# How do I calculate the delta of a convertible bond?

How can I find the delta of a convertible bond to be used for hedging?

• Delta w/r to what, stock price? Apr 26, 2011 at 18:03

• I'm not sure how it takes more information, I didn't provide details for a particular bond, because I was looking for a general formula or explanation on its relation to an option's delta. Apr 26, 2011 at 14:51
• There is no simple formula, as you may gather from the pdf Tangurena gave you. Apr 26, 2011 at 18:03

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…

This is certainly late but in case someone else has the same question, you will need to do a rolling linear regression (StockPx; CBPx) over x days, retrieve the slope. Then multiply that slope to the conversion price. Roughly that is how I do it, and I got to the same result as Bloomberg with their regressed Delta.