# Interest rate volatility impact

If interest rate volatility increases, price of a callable bond increases or decreases? Why?

at increases in volatility, the price of the call option increases, the price of the callable bond should decrease (more is deducted from the price of an otherwise straight bond).

Pcallable=Pnoncallable - Pcall If interest volatility increase, the price of a call option increase and hence Price of a callable decrease

Value of option increases, decreasing price of bond. More of a chance that the bond will be called if the volatility makes rates drop. Bond price is cheaper than a non-callable bond b/c you should be compensated for that risk of losing a high coupon in a low interest rate environment.

works in the opposite direction for a putable bond: put option increase, added to the price of an otherwise straight bond, it increases the value of the putable bond.

map1 Wrote: ------------------------------------------------------- > works in the opposite direction for a putable > bond: put option increase, added to the price of > an otherwise straight bond, it increases the value > of the putable bond. Yes do to the relationship: Pputable= Pnonputable + Pput

Isn’t Call option price fixed at issuance?

The price you will receive for the bond when it is called is fixed, usually at par, may have a premium. But if the bond is called early, you don’t really receive the YTM that you originally thought you would receive b/c the YTM includes coupon reinvestment. ETA, the above is different from figuring in the actual value of the call after you originally bought it if rates start to become volatile.

Simplest way to think of it. Volatility makes both the call and put option worth more (options LOVE volatility). The call is valuable to the bond issuer and the put is valuable to the bond holder. Therefore, you have to pay more for a bond with a put and less for a bond with a call.

I’m confused! Call option price is fixed, say bond sells for \$1000, but may be called at \$1100. The call option is \$100 (it doesn’t change no matter how volatile interest rate are). But some of the explanations above assume that this call option value wil increase, which I don’t follow well. Anyone cares to clarify?

yeah. Interest rate volatility only applies to options. Options (regardless of call or put) are worth more if interest rates volatility shoots up. Interest rate volatility shooting up is not the same thing as interest rates rising. So now, if interest rate volatility is up, the call option is worth more. I.E. your price for callable bond is less, because a price of call option and the price of the callable bond are inversely related.