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anjoazul
Topic Author
Posts: 2
Joined: June 18th, 2017, 4:42 pm

### Option Pricing Using Binomial Tree

Hi everybody! I'm reading the chapter 3 about option pricing in "FINANCE Paul Wilmott Introduces Quantitative Finance" , in 3.17 VALUING BACK DOWN THE TREE,  an example says" with S = 100, δt = 1/12, r = 0.1(risk free rate), and σ = 0.2... Using these numbers we have u = 1.0604, v = 0.9431 and p' = 0.5567( where δt stands for time step, u for the upper underlying asset price after on tiem step, v for the lower price, and p' for risk neutral probability). ”
But, according to the formulas  u = 1 + σ(δt)^0.5, v = 1 - σ(δt)^0.5 and p'=1/2 + r(δt)^0.5/2σ, I got u = 1 + 0.2 (1/12)^0.5 = 1. 0577, v = 1- 0.2(1/12)^0.5=0.9423 and p’= 0.5 + 0.0722=0.5722. Could u please tell me if I have made any mistakes in the calculation? Thanks!

Paul
Posts: 7442
Joined: July 20th, 2001, 3:28 pm

### Re: Option Pricing Using Binomial Tree

You are v observant! I use two different algorithms, but haven't explained this!

There are three parameters to choose, u, v and p. But only two parameters to match, drift and vol. So there is one degree of freedom and an infinite number of possible choices! In the text I use the one that looks simplest, just for teaching purposes.

They give different answers for finite dt but for infinitesimal dt they'd give the same.

anjoazul
Topic Author
Posts: 2
Joined: June 18th, 2017, 4:42 pm

### Re: Option Pricing Using Binomial Tree

Dear Paul, thank u very much for your quick reply and now I finally understood the issue and get more interest in studying with your masterpiece. Thanks!