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Elements of Financial Risk Management, 2nd Edition by Peter Christoffersen

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11. Option Risk Management
In this chapter, we incorporate options into the portfolio risk model. The nonlinear payoff in options creates asymmetry in the portfolio return distribution, even if the return on the underlying asset follows a symmetric distribution. Getting a handle on this asymmetry is a key theme of this chapter. We first establish a delta-based approach to portfolio risk management. The idea behind this approach is to linearize the option return using the option delta but unfortunately it ignores asymmetry. We next use the gamma of an option to construct a quadratic model of the portfolio return distribution that can capture asymmetry. We finally measure the risk of options using the full valuation method, which relies on an accurate ...

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