Monte Carlo VaR for Option Positions Using Theoretical Values

Summary

The document raises a practical question about estimating value at risk for a portfolio of options. Its proposed approach is to simulate future underlying prices, revalue the options theoretically at each simulated price, and examine the resulting distribution of position values. The example concerns an at-the-money call option, and the author asks whether VaR can be read from that distribution.

The text does not provide a worked calculation, model assumptions, or a resolution to the question. It therefore serves mainly as a prompt about translating simulated underlying moves into option portfolio risk. The distribution of option values may be harder to interpret than the underlying price distribution because option values respond nonlinearly to the underlying and can also depend on other pricing inputs. The document does not specify how those inputs are treated, the confidence level or horizon, or how the option pricing model is calibrated, so it offers no empirical evidence or validated VaR result.

Key ideas

• Simulating underlying prices and repricing options can produce a distribution of option position values.
• The document asks whether that distribution can be used directly to estimate VaR.
• Option value distributions may be less intuitive than underlying price distributions because option payoffs are nonlinear.
• The text leaves model assumptions and treatment of other pricing inputs unspecified.

Tags

# Simulating Option Positions VaR with Monte Carlo in Python


# Simulating Option Positions VaR with Monte Carlo in Python












I'm trying to calculate VaR for overall option positions. Currently I do a MC simulation for the underlying, and derive the theoretical value of the option from those theoretically. Then I calculate what the position is worth in relationship to the simulated underlying price. Can I then say what the VaR is from the theoretical options prices?

This is where I am now, but my VaR numbers don't seem as understandable as the plain underlying calculations. The distribution is my value of the ATM call option.

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