Explanation

When interest rate models forecast negative short-term interest rates, the most appropriate and commonly used approach is to set the interest rate to zero (Option C). Here's why:

Why Option C is Correct:

1. Economic Reality: Negative interest rates are theoretically possible but practically problematic in many markets. Setting rates to zero creates a lower bound that reflects the economic reality that nominal interest rates cannot go significantly negative.

2. Model Stability: This approach prevents the model from generating unrealistic negative values that could distort option pricing calculations.

3. Industry Standard: Many financial institutions and risk management frameworks use zero floors in interest rate models to handle this issue.

Why Other Options Are Incorrect:

• Option A (Adjusting risk-neutral probabilities): This would fundamentally change the pricing framework and could introduce arbitrage opportunities.
• Option B (Increasing volatility): This would exacerbate the problem by making extreme negative rates more likely.
• Option D (Setting mean-reverting parameter to 1): While mean reversion helps, setting it exactly to 1 doesn't guarantee prevention of negative rates and may not be the most direct solution.

Additional Context:

In interest rate modeling, particularly with models like the Cox-Ingersoll-Ross (CIR) model or Black-Karasinski model, practitioners often implement zero floors or non-negative constraints to prevent negative interest rate scenarios that are economically unrealistic in many contexts.