Hi, im currently working on my bachelor thesis for the finance department. I’ m writing about the valuation of european options with the monte carlo simulation, to be more specific the valuation of a long straddle.
I encountered a probelm when attempting to reduce the standard error of the monte carlo estimator. I know that you can you can just increase the number of simulations (n) or make use of a variance reduction technique.
I used antithetic variates, which I’ m sure everybody in this particular forum has already heard of. I have never worked with the monte carlo simulation before.
As i understand antithetic sampling (AS) should reduce the estimators variance by generating a negativ correlated path to the already existing path of random numbers . ( Z and -Z) , therefore out flattening any jumps in the simulation and the payoff of the straddle. the standard error is defnied as [sup:1yku76h4](Sigma estimator)[/sup:1yku76h4] / [sub:1yku76h4]root (n )[/sub:1yku76h4]. Antithetic sampling is supposed to deliver a smaller standard error than 2n “normal” simulations.
This works quite well when calculated for the put option or the call option on their own. But the straddle standard error increases when AS is used, and i don’t understand why. I’m not sure if it’s an accurate result and anthitetic variates don’t work in this case (unlikely) or if i just don’t get the concept right.
I will also enclose an excerpt of my excel sheet.
I hope one of you could help me out with this problem.