The rates in the original tree are referred to as the shadow rates of interest, while the adjusted rates in the tree are known as the observed rates of interest. The term 'shadow rates' is used to describe the rates in the original tree because they represent the underlying or 'shadow' rates that would exist in the absence of the zero lower bound constraint. On the other hand, the adjusted rates, which are set to zero in the case of negative rates, are referred to as 'observed rates' because they are the rates that are actually observed in the market after the adjustments have been made. When the observed rate hits zero, it would 'stay put' until the shadow rate crosses back to a positive rate. This method of dealing with negative interest rates is commonly used in financial modeling and risk management.

Choice A is incorrect. While it is true that the rates in the original tree can be considered as volatile market rates, the adjusted interest rates are not referred to as expected rates of interest. The term "expected rate of interest" does not accurately reflect the adjustments made to mitigate negative interest rates.

Choice B is incorrect. This choice incorrectly labels both types of rates. The original tree does not necessarily represent volatile market rates and the adjusted ones are not called shadow rates of interest. Shadow rate refers to a hypothetical rate that would exist if there were no lower bound on nominal interest, which doesn't align with this context.

Choice C is incorrect. It inaccurately categorizes both types of interests in this context. The original tree's interests aren't specifically short-term and again, shadow rate isn't an appropriate term for adjusted interests in this scenario.

Things to Remember

• Interest Rate Trees: These are graphical representations of possible interest rate movements over time, typically used in option pricing and risk management.
• Zero Lower Bound Constraint: This refers to the situation where nominal interest rates cannot go below zero (or are bounded), prompting the use of shadow rate models.