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The stock specific volatility (also known as idiosyncratic volatility) is the volatility that remains after controlling for beta. I suppose you have $$R_i = R_f + \beta_i \cdot \big(R_m-R_f\big) + \varepsilon_i.$$ Then, the standard deviation of epsilon is your stock specific volatility. One frequently assumes $\varepsilon_i\sim N(0,\sigma^2_{\varepsilon_i})$...

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To trade forward starting volatility swaps, see this paper (actually more a practitioner's scribble than a paper) and all references therein: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3354408 Just to let you know, I think there may be a small error term in the paper that needs to be included still, but based on some simple numerical tests I was ...

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A standard book in the volatility literature is Gatheral (2006). The book begins with stochastic volatility, llocal volatility and the Heston model. Then he adds jumps and default risks. He concludes with barrier options, exotic options and volatility derivatives. He includes many tables and graphs and writes rather well. The only downside is that he does ...

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