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Risk Management and Financial Institutions, 4th Edition by John C. Hull

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CHAPTER 7 Valuation and Scenario Analysis: The Risk-Neutral and Real Worlds

Valuation and scenario analysis are two important activities for financial institutions. Both are concerned with estimating future cash flows, but they have different objectives. In valuation, a financial institution is interested in estimating the present value of future cash flows. It does this by calculating the expected values (i.e., average values) of the future cash flows across all alternative outcomes and discounting the expected values back to today. In scenario analysis, a financial institution is interested in exploring the full range of situations that might exist at a particular future time. Usually, it is the adverse outcomes that receive the most attention because risk managers working for the financial institution are interested in answering the question: “How bad can things get?”

Suppose that a company sells one million one-year European call options on a stock. The stock price is $50 and the strike price is $55. The company might calculate the theoretical value of the options as +$4.5 million to the buyer and −$4.5 million to itself. If it sells the options for, say, $5 million, it can book $0.5 million of profit. But a scenario analysis might reveal that there is a 5% chance of the stock price rising to above $80 in one year. This means that there is a 5% chance that the transaction will cost more than $20 million, after the initial amount received for the options has been taken into ...

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