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Suppose we follow the assumptions of the Black-Scholes Model, including unlimited borrowing, continuous prices, and frictionless markets. For simplicity assume the risk-free rate is 0.

In this world, why can we not construct a call option at strike K (assume K>S) by doing the following (assume K=100 for this case):

1) If stock price (S) hits 100, borrow money and buy stock.

2) If stock price then falls below 100, sell stock at 99.999999 (=100) and return money (continuous price assumption).

3) If stock price never hits 100, do nothing.

In theory, this generates the same payoff as a call option, but for free. Assuming we are in the world of the Black-Scholes assumptions, where does this argument break down?


marked as duplicate by vonjd, skoestlmeier, Bob Jansen Apr 29 at 7:40

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  • $\begingroup$ This is called the The Stop-Loss Start-Gain Paradox and is the subject of a famous article, linked and discussed here quant.stackexchange.com/questions/38582/… In a nutshell the issue is that the "self-financing condition" is not satisfied. $\endgroup$ – noob2 Apr 28 at 21:47