John Crosby, UBS
We introduce generalized variance swaps, which generalize and include, as special cases, popular derivatives such as variance swaps and gamma swaps. We also consider other types of volatility-related derivatives such as proportional variance swaps and skewness swaps. We obtain pricing formulae for both discretely monitored swaps and continuously monitored swaps and discuss the convergence of the former to the latter as the number of monitoring dates is increased. We discuss the implications for trading and hedging these instruments. The use of high-frequency data to estimate realized variance (and, more generally, to estimate model parameters) has been a "hot" topic in finance in recent years. We discuss the implications of our work on this topic focusing, in particular, upon the "leverage effect". This is new joint work with Mark Davis in the Mathematics Department at Imperial College London.
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