I’m currently stuck in proving that for a discount bond: YTM > current yield, with:
$$\text{current yield} = c \frac{100}{P}$$ with $P=100-d$ the price of the discounted bond and $c$ the coupon rate.
With numerical simulations in Python, I’ve seen that indeed the relation is true, but I’m stuck in trying to prove it theoretically.
Here's what I've tried:
I’ve expressed the current yield as a function of YTM and considered the function f(YTM) = YTM – Current Yield.
To prove the relation, my approach was to derivate the function, see that the derivative is positive and then see that YTM – Current Yield > 0 for Current Yield > Coupon Rate.
However, in that approach, the expression I get for the derivative is very complex and cannot be interpreted easily.
Do you have any advice on how to tackle this proof?