Why is it for an upward sloping yield cure, call values will be lower, and put values will be higher? Doesn’t an upward sloping yield curve mean short term interest rates are going to go up. That means Rf rate will go up, and Rf rate and Call options have positive relationship, which means call option value will go up?
Another question is, what is one sided duration? It says callables have lower down duration, and putables have lower up durations. What does this even mean?
Thanks.
Ironically this answers the question. Yes - an upward sloping yield curve means rates will rise (i guess if you are assuming pure expectations theory holds). Now if rates go up then that means the option will expire out of the money. Think about it - what company is going to refinance their debt at a higher rate??? Therefore the call option you have “sold” to the company becomes less valuable.
One sided duration is simple - its just the duration of the bond (i.e. the price change for a change in yields) when rates move in the opposite direction that makes the bond’s option attractive to evercise (rates moving up for callable bonds and rates moving down for putable bonds).
For a callable bond, if the option is at the money (i.e. it is advantageous for the issuer to refi their debt) then who is going to pay a significantly higher price for that same bond that is about to be called if rates go down further? Therefore the price change will be larger for an increase in rates for a callable bond and the price change will be lower for the same decrease in rates for that callable bond. Hints the phrase they have lower “downside” (meaning rates going down) duration.
To sum it up the price change for a callable bond with a call option at the money will be lower if rates fall by say 100 bps than if rates rose by that same 100 bps. This is tied together with the concept of negative convexity and the fact that the call option on the bond puts a ceiling on how high the bond’s value will go with a drop in rates.
The inverse is true with putable bonds.
Not exactly.
Rates don’t have to move in a direction that makes the option less attractive.
One-sided duration is just what the name says: you don’t use both an up move and a down move; you use only one:
(P− − P0) / (P0 × Δ_y_)
and,
(P0 – P+) / (P0 × Δ_y_)
But isn’t the point that the rate movement that corresponds with the option being less attractive to exercise (a rise in rates for a callable bond) will have a greater impact on the price change versus the impact of that same rate change that makes the option more attractive to exercise (rates going down on a callable bond)?
Again - if rates move down by 100 bps the price change of a callable bond will be less than if rates move up by that same 100 bps, especially when that option is at/near the money. Hence the phrase - “lower downsided duration”. And again tying in with the concept of negative convexity. You are right just calculating the duration assuming a one direction rate change will mathematically point you to the above logic.
The point is that they’re materially different from each other.
But each one is a one-sided duration.
Thanks guys, I think I have mistaken call options on a stock and call options on a bond for the Risk free rate ?
My pleasure.