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This chapter is from the book

An Integrated View of Risk Management

I have asked myself many times why Paul Samuelson thought studying Black-Scholes was so important. I don’t think it is just for the purpose of pricing options. I think it is because the mathematics of option pricing give us a roadmap to risk management. Risk management, in its simplest terms, is a three-step process:

  1. Think about what might happen in the future.
  2. Know which of those outcomes will hurt you and how likely they are.
  3. Decide what to do about it.

Most people weigh the cost of risk management against doing nothing. If the cost of insurance is too high, you can self-insure. But the factors involved are mainly financial.

In the capital markets, another factor is at work. It is hope, which is related to a historical precedence of mean reversion. Most investors believe that markets that fall will also rise again at some point. If you can suffer the pain, you will be rewarded in the end. Maybe. The turbulence of the 2000–2002 and 2008–2009 markets makes it harder to ignore previous bear markets, and consider the Japanese experience, with a 75% decline in the equity market over a 20-year period.

The desire of investors to impose some downside protection is understandable and requires some form of risk management. The three generally recognized ways to manage risk are diversifying, hedging, and buying insurance, and all are related to options. Diversification can be enhanced through options, delta hedging was the most elegant interpretation of option pricing, and put options are the purest form of market risk insurance.

The process of defining possible future events, assigning probabilities to those events, and using that information to price risk is the same as the process of pricing options. In that sense, option pricing is the central analytic framework for quantitative finance, risk management, and options-related structured securities.

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