Abstract

It is well-known that in normal stochastic volatility models with zero correlation the fresh volatility swap price is exactly equal to the at-the-money implied volatility. To replicate a volatility swap, however, the price of a volatility swap at inception is insufficient. Its price throughout its life must be calculated. This short note proves that the exact price and replicating portfolio for seasoned volatility swaps when correlation is zero is a strip of vanilla options with simple Gaussian weights. For non-zero correlation it is shown that the error is of order correlation-squared.

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