Interest rates bond prices, relationship with

The convexity is a more correct measure of the price sensitivity. It measures the curvature of the price-yield relationship and the degree in which it diverges from the straight-line estimation. Like the duration, the standard measure of convexity does not consider the changes of market interest rates on bond s prices. Therefore, the conventional measure of price sensitivity used for bonds with embedded options is the effective convexity. It is given by (11.2) ... 

The two most common types of embedded options are call (or prepay) options and put options. As interest rates in the market decline, the issuer may call or prepay the debt obligation prior to the scheduled principal repayment date. The other type of option is a put option. This option gives the investor the right to require the issuer to purchase the bond at a specified price. Below we will examine the price/yield relationship for bonds with both types of embedded options (calls and puts) and implications for price volatility. 

This section describes the relationships among spot interest rates and the actual market yields on zero-coupon and coupon bonds. It explains how an implied spot-rate curve can be derived from the redemption yields and prices observed on coupon bonds, and discusses how this curve may be used to compare bond yields. Note that, in contrast with the common practice, spot rates here refer only to rates derived from coupon-bond prices and are distinguished from zero-coupon rates, which denote rates actually observed on zero-coupon bonds trading in the market. 

A rise in interest rates increases the value of most call options. For stock options, this is because the equity markets view a rate increase as a sign that share price growth will accelerate. Generally, the relationship is the same for bond options. Not always, however, since in the bond market, rising rates tend to depress prices, because they lower the present value of future cash flows. A rise in interest rates has the opposite effect on put options, causing their value to drop. The risk-free interest rate applicable to a bond option with a term to expiry of, say, three months is a three-month government rate—commonly the government bond repo rate for bond options, usually the T-bill rate for other types. 

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