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BerndSchmitz
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Posts: 41
Joined: August 16th, 2011, 9:48 am

Statistical significance in standard Monte Carlo

February 5th, 2012, 7:33 am

hey,I calculated some exotic option prices based on either a Heston-Stochastic-Volatility, Merton-Jump-Diffusion or Bates model by means of Monte Carlo simulation. Now I want to say something about whether the obtained prices are significantly different from each other. As I understand it this works in the following way:- I look up the (e.g.) the 99.5% quantile of the standard normal distribution (2.576 in this case)- then I calculate for each model: mean +/- 2.576*stdev to obtain the 99% confidence intervall- if these intervalls are distinct for two models then the obtained prices (i.e. the means) are significantly different from each other at the 99% confidence niveauis this correct?thanks, bernd
Last edited by BerndSchmitz on February 4th, 2012, 11:00 pm, edited 1 time in total.
 
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bwarren
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Joined: February 18th, 2011, 10:44 pm

Statistical significance in standard Monte Carlo

February 5th, 2012, 2:08 pm

QuoteOriginally posted by: BerndSchmitzhey,I calculated some exotic option prices based on either a Heston-Stochastic-Volatility, Merton-Jump-Diffusion or Bates model by means of Monte Carlo simulation. Now I want to say something about whether the obtained prices are significantly different from each other. As I understand it this works in the following way:- I look up the (e.g.) the 99.5% quantile of the standard normal distribution (2.576 in this case)- then I calculate for each model: mean +/- 2.576*stdev to obtain the 99% confidence intervall- if these intervalls are distinct for two models then the obtained prices (i.e. the means) are significantly different from each other at the 99% confidence niveauis this correct?thanks, berndNo, you should take the difference and test if it is different than zero. The variance of the difference is the sum of the two variances.
 
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BerndSchmitz
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Posts: 41
Joined: August 16th, 2011, 9:48 am

Statistical significance in standard Monte Carlo

February 5th, 2012, 2:31 pm

thanks! just to get this straightI calculateabs(mean(model1)-mean(model2)) - 2.576 * sqrt(variance(model1)+variane(model2))and if the values is larger than 0 then the models produce prices that are significantly different from each other at the 99% confidence niveauis this correct?bernd
 
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bwarren
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Joined: February 18th, 2011, 10:44 pm

Statistical significance in standard Monte Carlo

February 5th, 2012, 2:35 pm

QuoteOriginally posted by: BerndSchmitzthanks! just to get this straightI calculateabs(mean(model1)-mean(model2)) - 2.576 * sqrt(variance(model1)+variane(model2))and if the values is larger than 0 then the models produce prices that are significantly different from each other at the 99% confidence niveauis this correct?berndyeah, that should work