| Abstract: |
| We study the convergence of the price of European options when the
underlying asset is approximated by a general class of binomial trees. We
show that under mild conditions, when the payoff is a $C^{1}$ function, the
convergence is smooth and occurs at a rate of $1/n$. More importantly, we
find an expression for the coefficient of $1/n$ in terms of the derivatives
of the price in the Black-Scholes model. Using a known formula for call
options, we extend our formula to payoffs which are merely continuous. |
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