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mgale
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Posts: 3
Joined: January 27th, 2011, 10:00 am

QMC in path dependent options

January 28th, 2011, 11:41 am

I am trying to price an option with multiple fixings using Halton Sequence. For example, imagine an option with 1-year Tenor and 3 fixings. For each of the 'N' simulations or paths, I use Halton with base = 2 to obtain the underlying asset price at first fixing, then use Halton again with different bases to obtain prices for the remaining two fixings. If there are many fixings, say 60, then what is the recommended approach?
 
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spv205
Posts: 478
Joined: July 14th, 2002, 3:00 am

QMC in path dependent options

January 28th, 2011, 1:19 pm

sobol and brownian bridge?
 
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Costeanu
Posts: 189
Joined: December 29th, 2008, 5:33 pm

QMC in path dependent options

January 28th, 2011, 2:53 pm

Hi Mgale, If you want to simulate times t1<t2<...<t10 for example, you need a 10-dimensional QRN generator for a 1-factor model. For a 2-factor model you need a 20-dim QRN generator. If you have n factors and m timepoints you need n*m dimensions. This number can sometimes be big, for example in the hundreds. If you don't trust your QRN generator up to this dimension, you need to use QRN for "important" dimensions and usual pseudo-random numbers for the remaining dimensions. Here's what spv205 meant by the brownian bridge: instead of simulating the Brownian motion by its increments, use the Brownian bridge. Use quasi-random numbers for the total increment and for the two half increments, for example, and use pseudo-random numbers for all other increments. This idea is based on the heuristics that an option value depends more strongly on the total increment. Another way is to use principal components; use qrn for the first 3 such components and pseudo rn for the remaining components. Best,V.
 
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mgale
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Posts: 3
Joined: January 27th, 2011, 10:00 am

QMC in path dependent options

January 31st, 2011, 5:45 am

Thanks Costeanu and spv205. I shall try this out.
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