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PILARA SHOULD HAVE NOT STARTED THIS_DERIVATIES AS INSURANCE PRODUCTS
To understand hedging whether static or dynamic treat it as an insurance. You purchase stock then an option in that stock.preferably a put.you are assured that(ensured that) the return will never be lower than the exercise on the put.you may fail to replicate the put in this case you use a synthetic put(the all famous black-scholes becomes useful) Black-scholes will give you whether you exercise call>underlying or put<underlying. If you know loss models you will see tht BS is a loss model function.Also it is cadlag and using hitting from the right or left you cn define it as a cumulative function. If you take discrete points within a ball centred an (x,y,t) and convergence theorem(time to exercise which is difficult for american options) then you see that you have a distributive function.Now you can describe the survival function.This will take you to the mathematics of insurance applying the actuarial function nPq (n and q are subscripts).DO i have you interested enough?. You need derivatives,and analysis and statistics to see the transition clearly.Also at exercise you may think you function as either truncated from above or below use that you still end with a cumulative function. Once you that define the corresponding 1-F(x) survival and run with the survival function. Applying Insolvency2 rules you arrive at the rules for novation of counterparties even though they dont call em that. So there is a clearing house and these can be OTC.....
insolvency 2 rules can be defined in a mathematical sense.e.g To require a company to honour all its financial obligations can be seen as a 1-1 function(1 claim one paychque)(one to many if you want to make it complex)This ensures you have a finite solution space which is not degenerate