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raheel88
Topic Author
Posts: 11
Joined: April 4th, 2010, 3:07 pm

### 2D payoff diagram

Hello all,I have a two-dimensional put option whose payoff is given by;V(S1,S2,T) = max[X1-S1, X2-S2,0]where X1 and X2 are the strike prices corresponding to each underlying.What I'm interested to know is what would a payoff diagram look like for this option?What I think, is that I have to parametrise S1 and S2 somehow...but unsure as to the method.Can anyone help?

untwigged
Posts: 262
Joined: January 14th, 2006, 3:21 pm

### 2D payoff diagram

You'll need some sort of 3d plot

raheel88
Topic Author
Posts: 11
Joined: April 4th, 2010, 3:07 pm

### 2D payoff diagram

Yes I was thinking about that, but I'm sure a 3D plot is avoidable.I was wondering if it would be possible to parametrise S1 and S2 somehow so that I can draw the payoff diagram in 2D.

ACD
Posts: 107
Joined: April 19th, 2004, 8:09 am

### 2D payoff diagram

Since there are only 2 variables you should be able to knock up an Excel surface plot in a few seconds for it.

raheel88
Topic Author
Posts: 11
Joined: April 4th, 2010, 3:07 pm

### 2D payoff diagram

Thanks ACD and untwigged.I think I'm trying to over-complicate a simple thing.

mynetself
Posts: 187
Joined: March 27th, 2010, 6:40 pm

### 2D payoff diagram

raheel88 -> What you can do is to draw a series of S1=const (or S2=const) lines on the same graph. Another possibility is to draw a series of "equal height" lines (mathematically "level sets"). These are the lines you obtain by setting V(S1,S2,T) = const, and then vary the const. The result will be essentially like a 2D map of a mountain where "equal hight" lines are drawn. Finally, you could try drawing it "in perspective", i.e. drawing the 3D space on 2D, just like 3D plots do. Your function is esentially a piece of a plane in 3D space, so kinda simple to draw. Just need to find intersections with the S1 an S2 axis.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

### 2D payoff diagram

contour plot

raheel88
Topic Author
Posts: 11
Joined: April 4th, 2010, 3:07 pm

### 2D payoff diagram

yep..i think a contour plot is the way to go.thanks alot guys!

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