How can I find the delta of a convertible bond to be used for hedging?
Tangurena's answer and links give the right idea. You can get a rough approximation by finding the conversion price $K$ and using that $K$ as the strike in a standard Black-Scholes option pricer.
In practice, most people work with 3rd party models such as the ones built into Bloomberg, Monis, or Kynex.
To find the delta of a convertible you can apply the basic definition foe the derivative number : lim h->0, P(So+h)-P(So-h)/h, However because a lot of convertible are callable and putable you have to use this formula: P(So+h) - P(So-h) / 2h , with h=0.0001 for instance.
I a not a quant but, the BlackScholes PDE does not work for convertible because the delta hedged portfolio as defined in BS demonstration does not hold for a convertible bond…