Twofish's Blog

July 19, 2006

Question and answer:

Filed under: quantitative finance — twofish @ 12:11 am

Question: Give a volatility curve at time T, and the knowlege that the process is an exponental Levy process, is the volatility curve determined for all time?

Answer: Yes?  A volatility curve s(t, x-x_0) corresponds to a given probability distribution function p(t, x-x_0).  p(0, x-x_0) is a delta function \delta(x-x_0).  These two curves create a unique interpolation which corresponds to a unique Levy process which determines the volatility curve for all time.

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