The Black-Scholes-Merton (BSM) model is not suitable for valuing derivatives on fixed-income securities due to several assumptions it makes. These assumptions include: (I) The model assumes there is no upper limit to the price of the underlying asset. This is not true for bonds, which have a maximum value. (II) The model assumes bond price volatility is constant. However, bond price volatility decreases as maturity approaches since bonds are redeemed at par. (III) The model assumes the risk-free rate is constant. In reality, short-term rates do change, causing rates along the yield curve and bond prices to change. Therefore, all the options listed are correct, making choice D the correct answer.

Choice A is incorrect. While the BSM model does assume that there is no upper limit to the price of the underlying asset, this assumption does not make it unsuitable for valuing derivatives on fixed-income securities. This assumption applies to all types of assets, not just fixed-income securities.

Choice B is incorrect. The BSM model assumes that volatility is constant, but this assumption isn't specific to bond price volatility. It's a general assumption made for all underlying assets in the model, and it doesn't specifically contribute to its unsuitability for valuing derivatives on fixed-income securities.

Choice C is incorrect. The BSM model does assume a constant risk-free rate over time; however, this isn't an issue exclusive to fixed income derivatives valuation. This limitation affects all derivative pricing under the BSM framework and doesn't specifically make it unsuitable for valuing derivatives on fixed-income securities.

Things to Remember

• Fixed-Income Securities: These are investments that provide a return in the form of periodic interest payments and eventual return of principal at maturity. Because of characteristics like a finite maturity value and declining price volatility over time, BSM assumptions generally do not hold well for them.