In probability theory and quantitative finance, a forward measure is a measure that is used to discount future cash flows. It provides a way to value financial assets and derivatives that depend on uncertain future events, such as fixed income securities like bonds.
The main advantage of using a forward measure is that it takes into account the time value of money by assuming a risk-neutral investor who does not require a risk premium for holding an asset. This measure is constructed by assuming that the expected rate of return on an investment is equal to the risk-free rate, which is the rate of return on a risk-free asset such as a government bond.
In fixed income securities, the forward measure is often used for pricing and valuing interest rate swaps, fixed-rate bonds, and other derivative instruments. The forward rate agreement (FRA) is a common application of the forward measure, which is used to hedge against interest rate risk.
For example, let’s say an investor purchases a fixed-rate bond that pays a coupon of 5% p.a. over five years. The bond price would be calculated based on the forward measure that considers the expected interest rates over the next five years. The interest rates are predicted using the yield curve, which is a graph that shows the interest rates for different maturities.
If the forward measure indicates that the interest rates are expected to increase over the next five years, the bond price will be lower than the face value, reflecting the higher interest rates. On the other hand, if the forward measure indicates that the interest rates are expected to decrease, the bond price will be higher than the face value.
In summary, the forward measure is a useful concept in valuation and risk management of fixed income securities. It enables market participants to price assets and derivatives that depend on future events and to manage the associated interest rate risk.