so i came across this solution,
A callable bond is made up of a straight bond and a written call option. An increase in volatility increases the value of the call option and decreases the value of the callable bond. On the other hand, a putable bond is made up of an option-free (or straight) bond and a long put option. An increase in volatility increases the value of the put option and therefore increases the value of the putable bond.
don’t really understand how an increase in volatility increases a putable bond’s value but decreases a callable bond’s value using this.
thanks in advance!
Let me try this. If volatility is high, prices (and interest rates) will fluctuate more often and in greater proportions. A put option gives the right to the security holder to “return” “sell back” the security if the price falls below a certain threshold (the strike price). The put option is a protection to the bondholder. In times of high volatility (uncertainty), bondholders will be more willing to protect themselves against price declines, which will increase the demand of putable bonds (bonds with protection against losses), and therefore, the price of these putable bonds will increase.
“Don’t really understand how an increase in volatility increases a putable bond’s value but decreases a callable bond’s value using this.”
I think it has to do with this:
Put-Call Parity of European Options
c + K·e^–rT = p + S0
c — the European call option price,
p — the European put option price,
S0 — the current stock price,
K — the strike price at maturity,
e — the mathematical constant number with value of approximately 2.71828,
r — the risk-free interest rate,
T — the time to maturity,
e–rT — the discount rate for the strike price K,
K·e^–rT — the present value of the strike price today, which is expressed sometimes as K·B or PV(K).
If volatility is high (K·e^–rT) will be high. Call and Put values will be affected this way (based on the above equation):
c = p + S0- K·e^–rT – If K·e–^rT is high, call value decreases
p = c -S0 + K·e^–rT – If K·e–^rT is high, put value increases
Refer to this link for example problems:
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