I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM.

Is there any place to look into?

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    $\begingroup$ For what model? How would you price the option? You can always approximate the Greeks by a finite difference once you know the price. You can then generate plots comparing how the Greeks change for varying parameters $\endgroup$ – Alex 2 days ago
  • $\begingroup$ @Alex Under standard GBM. I have added this information in original post. $\endgroup$ – Bogaso 2 days ago
  • $\begingroup$ How do you price such an Asian option? Monte Carlo? Finite difference? Tree? Fourier method? Closed form (for geometric averaging)? $\endgroup$ – Alex 2 days ago
  • $\begingroup$ For GM, I think a closed form solution is available. However for AM, I would use MC. My question if profiling of Greeks are available for such options? $\endgroup$ – Bogaso 2 days ago
  • $\begingroup$ What do you mean with profiling of Greeks? $\endgroup$ – Alex 2 days ago

For the Geometric Average Asian Option in BS, there is an arithmetic formula for the price - in fact, it is possible to price it using a BS vanilla options calculator, if you adjust the parameters slightly - as discussed in this blog post: http://www.quantopia.net/asian-options-iii-geometric-asian/

As the pricing formula is the same, the Greeks can be derived in the same way as BS, although you need to be a bit careful with chain rule terms (and you can check correctness by bumping the parameters directly and calculating the difference from the pricing formula).

For an arithmetic Asian, you need to use a numerical technique like Monte Carlo to calculate either prices or Greeks. However, these will both be close to the geometric price and Greeks, so these can be used either as a direct approximation or as a control variate in the MC calculation.

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