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Q. Example on interest rate movements?
Cap/floor volatility is consideration to be higher than swaption volatility because the market buys volatility trough swaptions as well as sells volatility trough cap/floors. Everything else being the similar the bid-ask difference should make cap/floor volatility a little higher.
(a) A callable bond has a higher coupon for the reason that the bond incorporates a short swaption. If rates drop below a level the issuer has the right to call the bond at par. From bondholder's viewpoint this is equivalent to selling a swaption. The choice holder has the right to get into a fixed receiver swap that pays the same coupon at the call date.
This embedded choice will have a premium and this premium will make the coupon of the callable bond higher. Investors may perhaps consider these higher coupons as yield enhancement and buy these bonds. Callable bonds are typically not callable for a certain period after the issue date. Throughout this period the investor will receive the high coupon regardless of the interest rate movements.
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