# assume higher/lower volatility than reality and how that lead to over under pricing for putable and callable bond

hi can someone help me how the assumed higher/lower volatility than reality and how that lead to over under pricing for putable and callable bond? thanks

As interest rate volatility increases, the value of call options and put options increase.

If you overestimate volatility, you will underestimate the value of a callable bond and overestimate the value of a putable bond.

If you underestimate volatility, you will overestimate the value of a callable bond and underestimate the value of a putable bond.

The two key formulas to remember throughout bonds with embedded options are:

Vc=V-c (value callable=value straight-call)

Vp=V+p (value putable=value straight+put)

Using these formulas, how do Vc and Vp change when volatility changes? (remember volatility=vega from the option Greeks and how does volatility affect options price…?)

The easy way for me to remember this, is to quickly jot down the formulas:

Value of callable bond = Value of straight bond - Value of option

Value of putable bond = Value of straight bond + Value of option

Knowing that the value of the option increases when volatility increases, it’s easy to see its impact on bond valuation.

Edit - krok beat me to it.  