Option Pricing Calculation with Binomial Tree Model

This article demonstrates the calculation of option prices using the binomial tree model. We'll use the following formula to determine the option prices at each stage:

$V_n = e^{-rn} * [rac{1}{1+r} * (puV_{n+1} + pdV_n)]$

Where:

$V_n$ represents the option price at time $n$.
$r$ is the risk-free interest rate.
$p = \frac{e^{r}-d}{u-d}$ is the probability of an up movement.
$u$ is the up movement factor.
$d$ is the down movement factor.

Scenario:

Let's consider an example with the following parameters:

Initial stock price ($S_0$): 6
Up movement ($u$): 3/2
Down movement ($d$): 2/3
Risk-free interest rate ($r$): 0.07

We need to calculate the option prices for the following scenarios:

$V$ = $V_0$ = 0.00
$V(H)$ = $V_1$ = e^-0.07 * [ 1/1.07*(0.5V_2+0.50) ] = $2.054
$V(T)$ = $V_1$ = e^-0.07 * [ 1/1.07*(0.50+0.50) ] = $0.000
$V(HH)$ = $V_2$ = e^-0.07 * [ 1/1.07*(0.50+0.50) ] = $0.000
$V(HT)$ = $V_2$ = e^-0.07 * [ 1/1.07*(0.5*(max(0, (S_0uu-7))) + 0.5*0) ] = $1.774
$V(TH)$ = $V_2$ = e^-0.07 * [ 1/1.07*(0.5*(max(0, (S_0ud-7))) + 0.5*0) ] = $0.000
$V(TT)$ = $V_2$ = e^-0.07 * [ 1/1.07*(0.5*(max(0, (S_0dd-7))) + 0.5*0) ] = $0.000

As you can see, the option prices for each scenario are calculated by working backward through the binomial tree. The final option price at time 0 ($V_0$) represents the value of the option today.

Conclusion:

This demonstrates how to calculate option prices using the binomial tree model. It's a valuable tool for understanding the dynamics of option pricing and can be used to generate insights into various scenarios.

Option Pricing Calculation with Binomial Tree Model