5 research outputs found
A Quick Tool to Forecast VaR Using Implied and Realized Volatilities
We propose here a naive model to forecast exante ValueatRisk (VaR) using a shrinkage estimator between
realized volatility estimated on past return time series, and implied volatility extracted from option pricing data.
Implied volatility is often indicated as the operators expectation about future risk, while the historical volatility
straightforwardly represents the realized risk prior to the estimation point, which by definition is backward looking.
In a nutshell, our prediction strategy for VaR uses information both on the expected future risk and on the past
estimated risk. We examine our model, called Shrinked Volatility VaR, both in the univariate and in the multivariate
cases, empirically comparing its forecasting power with that of two benchmark VaR estimation models based on the
Historical Filtered Bootstrap and on the RiskMetrics approaches. The performance of all VaR models analyzed is
evaluated using both statistical accuracy tests and efficiency evaluation tests, according to the Basel II and ESMA
regulatory frameworks, on several major markets around the world over an outof sample period that covers
different financial crises. Our results confirm the efficacy of the implied volatility indexes as inputs for a VaR model,
but combined together with realized volatilities. Furthermore, due to its ease of implementation, our prediction
strategy to forecast VaR could be used as a tool for portfolio managers to quickly monitor investment decisions
before employing more sophisticated risk management systems
Valuation of Convexity Related Derivatives
We will investigate valuation of derivatives with payoff defined as a nonlinear though close to linear function of tradable underlying assets. Derivatives involving Libor or swap rates in arrears, i.e. rates paid in a wrong time, are a typical example. It is generally tempting to replace the future unknown interest rates with the forward rates. We will show rigorously that indeed this is not possible in the case of Libor or swap rates in arrears. We will introduce formally the notion of plain vanilla derivatives as those that can be replicated by a finite set of elementary operations and show that derivatives involving the rates in arrears are not plain vanilla. We will also study the issue of valuation of such derivatives. Beside the popular convexity adjustment formula, we will develop an improved two or more variable adjustment formula applicable in particular on swap rates in arrears. Finally, we will get a precise fully analytical formula based on the usual assumption of log-normality of the relevant tradable underlying assets applicable to a wide class of convexity related derivatives. We will illustrate the techniques and different results on a case study of a real life controversial exotic swap