# 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?

• You would calculate the derivative (calculus one) of the other derivatives (financial ones) wrt the stock price movement, and calculate the VaR using that. Edit: covariance matrix and weights in the portfolio also take into account your exposure. Apr 28, 2020 at 20:05
• Isn't the delta of e.g. an interest swap simply zero? Apr 28, 2020 at 20:09
• The interest rate swap's delta is non-zero wrt interest rates. For swaps related to interest rates you will want to look at the duration of the underlying contracts. Apr 28, 2020 at 20:18

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

1. 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, ...
2. Then, simulate the shift of each risk factor
3. If you use market quotes as risk factors, re-run your calibration for curves, vol surfaces etc.
4. (*) 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
5. 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.

• How would a full risk simulation under full revaluation look like though for non-equity instruments. Take an FX forward or interest rate swap, would doing a full revaluation for those entail simulating the exchange rate or the short rate (together with the equities)? how could that be done? Apr 29, 2020 at 6:57
• see my updated answer. HTH? Apr 29, 2020 at 9:45