ON THE CALCULATION OF RISK MEASURES USING LEAST-SQUARES MONTE CARLO

Giuseppe Benedetti ()
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Giuseppe Benedetti: Fastval (FIS), 42 Rue Notre Dame des Victoires, 75002 Paris, France

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 03, 1-14

Abstract: The paper establishes a convergence result for the Least-Squares Monte Carlo method, applied to the estimation of risk measures (such as VaR) depending on the distribution of the future value of some derivative contract (or portfolio). We extend previous results in the literature by focusing on the specific case where the distribution of the underlying factors is known. In particular, we are able to remove the requirement of bounded conditional variance which is usually not satisfied by common financial models and payoffs at the cost of using a weaker notion of convergence. Our main result shows the convergence of the empirical distribution function when the number of simulations n and of basis variables m are jointly sent to infinity under certain conditions on the payoff and the basis. With a suitable choice of basis functions, we finally prove that convergence can be ensured when (m2ln m)/n → 0.

Keywords: Derivative pricing; risk management; Monte Carlo methods (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500200

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DOI: 10.1142/S0219024917500200

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