Volatility Derivatives for Children

We describe the steps required to approximately price volatility derivatives by making use of only three near the money vanilla index options per maturity. When three near the money forward starting options per maturity are also available, a straightforward generalization enables the pricing of forward starting volatility derivatives such as volatility swaptions and so forth. The only assumption we make is that the index process is a diffusion with a volatility process that does not depend on the index level. No pretence of mathematical rigor or sophistication is made; this note should be seen as a playful and rudimentary attempt at pricing volatility derivatives with a minimum set of assumptions and market instruments.