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Putting VaR at Work

6 important questions on Putting VaR at Work

What about non-linear derivatives?

Options are non-linear due to their moneyness point! For the same percentage decline in the underlying we see a larger percentage decline for the more levered out-of-the-money option; i.e. change in the value of the underlying is state dependent (for an option the level of moneyness).

Fixed-income securities with embedded optionality?

Delta-gamma or Taylor series does not perform well in the case of derivatives with extreme nonlinearities. Sometimes the coefficient is conditional in the sense that the estimate is for the local sensitivity of prices to rates in the vicinity of the given factor (small changes). Moreover, duration rises normally when interest rates fall, but as interest rates fall further duration starts to fall or flatten as well due to call or prepayment options.

Sharp change in duration may make the duration-convexity approximation weaker. Thereby convexity/curvature alone cannot be used to correct for the change in duration.

Delta-normal vs. Full revaluation?

- Full revaluation: Move one-for-one or one-for-delta with the underlying factor. Pretty straightforward, can be parametric or non-parametric (use appropriate percentage decline at percentile). Computationally burdensome and expensive.
- Delta-normal is delta (linear) or delta-gamma (Taylor Series) approximation. Advantage is that it is inexpensive computationally (opposed to full reval). Works good when trading at par.

Motivation for Structured MC, Stress Testing and Scenario Analysis?

Linearity makes things easy, but practical issues remain with respect to implementation and accuracy of VaR. Example of clear limitation is the value of a straddle (long call and long put). Thing is that the most extreme loss scenario comes from staying close to the current state.

Combining with historical simulation?

Focus on worst outcomes based on current portfolio. Normally the extreme events are assumed extreme valuations, as opposed to extreme movements in underlying risk factors. The latter is what we do here. Unfortunately every crisis has new triggers.

What about WCS, worst-case scenario?

Complementary to VaR. Care more about the magnitude of losses, given that a large loss occurs. Rather than the number of times we should expect it to happen. Key point is that a worst period will occur with probability one, how bad will it be?

WCS gives the distribution of the maximum loss will be.

Caveats:
- Model assumptions/specifics
- Time-varying volatility is ignored (model risk)
- Tail behavior of financial series (understate the likelihood and size of extreme moves), primarily due to issue of correlations.