Question

The book says: If risk-free rate rises, time value of option declines. Why?

Answer 1

Any change in Interest rate has an impact on the overall economy, stock market, bond market and other financial markets. Change in interest rates also impacts option valuation which is computed based on multiple factors, including the price of the underlying asset, exercise or strike price, time to expiry, risk-free rate of return (interest rate), volatility, and dividend yield. These variables which are used in computation of option price are unknown variables that can change until the time of an option's expiry.

Option pricing is a complex process. Multiple factors impacts the option valuation, which can lead to very high variations in option prices over the short-term. Call option and put option premiums has an inverse impact when interest rates change. However, option pricing is more sensitive to changes in other input parameters, such as underlying price, volatility, time to expiry, and dividend yield than the changes in interest rates.

Thus, When interest rates increase, call options benefit while put option prices are impacted negatively.

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