CODEWITHSUNDEEP
matlabquantitative-finance
anw
anw

Reputation: 11

Negative option prices for certain input values in MATLAB?

In the course of testing an algorithm I computed option prices for random input values using the standard pricing function blsprice implemented in MATLAB's Financial Toolbox.

Surprisingly ( at least for me ) ,
the function seems to return negative option prices for certain combinations of input values.

As an example take the following:

> [Call,Put]=blsprice(67.6201,170.3190,0.0129,0.80,0.1277)

Call =-7.2942e-15
Put = 100.9502

If I change time to expiration to 0.79 or 0.81, the value becomes non-negative as I would expect.

Did anyone of you ever experience something similar and can come up with a short explanation why that happens?

Upvotes: 1

Views: 182

Answers (2)

JejeBelfort
JejeBelfort

Reputation: 1663

I don't know which version of the Financial Toolbox you are using but for me (TB 2007b) it works fine.

When running:

[Call,Put]=blsprice(67.6201,170.3190,0.0129,0.80,0.1277)

I get the following:

Call = 9.3930e-016
Put = 100.9502

Which is indeed positive

Upvotes: 2

Jimmy
Jimmy

Reputation: 187

Bit late but I have come across things like this before. The small negative value can be attributed to numerical rounding error and / or truncation error within the routine used to compute the cumulative normal distribution.

As you know computers are not perfect and small numerical error always persists in all calculations, in my view therefore the question one should must ask instead is - what is the accuracy of the input parameters being used and therefore what is the error tolerance for outputs.

The way I thought about it when I encountered it before was that, in finance, typical annual stock price return variance are of the order of 30% which means the mean returns are typically sampled with standard error of roughly 30% / sqrt(N) which is roughly of the order of +/- 1% assuming 2 years worth of data (so N = 260 x 2 = 520, any more data you have the other problem of stationarity assumption). Therefore on that basis the answer you got above could have been interpreted as zero given the error tolerance.

Also we typically work to penny / cent accuracy and again on that basis the answer you had could be interpreted as zero.

Just thought I'd give my 2c hope this is helpful in some ways if you are still checking for answers!

Upvotes: 1

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