Does IR volatility and Price volatility have the same effect on value of call/put option and callable/putable bond?

Interesting question! Probably good topic for thesis research! =) I don’t think its in our curriculum, right?

We know that higher price volatility would increase call and put option prices. **My guess is** higher IR volatility would also increase call and put option prices, but to a smaller extent. As the curriculum states that *“the price of a (European) option on an asset is not very sensitive to the risk-free rate. When the underlying is an interest rate however, there is a strong relationship between the option price and interest rates”*

Some Googling also reveal that **Scott** ( **1993** ) **finds** that **interest** **rate** **volatility** **has** **little** **impact** on **short** - **term** **options.**

Scott, L.O. 1993, “Pricing Stock Options in a Jump Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods” University of Georgia