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HOW CLOSE ARE THE OPTION PRICING FORMULAS OF BACHELIER AND BLACK–MERTON–SCHOLES?
Author(s) -
Schachermayer Walter,
Teichmann Josef
Publication year - 2008
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2007.00326.x
Subject(s) - black–scholes model , valuation of options , economics , mathematical economics , simple (philosophy) , mathematics , econometrics , financial economics , philosophy , volatility (finance) , epistemology
We compare the option pricing formulas of Louis Bachelier and Black–Merton–Scholes and observe—theoretically as well as for Bachelier's original data—that the prices coincide very well. We illustrate Louis Bachelier's efforts to obtain applicable formulas for option pricing in pre‐computer time. Furthermore we explain—by simple methods from chaos expansion—why Bachelier's model yields good short‐time approximations of prices and volatilities.