Monte Carlo VaR for Derivatives: Full Revaluation and Sensitivity Methods
Summary
The document discusses how to include swaps, FX forwards, and other non-equity derivatives in Monte Carlo Value at Risk simulations. It contrasts sensitivity-based approximations with full revaluation under simulated market scenarios. Sensitivity methods remain common, though the answer says they are becoming less favored as computing capacity improves. For risk-control VaR, full revaluation is presented as feasible for most products; for time-sensitive front-office use, a hybrid approach may revalue exotic positions fully and approximate others with sensitivities.
For linear instruments and vanilla options, the proposed workflow identifies risk drivers, simulates shifts in market quotes, recalibrates curves or volatility surfaces when those quotes are used as factors, and reprices positions. Nonlinear or multi-factor exposures may require gamma and cross sensitivities as well as delta and vega. Recalibrating and simulating complex products inside each outer scenario creates nested simulation cost. The answer mentions least squares Monte Carlo as a rare alternative that can reuse information across scenarios; it does not provide implementation details or comparative performance evidence.
Key ideas
- Sensitivity-based VaR approximations remain common, while full revaluation is often practical for risk-control use.
- A hybrid workflow can fully revalue exotic instruments and approximate other positions with sensitivities.
- Market risk drivers should be simulated, with curves or volatility surfaces recalibrated when built from simulated quotes.
- Nonlinear and multi-factor exposures may require gamma and cross sensitivities in addition to delta and vega.
- Nested calibration and simulation can be costly, and least squares Monte Carlo is mentioned as a possible way to reuse scenario information.
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Full text
# How are non-equity derivatives handled in monte carlo Value at Risk simulations # How are non-equity derivatives handled in monte carlo Value at Risk simulations If you have a portfolio of stocks and options it's straight forward enough to generate correlated stock paths and evaluate the positions at the end of the time horizon, but what do you do if your portfolio also consists of other derivatives like swaps, FX forwards etc. I know you can calibrate stochastic processes to short rates as well but that seems far too convoluted to be practically feasible. What are some alternatives? ## Answer by Kermittfrog (score 1) https://quant.stackexchange.com/a/53698 In practice, using sensitivity based methods (i.e. those methods @python_enthusiast mentioned in his comment) is still quite common, but it is going out of fashion. Given today's technical infrastructure (parallelisation, fast codes etc.) a risk simulatoin under full revaluation is - for most of the products - quite feasible in a risk controlling type Value of Risk context. Of course, this does not hold for front office applications, where a speedy calculation is of the essence. In that case, you may either do full reval of your (highly) exotic stuff, only; or you indeed implement some sensitivity based approximation. This should commonly entail not only Deltas and Vegas, but also Gammas / cross effects for all products that are materially affected by non-linearities / multiple risk factors. Re your comment to this answer: For linear / market instruments like bonds, fix/float swaps, float/float swaps, vanilla options etc., risk is usually calculated by - Identification of the risk drivers. This could be parallel swap rate shift, a node-level swap rate shift, node-level swap rate shifts across multiple swap curves, ATM vola shift, parallel vola shift, shift of all vola points, ... - Then, simulate the shift of each risk factor - If you use market quotes as risk factors, re-run your calibration for curves, vol surfaces etc. - (*) If you have a highly non-vanilla instruments, then you need to calibrate those as well, of course. But you may want to reduce the number of effective parameters for recalibration, e.g. you could keep correlations constant - Price under the scenario. The problem with (*) is that this is a nested simulation. Under each 'outer' scenario produced in step 2, you need to a) calibrate and b) simulate. Another approach I have seen in the market (once, at most -_-) is to make use of LSMC (least squares monte carlo originally in Longstaff / Schwartz), where you can 're-use' information from the outer scenarios for the inner simulation.
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