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Volatility and Correlation

Umberto Cherubini · Giovanni Della Lunga

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Risk Management in Financial Firms

Abstract

The value of a product can change even though the underlying risk factors do not change, but simply because the volatility of each risk factor and its co-movements change. Both the structure and the client pay a lot of attention to the volatility of the risk factors and the way they are wrapped together in a product from an overall point of view, and very often a deal may be directed at exploiting expected changes in volatility and correlation, rather than the direction of the risk factor. This chapter highlights the key concepts used by the financial engineer to analyse the joint distribution of the risk factors, namely volatility and correlation.

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References

1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1999An Introduction to Copulas 2002Dynamic Conditional Correlation 1976Option pricing when underlying stock returns are discontinuous 1995Multivariate Simultaneous Generalized ARCH

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2011The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes 2006Parameterizing correlations: a geometric interpretation 2005Iterative construction of the optimal Bermudan stopping time 2007On extracting information implied in options 2014Range Volatility: A Review of Models and Empirical Studies 2011Option Data and Modeling BSM Implied Volatility

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