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Dear all,
though I haven't started university yet, I have started reading an introductory book called: A Course in Derivative Securities by Kerry Back. On page 12 they mention the following:
The delta of the call option is \(\delta = (C_{u} - C_{d}) / (S_{u} - S_{d})\) and then they rewrite this to \(\delta S_{u} - C_{u} = \delta S_{d} - C_{d}\), where \(S_{u}\) is the stock price in the "up state", \(S_{d}\) for the "down state" and \(C_{u} = max(0, S_{u} - K)\), \(K\) is the exercise price.
Now I am wondering, besides from the math, why is it intuitive that \(\delta S_{u} - C_{u} = \delta S_{d} - C_{d}\) on day 0. Does this also hold on any other day? If so, could someone intuitively tell me why (I get the derivation though, but I lack the deeper understanding of why).
Thanks a lot!
though I haven't started university yet, I have started reading an introductory book called: A Course in Derivative Securities by Kerry Back. On page 12 they mention the following:
The delta of the call option is \(\delta = (C_{u} - C_{d}) / (S_{u} - S_{d})\) and then they rewrite this to \(\delta S_{u} - C_{u} = \delta S_{d} - C_{d}\), where \(S_{u}\) is the stock price in the "up state", \(S_{d}\) for the "down state" and \(C_{u} = max(0, S_{u} - K)\), \(K\) is the exercise price.
Now I am wondering, besides from the math, why is it intuitive that \(\delta S_{u} - C_{u} = \delta S_{d} - C_{d}\) on day 0. Does this also hold on any other day? If so, could someone intuitively tell me why (I get the derivation though, but I lack the deeper understanding of why).
Thanks a lot!
