# equity/bond calls in relation to interest rates

I am trying to understand the differences in call values between the ‘calls in equities’ and ‘call-embedded options in bonds’. Bonds: We know that an increase in interest rates decrease the values of both call and put options of an option-embedded bond. Similarly, a risk free rate rise in the bond will decrease the value of both options. Increase in price volatility, however, will increase the value of both the put and the call. Equity: If risk free rate rises, value of put on equities will decrease and value of call will increase. This can be determined using a put-call parity equation. And a rise on price volatility will increase the value of both the put and the call. The call/put relationships between equities and bonds seem to be similar except for the calls: during a rate rise, a value of a call in a callable bond will decrease while a call option on an equity will increase. Can someone please explain the relationship that makes them different? Is there something else that I am missing?

There are two issues here that you are getting confused. One is the effect of interest rates on the value of the option itself without regard to its underlier. This is called rho. The other is the effect on the value of the underlier when interest rates move causing the option to have a different value. This is delta. The key messed up sentence is "We know that an increase in interest rates decrease the values of both call and put options of an option-embedded bond. " An increase in interest rates has two effects on the embedded call option. The first is the rho effect which in some non-interest rate sensitive asset says that as interest rates go up you would rather own a call and keep your cash in interest bearing assets than own the asset, so the call value increases. On the other hand, when interest rates increase the bond become worth less money so the call option is less likely to be exercised thus decreasing its value. This is the delta effect. Note that delta and rho are pulling the embedded call in different directions. I believe that delta always overwhelms rho in bond options, although I guess you could invent some crazy option for which this wasn’t true.

Thanks for articulating the concepts…I do have follow up questions on the applications of rho and delta but will wait after the exam.

Actually, you will have plenty of chance to explore those on Level II.