Question: Suppose the initial margin m0=50% and the maintenance margin m1=30%. The current stock price is $45 per share, and you sell short 1000 shares of

Suppose the initial margin m0=50% and the maintenance margin m1=30%. The current stock price is $45 per share, and you sell short 1000 shares of the stock now. Then you will close the short position when the stock price drops to $40 or when you receive the first margin call whichever comes first. What is the probability that you can close your short position with a loss if the stock price is assumed to be a martingale?

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