Analýza dlhopisov s vloženými opciami

This paper deals with the price sensitivity of fixed-income securities to the interest rate changes, expressing a dominant source of financial risk the financial institutions or other market participants manage. The most common modelling technique used by practitioners for measuring and managing the bond price sensitivity is the Macaulay's duration normally expressed in the modified duration form, also known as weighted average maturity of the bond, or the bond price sensitivity to the interest rate changes. Taking into account the fact that the standard concept of the duration has its limitations as the accuracy for small yield changes, a nonparallel shift in the yield curve or option-free bond assumption, we derive and describe the effective duration and convexity models for determining the expected theoretical price of the bonds with embedded options enabling the bond redemption prior to the maturity. To demonstrate computation and effect of the embedded option in a bond contract we use fundamental characteristic of an option-free bond and two most common types of embedded options - call option and put options giving the issuer the right to call or prepay the debt obligation prior to the scheduled principal payment date (call option) or giving the investor the right to require the issuer to purchase the bond at a specified price (put option). To determine the theoretical price of the embedded option rights we use these two methods coupled with the modified Black model to cope with limitation of the traditional Macaulay's duration approach. The results show a significant impact of the embedded options on the effective duration and convexity of fixed income securities.