[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have...

A 'hard call protection' means the bond cannot be called until a certain date, regardless of what the share price is. Therefore statement I is false. Also note that a 'soft call protection' means that a bond can be called only if the share price reaches a certain threshold.

It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price - because these shares can instead be sold in the market at the higher share price than the lower conversion price. Statement II is true.

When the issuer's share price is very high, the convertible bond trades at a discount to the share price because it is almost certain to be called by the issuer and be redeemed at par. Therefore statement III is right. Statement IV is incorrect because convertible bonds need to pay less coupon than equivalent non-convertible bonds because of the value of the option embedded in them.