My goal is to obtain some weights to calculate greeks for lookback options.

It boils down to calculate the malliavin derivative of the following process : $Y_{t} = 8(4(\int_{0}^{t}\int_{0}^{t}\frac{||\mu (s-u) + \sigma (W_{s}-W_{u})||^{\gamma}}{|s-u|^{m+2}}dsdu)^{1/\gamma} \frac{m+2}{m}t^{m/\gamma}$

The discrete version i have to use is $Y_{t} = \sqrt{N \sum_{1\le j \le T :t_{j}\le t} || \mu (t_{j}-t_{j-1}) + \sigma (W_{t_{j}}-W_{t_{j-1}}) ||^{2}}$

Would somebody know how to properly derive this process , im not very familiar with Malliavin Calculus.



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