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seen Aug 3 '12 at 12:35

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asked Can we replicate a call option without borrowing and make it cheaper in this way?
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comment Why a self-financing replicating portfolio should always exist?
thank you for the answer. My problem is not in the assumptions but in the logic which combines these assumptions to obtain the Black-Scholes PDE. It is OK for me to assume that the stock prices is given by the diffusion process (equation 2) and that the bond is deterministic (i.e. not stochastic). I also can accept the fact that it is always possible to construct a self-financing replicating portfolio. what is not clear is why all that restricts the price of the options (as function of S and t).
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accepted What is a self-financing and replicating portfolio?
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accepted What tools are used to numerically solve differential equations in Quantitative Finance?