medium · FRM Part 1 Valuation and Risk Models
A risk analyst is comparing a 10-step tree and a 100-step tree to value an American option.
Why is the 100-step tree generally preferred despite the higher computational cost?
- Volatility can only be correctly modeled when the tree has a very large number of steps
- The risk-free rate r must be set to zero for a small binomial tree to produce theoretically valid prices
- It provides a better approximation of the continuous price process and the early-exercise boundary
- The risk-neutral probability p is only mathematically valid for trees built with more than fifty discrete steps
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