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Implied value-at-risk and model-free simulation.

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  • 1Department of Accounting, Law and Finance, Grenoble Ecole de Management (GEM), 12 Rue Pierre Semard, 38000 Grenoble, France.

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Summary

This study introduces a new model-free method to derive asset risk-neutral quantiles from option prices. This approach enhances simulations for stochastic volatility models and directly estimates option implied value-at-risk (VaR) and tail value-at-risk (TVaR).

Keywords:
Exact simulationHeston modelImplied value-at-riskModel-free simulation under risk-neutral probability measureSABR modelStochastic volatility models

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Area of Science:

  • Quantitative Finance
  • Financial Econometrics
  • Computational Finance

Background:

  • Extracting risk-neutral distributions from option prices is crucial for financial modeling.
  • Existing methods for simulating asset values under risk-neutral measures can be computationally intensive or inaccurate for complex models.
  • Direct estimation of risk measures like Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) from option data is challenging.

Purpose of the Study:

  • To propose a novel model-free approach for extracting the risk-neutral quantile function of an asset using its options.
  • To demonstrate the application of this method in simulating asset terminal values under risk-neutral measures.
  • To directly estimate option-implied Value-at-Risk (VaR) and Option-Implied Tail Value-at-Risk (TVaR).

Main Methods:

  • Development of a model-free algorithm to infer the risk-neutral quantile function from option prices.
  • Application of the method to simulate asset terminal values for stochastic volatility models (Heston, SVI, SABR).
  • Direct calculation of option-implied VaR and TVaR using the derived risk-neutral quantiles.

Main Results:

  • The proposed model-free approach successfully extracts the risk-neutral quantile function.
  • Simulations of asset terminal values show superior performance compared to existing methods for Heston, SVI, and SABR models.
  • Direct estimation of option-implied VaR and TVaR is achieved, with an empirical illustration using S&P 500 options.

Conclusions:

  • The novel model-free method provides an efficient and accurate way to obtain risk-neutral quantiles from option prices.
  • This approach offers significant improvements for simulating asset values in advanced stochastic volatility settings.
  • The direct estimation of implied VaR and TVaR offers valuable insights for risk management and financial market analysis.