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Say you have a portfolio with long exposure to a few linear assets (stock indices) and short exposure to a nonlinear asset (say call options on one of the linear assets).

I am interested in modelling extreme returns (negative returns) on this total portfolio for a 1-day horizon for calculation of risk measures. For linear assets this can be done with Extreme Value Theory by fitting a Generalised Pareto Distribution (GPD) to observations over a high threshold. When it comes to portfolios including nonlinear exposure, I can only come up with two approaches which I will briefly explain:

  1. Calculate the portfolio pseudo-historical returns (similar to historical simulation) by estimating tomorrows portfolio return from past returns, where the options would be priced (e.g. by Black-and-Scholes). Then lower tail of this empirical distribution would be fitted by GPD.

  2. Fit GPD to both the upper and lower tail of the linear assets empirical distributions and a kernel smoother to the middle. Then do a number of Monte Carlo simulations from these, connecting the simulated returns by a copula. The option position will priced based on the simulation.

I have not found much literature on EVT and more complex portfolio.Are any of these approaches adequate for my problem?

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Are you aware of Lisa Goldberg's work on the topic? –  Brian B Oct 2 '13 at 17:43
    
Not particularly, but now that you mentioned it I skimmed through some of her papers and it looks interesting. Can you refer to a single paper by her where EVT is applied to options? Thank you for your tip! –  Chris Oct 2 '13 at 19:36
1  
Last time I talked to her, she was having trouble enough applying it to equities, but it's the only decent EVT work I've ever seen in finance. –  Brian B Oct 2 '13 at 19:53

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