Option valuation toolkit

Four option problems recur in valuation work.

Employee options are a claim on equity. They have to be priced and subtracted before you divide by shares. The equity of a deeply indebted firm behaves like a call option on the firm's assets, which is why a stock keeps trading after a discounted cash flow model says the company is worth nothing. A patent, a licence or an undeveloped reserve can carry value that a static DCF misses. And some options get exercised early, which a European formula cannot see.

The arithmetic here is exact. The inputs usually are not. When the underlying asset does not trade, no replicating portfolio can be built and no arbitrage disciplines the answer. Treat the output as an estimate with a wide band around it, and never quote it to the dollar.

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