Let B be the price of a perpetual bond. For a perpetuity the price is equal to the rate of payment per year divided by the rate of interest per year (assuming the payment frequency and interest conversion frequencies are the same). Assume the bond's payment rate is $1 per year payable continuously (this is the interest or coupons paid by the bond). The yield rate on the bond is x per year compounded continuously. The price of the bond is therefore B : 1/x. As x changes the price of the bond changes, which generates capital gains/losses. Assume that x follows the process: - dx = a(xo x)dt + sxdz where a, xo and s are constants. a) Find the process followed by the bond price. b) What is the expected instantaneous return (including interest and capital gains) to the bond holder? Let B be the price of a perpetual bond. For a perpetuity the price is equal to the rate of payment per year divided by the rate of interest per year (assuming the payment frequency and interest conversion frequencies are the same). Assume the bond's payment rate is $1 per year payable continuously (this is the interest or coupons paid by the bond). The yield rate on the bond is x per year compounded continuously. The price of the bond is therefore B : 1/x. As x changes the price of the bond changes, which generates capital gains/losses. Assume that x follows the process: - dx = a(xo x)dt + sxdz where a, xo and s are constants. a) Find the process followed by the bond price. b) What is the expected instantaneous return (including interest and capital gains) to the bond holder