Quote from dd4nyc:
X-axis is the strike.
Blue line is the price of a call option (I picked some parameters like stock at $100, 1 month to expiration and 30% vol )
Red line is 100 - strike .
The point where two curves intersect is your "golden strike" , C(X,T,K*)=K*-X
I don't really see how you can have an analytical solution for K*, even in the case of Black-Scholes. I think you would have to just use a numerical method, but you obviously came up with something different. Guess your math is better than mine. Could you explain how you figured this out and what it has to do with the golden number?
By golden number I assume you refer to golden ratio, 1.618 ... ?
You have a good intuition, and that is what's most important. It is probable that I have more math tools than you, but human intelligence is greater than all tools.
By the way the golden number does not appear in the solution formula, it appears somewhere else. That somewhere else is the thing I want to keep in the inside for the moment. If I were to say where the number is at this point, I will also reveal some of the edges that I am building. I may share some of all of the information in the future with a select group. If so, I will be happy to put you in that group.
Let me make some remarks:
1. The golden strike will always be out of the money (because premium is positive, therefore K*-X is positive because of the equality, which means K* greater than X).
2. There is only one Golden strike per expiration.
2. You are right that one does not need a formula. There are approximation however. If computed numerically, one can do so for instance in log (I) steps, where I is an interval that brackets K*. For instance even if the largest strike is 1000, you can do it in less than 10 steps for sure, at each point you zero in on the K*. Your graphical representation is even better as it is visual. The calculation of K* is however not what is most important.
3. You asked of examples that might be useful. I will give this quick example.
Suppose that you held stock, and you wanted to write a covered call. Suppose further that you are bullish, but you believe that the stock will behave in a random manner and therefore not sure where it will end at the end of expiration. You want to take some profits by writing a call, and keep space for the stock to move. If K is the short strike, then C(K) is the call sale proceeds, and K-X is what you would hope to make from the movement of the stock. If you decide to split your potential profits equally, then the short strike is the golden strike.
Note that if you weight them equally then the golden strike minimizes the sum of the areas under the two curves. The area of the call has to be measured right to left, and the other from left to right.
The covered call is not the reason I was interested in it, but knowing the properties associated with that strike help understand many things. So, obtaining the value of K* is not what most important, but rather studying its behaviour, its relation to other strikes, and across other variables, etc, etc, that is more important.
I agree that to see some "hidden things", mathematical analysis is an advantage, but I also think the combined wisdom and knowledge of a forum is more powerful than what a single individual can achieve alone.
I noticed that you have just a few posts under your belt? May I ask what got you interested in this question. You are the only one who responded so far, so I am guessing that the majority may not have seen an interest in this topic for themselves.
Look forward to your response.
