CRR Tree

Since we are assigned to report on the CRR tree, our group made a powerpoint presentation on this. It includes the basics of a CRR tree.

Crr presentation from naojan

Notes: CRR presentation.pptx, CRRBOPMv2.xlsx

Jarrow-Rudd Tree (JR) tree is assumes 50% probability in the u and d. CRR don't.

Slide 6 

Step 1. Binomial model acts similarly to the asset that exists in a risk neutral world.

$$pu+qd = e^{i * \Delta t} = r$$

where

$$\begin{split} \Delta t &= \frac{t}{n} \\ t &= \text{term of the option} \\ n &= \text{number of periods} \end{split}$$

Its variance: 

  $$pu^2 + qd^2 – e^{(i* \Delta t)^2} = \sigma^2 \Delta t$$

Slide 9 - Notice that the lattice is symmetrical, that is due to the assumption that d=1/u (ud=1). Thus , it is easier to program since it involves fewer steps.

References:

• Cox, J.C., Ross S.A, Rubinstein, M., Option Pricing : A Simplified Approach. (1979). Published in Journal of Finance and Economics
• Watsham, Terry J., and Parramore, Keith. Quantitative Methods in Finance. (1997)
• http://investexcel.net/736/binomial-option-pricing-excel/
• http://www.sitmo.com/article/binomial-and-trinomial-trees/
• http://en.wikipedia.org/wiki/Binomial_options_pricing_model
• http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/xlghtmlnode63.html#bin-fig2
• http://www.terry.uga.edu/~mayhew/Old/chapter9.pdf
• Other books:
• Hull book 
• Paul Wilmott
• Advance Modelling in Finance Using Excel and VBA