A nonparametric approach for value-at-risk and option pricing (Risk management)

Financial time series are often nonnormal, nonstationary, serially correlated and with changing volatility. The main theme of this research is to develop a new nonparametric approach for evaluating the probability distribution functions (PDF) of multiple-period returns in the context of real-world financial applications. An adaptive historical simulation scheme is proposed to estimate one-day asset returns and an adaptive bootstrapping scheme is proposed to estimate multi-day asset returns. This research has two direct application fields, Value-at-Risk (VaR) and option pricing.; This research first demonstrates that adaptive historical simulation can enhance the accuracy of estimation on one-day VaR. The result suggests that the PDF of standardized returns (empirical returns divided by volatility) tends to persist over a period of time. A standardized time series has unit standard deviation and preserves the serial correlation structure of the original time series. The adaptive bootstrap scheme draws bootstrap samples from the standardized time series with a exponentially decayed probability. Therefore, with a proper choice of a decay factor, the adaptive bootstrapping scheme can deal with non-normality, nonstationarity, and serial correlation of financial time series. Empirical results of S&P 500 index and two foreign exchange portfolios suggest that the adaptive bootstrapping scheme can improve the accuracy of multi-day VaR up to more than 60 days.; A new risk measure, duration VaR, is proposed to take into account possible losses during a time period. The duration VaR model can be easily implemented with the bootstrapping scheme. This research also shows that nonparametric VaR models can be extended from a univariate setting to a multivariate setting with the concept of implied volatility.; Since adaptive bootstrapping is a nonparametric approach for estimating the PDF of asset returns, it can be used for option pricing. This research demonstrates how the scheme can achieve better estimates on risk neutral values of simple European, Asian, and other path-dependent options. This research also develops a closed formula for pricing deep out-of-the-money options that the formula links VaR with option prices. Computation algorithms for the Greeks are also developed for the adaptive bootstrapping scheme. Empirical results suggests that the bootstrapping scheme can capture the properties of typical financial time series, which are nonnormal, non-stationary, serially correlated and with changing volatility. Further research and possible applications of the adaptive bootstrapping scheme are also discussed.