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Boundary condition of a special double barrier option

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Haoyun XU

Boundary condition of a special double barrier option

Hi All,

I am pricing a special double barrier option with finite difference in the BS framework. But I get a little confused when setting up the boundary conditions.

It is a double barrier European put option. The upper barrier is a knock-out barrier, while the lower barrier is a knock-in barrier. KO barrier prevails KI barrier.

So whenever the KO barrier is touched, the holder gets nothing. If KO not touched and KI touched, holder get put option payoff at maturity. If both untouched, the holder gets nothing.

In the beginning, I specified the boundary condition at KI barrier asthe value of a vanilla option. But after some thought, I found it was actually pricing a different product, in which KO & KI are equally treated. In this case, the holder receives payoff of a put when the KI is touched earlier even if it touches KO later. This is not I want.

Please kindly help.

Best,

Henry

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Klaus Spanderen-2

Re: Boundary condition of a special double barrier option

Hi Henry,

IMO it seems that this little detail turns it into a plath dependent option.You can use either Monte-Carlo simulations or if you want to stick with FDM then the path dependency adds another dimension to your problem and you'll have to solve a 2d partial differential equation.

regards

Klaus

Haoyun XU <[hidden email]> hat am 28. August 2013 um 04:49 geschrieben:

Hi All,

I am pricing a special double barrier option with finite difference in the BS framework. But I get a little confused when setting up the boundary conditions.

It is a double barrier European put option. The upper barrier is a knock-out barrier, while the lower barrier is a knock-in barrier. KO barrier prevails KI barrier.

So whenever the KO barrier is touched, the holder gets nothing. If KO not touched and KI touched, holder get put option payoff at maturity. If both untouched, the holder gets nothing.

In the beginning, I specified the boundary condition at KI barrier asthe value of a vanilla option. But after some thought, I found it was actually pricing a different product, in which KO & KI are equally treated. In this case, the holder receives payoff of a put when the KI is touched earlier even if it touches KO later. This is not I want.

Please kindly help.

Best,

Henry

Haoyun XU

Re: Boundary condition of a special double barrier option

Hi Klaus,

Thanks for your reply. Yes, it is path-dependent. But it is just weakly path-dependent, like single barrier options. I wish to stick with 1-D PDE.

Can I specify the B.C. at KI as the value of a Up&Out put barrier option instead of a vanilla put. Will this account for the KO barrier dominance? What's your opinion?

Best,

Henry

2013/8/28 Klaus Spanderen <[hidden email]>

Hi Henry,

IMO it seems that this little detail turns it into a plath dependent option.You can use either Monte-Carlo simulations or if you want to stick with FDM then the path dependency adds another dimension to your problem and you'll have to solve a 2d partial differential equation.

regards

Klaus

Haoyun XU <[hidden email]> hat am 28. August 2013 um 04:49 geschrieben:

Hi All,

I am pricing a special double barrier option with finite difference in the BS framework. But I get a little confused when setting up the boundary conditions.

It is a double barrier European put option. The upper barrier is a knock-out barrier, while the lower barrier is a knock-in barrier. KO barrier prevails KI barrier.

So whenever the KO barrier is touched, the holder gets nothing. If KO not touched and KI touched, holder get put option payoff at maturity. If both untouched, the holder gets nothing.

In the beginning, I specified the boundary condition at KI barrier asthe value of a vanilla option. But after some thought, I found it was actually pricing a different product, in which KO & KI are equally treated. In this case, the holder receives payoff of a put when the KI is touched earlier even if it touches KO later. This is not I want.

Please kindly help.

Best,

Henry