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Continuous Time Finance( Carr and Dupire, Bloomberg LP and Courant Institute, NYU)

Carr和Dupire的《连续时间金融》讲义及幻灯片

A publicly traded insurer deals exclusively in the Manhattan earthquake market. In the event of a major earthquake hitting New York
City, the insurance giant will have to sell all of its assets to cover theclaims from the policies it sold, all of which expire tomorrow. The
company has no other liability, no employees, and no expenses. Its assetsconsist entirely of U.S. Government bonds, all of which are due to
mature tomorrow, giving the company $100 per share. This cashflowwill be passed on to the shareholders the next day -unless there is anearthquake - with no tax liabilities (due to a special exemption). Thecompany’s share price is $50, with no bid-ask spread, perfect liquidity,and infinite availability for shorting. There is a similarly perfect market for call options on the stock, struck at $90, trading at $4 an option. You are a tax-exempt trader with a great appetite for risk,who can borrow at the risk free interest rate of 0%, with no money of your own. The color-coded federal warning system indicates the threat of an earthquake striking New York City in the next 10 days is below
10%, and you believe it is actually 1%.