# Using a Parametric Implied Volatility Surface for Calculating Value At Risk

Value at Risk (VaR) is a widely used risk metric in finance, providing an estimate of the potential loss on a portfolio or investment over a specific time horizon, under normal market conditions. It quantifies the level of financial risk within a certain confidence interval, expressing the maximum loss that might be incurred over a given period.

Calculating VaR for linear instruments is straightforward, but for instruments with convexities, such as options, the process becomes more complex. Reference [1] has proposed a method for calculating the daily VaR of an options portfolio. The authors stated,

In our proposed method, we initiate the process by extracting the volatility surface for each day from option prices. Subsequently, volatility shocks are computed based on historical data on the volatility surface, resulting in a database of projected volatility surfaces. Simultaneously, employing Monte Carlo simulation, we generate next-day prices for the underlying asset. These volatility shocks and next-day prices are then input into the Black-Scholes formula pricing model to obtain forecasts for option prices the following day.

Numerical tests reveal the superior performance of the PSP method, particularly at high confidence levels (e.g., 95%). The DM test emphasizes the effectiveness of localized volatility models over reference volatility, capturing market conditions more accurately. Furthermore, incorporating volatility, regardless of its form (reference or localized), demonstrates potential improvements in forecasting accuracy.

The method essentially begins by calculating daily stock moves using historical data. Subsequently, it determines the distribution of implied volatility associated with each simulated stock price through a method known as Parametric Surface Projection. This generated set of implied volatilities is then utilized to calculate the daily VaR of an options portfolio.

We find this method interesting and think it’s a good complement to analytical methods such as the delta-gamma-vega approach.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Shiva Zamani, Alireza Moslemi Haghighi, Hamid Arian, Temporal Volatility Surface Projection: Parametric Surface Projection Method for Derivatives Portfolio Risk Management, https://arxiv.org/abs/2311.14985v1

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