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tapepae
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Joined: June 2nd, 2017, 9:09 am

Monte-Carlo shouldn't be used for validation

October 10th, 2017, 3:50 am

I received the statement claiming that "Monte Carlo is normally not accurate enough in a Local Volatility context to be a reliable validation tool for the desired accuracies in Finite Difference. (The other way around is Ok, though: Verifying Monte Carlo by Finite Difference)".

Nowadays, we developed other method such as Finite Difference to fast forward the computation (given MC is slow with million paths). I still personally think that MC is a good method that evades the curse of dimensionality to provide a good ballpark pseudo-truth - upon convergence, and MC should be used for validation against , for example, Finite Difference before rolling it out. It should not be on the opposite side like it is claimed by the statement above.

However, I might be wrong. 

Appreciate expertise here to give some comments/thoughts.
 
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Cuchulainn
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Re: Monte-Carlo shouldn't be used for validation

October 11th, 2017, 5:54 am

Appreciate expertise here to give some comments/thoughts.

Where to start? Maybe reduce the scope. Take a specific case and flesh it out.
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tapepae
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Joined: June 2nd, 2017, 9:09 am

Re: Monte-Carlo shouldn't be used for validation

October 11th, 2017, 9:31 am

Cuchulainn wrote:
Appreciate expertise here to give some comments/thoughts.

Where to start? Maybe reduce the scope. Take a specific case and flesh it out.

Hi Cuchulainn,
Apologies ... maybe i did not clarify good enough.

For example, we have Barrier Option with Local Vol implemented in system called "A" by using Finite Difference method.

In order to provide a good ballpark pseudo-truth - upon convergence for validation purpose, if somebody claimed that "Monte Carlo is normally not accurate enough in a Local Volatility context to be a reliable validation tool for the desired accuracies in Finite Difference".

In my opinion, any method is developed and check the accuracy with Monte-Carlo.

But, maybe I am wrong. Does it sound make sense?
 
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Billy7
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Re: Monte-Carlo shouldn't be used for validation

October 11th, 2017, 12:12 pm

Hi there,

I'm not sure about what extra complications local vol may cause for Monte Carlo.
Something to keep in mind though when talking barrier options and MC, is that continuous barriers cannot be priced accurately with (naive) Monte Carlo. Are you talking about continuously-monitored barrier options? If so, then bare in mind that naive MC may give you say 40% error, even if you use a billion paths and daily time steps. I think 40% error doesn't qualify even as a pseudo-truth. But there are some ways around it. But again, I haven't tried with local vol and not sure what extra problems (if any) it creates.
 
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berndL
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Re: Monte-Carlo shouldn't be used for validation

October 12th, 2017, 2:40 pm

Billy7 wrote:
Hi there,

I'm not sure about what extra complications local vol may cause for Monte Carlo.
Something to keep in mind though when talking barrier options and MC, is that continuous barriers cannot be priced accurately with (naive) Monte Carlo. Are you talking about continuously-monitored barrier options? If so, then bare in mind that naive MC may give you say 40% error, even if you use a billion paths and daily time steps. I think 40% error doesn't qualify even as a pseudo-truth. But there are some ways around it. But again, I haven't tried with local vol and not sure what extra problems (if any) it creates.

One specific thing in the combination of MC and Local Vol (by that i mean local vol as defined by dupire) is that you do not explicily know the density from which to sample in an mc context. If you just discretize the sde than you have some error due to this. That means: Even if the product you are valuing might not need a simulation on a fine time grid, then the discretization error might force you (doing simple sde discretization and for mc path gerenation) to still have quit a narrow time grid. And thus the fun could go out of this method as perfomance  degrades with the number of time points to sample.
But maybe you are lucky and mc is still fast enough to use it for model validation.
 
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Billy7
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Re: Monte-Carlo shouldn't be used for validation

October 12th, 2017, 3:58 pm

Yes, well same as Heston MC with simple Euler discretization? Aren't there more sophisticated schemes for local vol MC, just like there are for Heston?
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