how to plot the payoff of an call/put option with matlab

how can I plot:

- intrinsic value of a call/put option in matlab?

- how can I plot the call/put value including the time value?

Additionally, I would like to plot delta, gamma, vega, etc. for several strikes and time to maturity, is that possible?

thanks for your help

[the cyclist]

All of this is possible in MATLAB, but your question is far too general. We have no idea knowing what you already understand (and don't understand) about this problem.

For example, do you know anything at all about plotting in MATLAB? (Would you know how to plot the line y = 2*x?)

How much do you understand about options? Do you know and understand the formulas for the values?

I suggest you try to break down your question into small chunks that will be easier for people to digest and help you answer. You should show what coded you have written for yourself as well.

[Locks]

I know how to plot a line in matlab and I suppose I know enough abbout options, but I thought there could be a function where I do not need to do it by myself. Is there no function for this?

I do not really know how to get the axis an how to describe them

Furthermore, to plot the intrinsic value, I need the max function to get max(S-K,0)

For the option value I need the black scholes formula, which fortunately I have

I there an easy and efficient way to handle that problem

Answer 1

[the cyclist]

The Financial Toolbox has formulas for option prices [e.g. blsprice() for Black-Scholes model option pricing]. You can see the complete list of functions here:

http://www.mathworks.com/help/finance/functionlist.html

If you don't have that toolbox, then you might find something you can use in the File Exchange. Here's one:

http://www.mathworks.com/matlabcentral/fileexchange/33770-black-scholes-formula

(But I have no idea if it is any good.)

[Locks]

I have the finaancial toolbox, but from what I can see there is nothing to plot the intrinsic value for example, or am I mistaken?

[the cyclist]

I am left a little bit puzzled. You have stated that:

1. You have the Financial Toolbox, and therefore have the formula for the option price.
2. You know how to calculate the intrinsic value from the option price.
3. You know how to do plotting.

Therefore it seems that you know how to do all the steps for making a plot of the intrinsic value. Maybe you should start writing some code, and see where you get stuck, and we can help you get past the stuck part.

There is no MATLAB function "plot the intrinsic value of an option over the range I want", if that is what you were hoping for. (I guess that could be in the File Exchange, but I doubt it.)

[Locks]

    x=[1:0.01:20]
    y=blsprice(x,10,0.02,0.2,0.2)
    xlabel('Stock Price ($)');
    ylabel('Gain/Loss');
    plot(y)

I startet with that, but it doesn't show me the x and y label. then I would like to have the numbers 0 to 20 on the x label and the horizontal zero line should be drawn

concerning the intrinsic value, is there a max function?

[the cyclist]

You are plotting x vs. y, so you want to do

plot(x,y)

Yes, there is a max function. Type

doc max

for details

[Locks]

and to get the x and y label? that doesn't work, they aren't in the plot.

is there a way to draw a horizontal line through zero?

if I substract the option price, f.e. 2 from the blsprice(x,10,0.02,0.2,0.2), then I will receive a negative value for stockprices below 12 (something around 12) and I would like to have a line at zero

doc max doesn't work. I am aware that there is a max function, but I need a function such as

max (S-K,0) which displays 0 if S<K

[the cyclist]

Put the label commands after the plotting command, not before.

doc max

should show a documentation page with the syntax for the max() function. If that does not work, you could try

help max

Regardless,

max(x,0)

will indeed result in x when x>=0 and 0 when x<0. Maybe you could again paste in your complete code if it is still going wrong.

[Locks]

x=[0:0.01:20]
y=blsprice(x,10,0.02,0.2,0.2)-blsprice(10,10,0.02,0.2,0.2)

plot(x,y)

xlabel('Stock Price ($)');
ylabel('Gain/Loss');
axis([0 20  -2 10]);

this is now working, to get a horizontal zero line so it's clearer where an investor would make a gain an where he would make a loss?

additionally it would be great if there would be 2 seperate labels for the y-label, to show that from -2 to 0 the investor is making a loss and from 0 to 10 he makes a gain, is that possible?

[the cyclist]

You can use the line() function to draw a line on the plot. See

help line

for the syntax.

I don't understand what you mean by separate labels. (I understand what you mean by the two regions, but not how you want the labeling to differ.) You could use the text() command to label the two side of the plot, I guess.

[Locks]

I thought about it and what I really need is the following:

x=[0:0.01:20]
y=max(x-10,0)-blsprice(10,10,0.02,0.2,0.2)

plot(x,y)

xlabel('Stock Price at Maturity ($)');
ylabel('Gain ($)');
axis([0 20  0 10]);

this codes is giving me the intrinsic value, with both axis starting at point zero, which should stay, but like this I do not see the intrinsic value plot, als long as the intrinsic value is below 0

I tried this:

axis([0 20  -2 10]);

but then the the x axis starts at -2 and that's not what I want. I need the x-axis and the numbers to start at the point where y=0, but the y-axis should go from -2 to 10, is there a way to do that?

and the last thing I would like to have are arrows at the and of the axis, how can I do that?

additionally I would like to see only the x and y-axis and not the whole box around the plot, is that possible?

Can I plot both, the intrinsic value as well as the black scholes value in the same figure?

[the cyclist]

It is probably a bad idea for you to keep putting more and more questions here, where I am probably the only one reading this thread anymore. It might have been better for you to post your arrow question and box question separately, but I'll try to answer them.

First question: the axes.

This code makes x-axis (0,20) and y-axis (-2,10). I think that is what you want. If that does not work for you, I am not sure why.

x = 0:0.01:20;
y = max(x-10,0);

figure
plot(x,y)
xlabel('Stock Price at Maturity ($)');
ylabel('Gain ($)');
axis([0 20  -2 10]);

[I don't have blsprice(), so I can't include that in the formula.]

Second question, the box:

set(gca,'Box','off')

Third question, the arrow:

I don't know if there is a native MATLAB command to draw an arrow. Here is a utility from the File Exchange that you can download: http://www.mathworks.com/matlabcentral/fileexchange/278

[the cyclist]

Missed the last question.

Fourth question, multiple lines per plot:

plot(x,y1,x,y2)

or

figure
hold on
plot(x,y1)
plot(x,y2)

[Locks]

plotting both has worked now, but there is another thing I am not able to do.

I would like to plot a double arrow between the intrinsic value line and the black scholes line, to show the time value of the option. is there an easy way to do this?

additionally I would like to write 'time value' between the intrinsic value line and the block scholes line, how can I write something at a specific place in a plot?

thank you very much for your help

[the cyclist]

You can add text to a specific place on the plot using text function.

help text

for details.

I forgot about this when you asked about arrows earlier. You can do this using the annotation() command.

For example,

annotation(gcf,'doublearrow',[0.2 0.3],[0.3 0.5])

It is a little annoying that annotations use figure coordinates rather than axis coordinates. Read this for details:

http://www.mathworks.com/help/matlab/creating_plots/positioning-annotations-in-data-space.html

[Locks]

is there a way to make the arrow smaller?