• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering. Learn more Join!
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Learn more Join!
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models. Learn more Join!

Dual Delta - probability of exercise?

Hi all,

I am working on a project in the field of Convertible Bonds. Based on the paper by C.M. L.R.J. Rogalski and J.K. Seward (1996), I want to determine whether I can classify a convertible bond as debt or equity like. I currently replicate the embedded option of the convertible bond by creating an american option. To get the probability to exercise, I obtain the dual delta, rather than looking at the delta (due to the option/convertible bond's long maturity). The dual delta defined as: \[ \frac{\delta C}{\delta K} \]
I obtained the dual delta for my whole data sample and notice all values range (roughly) between -0.2 and -0.3. If I understand the dual delta correctly, this would imply that the exercise probability of the option is between 20-30%. According to the paper mentioned above, this would make these convertible bonds debt-like (<40% = debt-like, 40-60% in between, >60% = equity-like). What bugs me is that I have seen the method of the paper above applied in numerous papers, and for all of them they find majority of their convertible bonds to be equity like (over 95% of their data sample is equity like) with a exercise probability averaging around 80%.

My question is as follows:
1. Am I applying the dual delta correctly? Does it indeed give me the exercise probability similar to the paper, or am I actually retrieving a completely different aspect of the option?
2. Am I reading the values correctly. Does -0.3 indeed tell me it is 30% probability of exercise, or should I actually read it as 1-30% = 70% probability exercise..?

Below the formula by C.M. L.R.J. Rogalski and J.K. Seward (1996) (see page 9), I am aware this is based on a European call option, but results shouldn't differ as I assume my convertible bonds (and thus the option aswell) to not be dividend paying.