Linear Derivatives VaR Calculator

Estimate VaR for linear derivative portfolios with covariance. Enter exposures, volatilities, correlations, and horizon clearly. Review deviation, variance, and tail loss with downloads today.

Calculator Inputs

Linear Risk Factors

Enter exposure as delta adjusted monetary sensitivity. Volatility and mean use percent form.

Factor 1

Factor 2

Factor 3

Factor 4

Factor 5

Correlation Matrix

Use values from -1 to 1. Matching off diagonal cells are averaged.

Factor Equity Index Interest Rate FX Rate Credit Spread Commodity
Equity Index
Interest Rate
FX Rate
Credit Spread
Commodity

Example Data Table

Factor Exposure Volatility % Mean % Use Case
Equity Index 120,000 1.40 0.02 Index future or delta exposure
Interest Rate -75,000 0.70 0.00 Swap duration hedge
FX Rate 45,000 0.90 0.01 Currency forward exposure
Credit Spread 30,000 1.10 0.00 Credit derivative sensitivity
Commodity -25,000 1.80 0.03 Commodity hedge position

Formula Used

Linear portfolio change: ΔV = bTΔx

Portfolio variance: σp2 = bTΣb

Portfolio deviation: σh = √(bTΣb × time)

VaR: VaR = max(0, zασh − expected P&L)

Expected shortfall: ES = σhφ(zα) ÷ (1 − α) − expected P&L

Here, b is the exposure vector. Σ is the covariance matrix. α is confidence. φ is the normal density.

How to Use This Calculator

  1. Enter the confidence level for the VaR tail.
  2. Enter the holding period in days.
  3. Select daily or annual volatility basis.
  4. Add each linear derivative exposure.
  5. Enter volatility and optional mean return values.
  6. Fill the correlation matrix carefully.
  7. Press Calculate VaR to view results above the form.
  8. Use CSV or PDF buttons to save your output.

About Linear Derivative VaR

Linear derivative VaR measures possible loss for positions with near linear payoff behavior. It fits swaps, forwards, futures, and delta based option approximations. The method uses sensitivities, volatilities, correlations, and a chosen confidence level. It converts them into a single tail loss estimate for a selected holding period.

Why This Method Helps

Many derivative desks need a quick risk view before deeper simulation. A linear model is transparent. Each exposure shows how one risk factor affects portfolio value. The covariance matrix then combines single factor risk and diversification. This makes the result useful for review, limits, and scenario planning.

Key Inputs

Exposure is the value change for a one unit return in a factor. Volatility measures factor uncertainty. Correlation describes how factors move together. Horizon scales risk through time. Confidence selects the statistical tail. A higher confidence level gives a larger VaR. Mean return can adjust the estimate when a drift assumption matters.

Reading The Output

Portfolio variance is the core matrix result. Standard deviation is its square root. VaR is the selected tail multiple of that deviation. Expected shortfall estimates average loss beyond the VaR point. Risk contribution shows which factor drives the total number. Negative contribution can appear when hedges reduce risk.

Practical Notes

This calculator assumes normally distributed linear changes. Real markets can have jumps, skew, liquidity gaps, and basis risk. Nonlinear options may need gamma, vega, or full revaluation. Stress testing is still important. Use VaR as one risk lens, not a complete decision rule.

Good Workflow

Start with clean exposure mapping. Use consistent daily or annual volatility inputs. Check every correlation value. Compare the example table with your own portfolio. Review risk contribution before accepting the total. Large concentrations may hide inside a small diversified result. Save the CSV for audit notes. Use the PDF when sharing summary results with a team.

Validation Checks

Review signs before trusting results. A long asset exposure and a short hedge should offset. If correlation is one, combined risk may rise. If correlation is negative, risk may fall. A zero volatility factor adds no variance. A negative variance means inputs are inconsistent, so the calculator floors it at zero for display. Check inputs once more.

FAQs

What is VaR for linear derivatives?

It is an estimate of possible portfolio loss for derivatives whose value changes approximately linearly with market factors. The method uses exposures, covariance, confidence, and time horizon.

Which derivatives fit this calculator?

It works best for forwards, futures, swaps, and delta approximated options. Strongly nonlinear options need gamma, vega, or full revaluation methods.

What does exposure mean here?

Exposure means the monetary change in portfolio value caused by a one unit return in the selected risk factor. It may be delta adjusted notional.

Should I use daily or annual volatility?

Use daily when your volatility inputs are daily. Use annual when the inputs are annualized. The calculator scales the selected basis to the holding period.

Can correlations be negative?

Yes. Negative correlation can reduce portfolio risk when exposures offset. Use values between -1 and 1. Check the matrix before trusting results.

Why is expected shortfall included?

Expected shortfall estimates the average loss beyond the VaR point. It gives extra tail information and can support stronger risk review.

Why can contribution be negative?

A negative contribution can appear when a factor hedges other exposures. This usually means it lowers total portfolio variance under the entered correlations.

Is this calculator a complete risk model?

No. It assumes linear exposure and normal changes. Add stress tests, scenario analysis, liquidity review, and nonlinear valuation when positions require deeper analysis.


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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.