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Doc Fenton
LSU Fan
Member since Feb 2007
51088 posts

LaTeX test thread: Breeden-Litzenberger formula

Just to see if I can post equations from LaTeX properly if I want to do so.

For this post, I'll use the Breeden-Litzenberger formula, which provides a link between the risk-neutral probability distribution of a stock price at time T and current call prices.

The LaTeX code is as follows:

f_{T}^{S }\left( K\right) = e^{{r}\left( T-t\right)} \dfrac {\partial ^{2}C_{t}} {\partial K^{2}}

The image of the equation is shown below...

Image: http://texify.com/img/%5CLARGE%5C%21f_%7BT%7D%5E%7BS%20%7D%5Cleft%28%20K%5Cright%29%20%3D%20e%5E%7B%7Br%7D%5Cleft%28%20T-t%5Cright%29%7D%20%5Cdfrac%20%7B%5Cpartial%20%5E%7B2%7DC_%7Bt%7D%7D%20%7B%5Cpartial%20K%5E%7B2%7D%7D.gif


The f stands for the density function. The superscript S just indicates the particular stock/asset that the density function is for, while the subscript T represents the time. Also, f is a function of K, the strike price of the call option. C-subscript-t is just the price of the call option at some time t less than T, and r is the continuously compounded risk-free interest rate.



For anyone else trying to learn some LaTeX skills, you can go to a website at webdemo.visionobjects.com where you can just draw in an equation in etch-a-sketch fashion, generate some code automatically from that, edit out any errors, and then generate an image of a proper looking equation.


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