# 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?

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Delta w/r to what, stock price? –  quant_dev Apr 26 '11 at 18:03

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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. –  tshauck Apr 26 '11 at 14:51
There is no simple formula, as you may gather from the pdf Tangurena gave you. –  quant_dev Apr 26 '11 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.

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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…

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