🏦 Stock Option Risk-Free Rate

Definition

The risk-free rate is the theoretical return on an investment with zero risk of financial loss.
In options pricing models like Black-Scholes, it typically refers to the yield on short-term government securities (e.g., U.S. Treasury bills).

Why It Matters

• Option Valuation: The risk-free rate affects the present value of strike prices and premium calculations.
• Rho Sensitivity: Changes in the risk-free rate impact the rho of an option—its sensitivity to interest rate shifts.
• Model Accuracy: Using an appropriate risk-free rate ensures realistic pricing and hedging strategies.

Example

Suppose the current 1-year U.S. Treasury yield is 4.5%. This rate would be used as the risk-free rate in pricing a 1-year call or put option.
A higher risk-free rate increases the value of call options and decreases the value of put options, all else being equal.

Key Insights