Risk Management and Hedging with Derivatives

A futures hedge neutralizes both sides — upside and downside go together. A purchased option caps the loss at the premium and keeps upside open: it is insurance, not a risk exchange. Selling options earns premium but accepts a fat downside tail; as a hedge it makes sense mainly inside structures (a collar: buy put, sell call) that trade capped upside for cheaper protection. The right choice starts from the loss profile of the real exposure, not from instrument prices.

• Two-sided risk, full removal → futures/forwards sized by minimum-variance ratio.
• Protect from loss, keep upside → purchased put/call (insurance with a known premium).
• Premium too rich → collar or spread (accept capped upside).
• Contractual rate risk → IRS or caps/floors on the reference rate.

VaR at confidence α over horizon h is a single number: the loss not exceeded with probability 1−α. Three routes: historical (empirical distribution), parametric (normal/lognormal with variance-covariance) and Monte Carlo. VaR's structural weaknesses: it says nothing about the tail beyond the cut, and it is not additive. CVaR — the mean loss in the worst 1−α — fixes both to a large degree and is coherent under distribution shape. Stress testing inverts the question: 'if this scenario happens, what is the loss?' — and because you build the scenarios, it sees what VaR cannot by definition.

No metric is a 'maximum possible loss'. Tail events, correlation breakdowns and regime shifts outrun every linear, normal model. Metrics are maps, not walls — position sizes must survive leaving the map.