Measurement of average continuous-time structure of a bond and bond’s interest rate risk

Abstract

The expected continuous-time structure of a bond and bond’s interest rate risk in an investment settings was studied. We determined the expected number of years an investor or manager will wait until the stock comes to maturity. The expected principal amount to be paid back per stock at time ‘t’ was determined, while assuming that the present value of the stock follows a standard geometric Brownian motion, with constant drift and constant volatility at any time ‘t’. It was found that the higher the value of the expected return from the risky asset, the higher the expected duration of the bond and higher the value of the expected return from the risky asset, the higher the return from the investment. It was also found that the higher the value of the interest rate, the lower the duration and vice versa. When the interest rate of the bond was greater than the expected rate of return from the cash flow, then as ‘t’ become larger, the cash flow grew with bound. The cash flows grew without bound when the expected rate of return was greater than the interest rate from the bond.

Keywords: Bond, average continuous-time, interest rate, risk

International Journal of Natural and Applied Sciences, 6(2): 259-264, 2010