., 3%) causes rates to move a fixed number of basis points, but any interest rate below that level causes rates to move at a pace that is below the up states fixed amount. When rates move in this fashion, the movement process is known as state-dependent volatility, and it results in nonrecombining trees. From an economic standpoint, nonrecombining trees are appropriate; however, prices can be very difficult to calculate when the binomial tree is extended to multiple periods.
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Topic II Cross Reference to GARP Assigned Reading – Tuckman, Chapter 7
C o n s t a n t M a t u r i t y T r e a s u r y S w a p

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