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Alice1991
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Joined: March 20th, 2013, 10:48 am

Can I use antithetic variates with this path dependent swap? (see my graph of convergence)

May 21st, 2013, 9:02 am

Hello,I'm pricing a path-dependent swap which has the following features:leg 1: vanilla (ex:euribor6m)leg 2: structured ==> if the euribor is < strike (ex.1,5%) then the rate is euribor 6mif the euribor 6m is >= strike then the rate is a fixe rate (ex.3,5%) for the remaining periodsI did use this method (just in case, here is how I proceeded): (see graph obtained below)For each path: simulating short rate process using RANDOMNUMBER and another one (mirror) using -RANDOMNUMBER and then, I just calculate (r+r mirror)/2 for each step(I could have used z and -z, it should be the same no ?)Then I use the resulting paths for the next step of the monte carlo.When I use the antithetic variates, the pay-off is lower than when I don't use it.1) It could be the pay-off structure ? I read we cannot use this reduction technique when the payoff depends "only" or "a lot" on a a highest ? In this case, it could be true because the pay-off is like a digital2) it could be a problem with my methodology ? As you read, I don't calculate the NPV for both normal and mirror path and then /2 => I just calculate (r+r mirror)/2 for each stepThank you for your timeLink to the graph of Convergence
Last edited by Alice1991 on May 20th, 2013, 10:00 pm, edited 1 time in total.
 
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Jim
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Joined: February 1st, 2002, 5:20 pm

Can I use antithetic variates with this path dependent swap? (see my graph of convergence)

May 21st, 2013, 6:30 pm

I don't think you can just calculate (r+r mirror)/2 for each step. Wouldn't the numeraires be different on the antithetic and non-antithetic paths?
 
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Tad
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Joined: January 27th, 2010, 11:39 pm

Can I use antithetic variates with this path dependent swap? (see my graph of convergence)

May 22nd, 2013, 1:54 pm

see for example this linkyou will need to calculate (payoff(r) + payoff(r mirror))/2 for each simulation run.