  The option pricing formula of Black and Scholes (1973) hinges on the
continuous-time self-financing condition, which is a special case of the
continuous-time budget equation of Merton (1971). The self-financing condition
is believed to formalize the economic concept of portfolio rebalancing without
inflows or outflows of external funds, but was never formally derived in
continuous time. As a much bigger issue, however, we discover a timing mistake
in the model of Merton (1971) and show that his self-financing condition is
misspecified both in discrete and continuous time. Our results invalidate
seminal contributions to the literature, including the budget equation of
Merton (1971), the option pricing formula of Black and Scholes (1973), the
continuous trading model of Harrison and Pliska (1981), and the binomial option
pricing model of Cox, Ross and Rubinstein (1979). We also show that Black and
Scholes (1973) and Harrison and Pliska (1981) implicitly assumed their
replication result.
