Extending Monte Carlo VaR to Portfolios with Stocks, Bonds, and Options

Summary

The document asks how to extend a Monte Carlo portfolio Value at Risk calculation to holdings from different asset classes, using a stock, a Treasury bond, and an option as examples. It refers to a simulation approach involving correlated random returns and Cholesky decomposition, then asks whether bond duration and option Greeks such as delta and gamma should be used to represent the positions. It provides no worked solution, portfolio valuation method, or simulation results.

The central issue is how to express each holding’s risk under simulated market changes so that the portfolio can be revalued consistently. The question points toward combining equity price changes, interest-rate sensitivity for the bond, and nonlinear option sensitivity, but does not specify assumptions about return distributions, yield curves, volatility, or repricing. Consequently, it is a useful statement of a cross-asset VaR modeling problem rather than an implementable recipe. Any result would depend on the chosen risk factors, dependence model, valuation approach, and horizon.

Key ideas

• The document asks how to model portfolio VaR when holdings span equities, bonds, and derivatives.
• It raises Cholesky-based simulation as a way to generate correlated market scenarios.
• It asks whether bond duration and option delta and gamma can represent position risk.
• It does not specify a method for mapping simulated risk factors into portfolio values.
• Distributional assumptions, market-factor dependence, revaluation choices, and horizon would shape any VaR estimate.

Tags

# Monte Carlo VAR with differente asset classes


# Monte Carlo VAR with differente asset classes












I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is there a step-by-step guide for calculating portfolio VaR using monte carlo simulations

However, I don't understand if those same steps can be followed if I have different asset classes in my portfolio. For example, what if I have an Apple stock, a US Treasury Bond and a derivative (maybe an option on that same stock) with weights being 35%, 45%, 20% respectively?? Should I use duration, delta, gamma, etc?? How would this work? Thanks a lot.

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