# Hedging the Black-Scholes Call Option

Hedging the Black-Scholes Call Option

We demonstrate hedging of a vanilla European call option on stock paying no dividend in the Black–Scholes model. The top picture shows the path of an exponential Brownian motion (actually, a random walk approximation with a very small time step) representing the price of stock (colored red), the strike price of a European call option (colored dark blue), and the values of a hedging portfolio. The hedging portfolio itself, consisting of some stock (colored green) and a short position in a riskless bond (colored red) is shown below. The graph at the lower right shows the "cash flow" from the transactions performed in holding the portfolio. For a perfectly self-financing portfolio this graph ought to be perfectly flat and coincide with the horizontal axis.

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