(-) A significant advantage is a multi-period view the model provides for the underlying asset’s price and the transparency of the option’s value over time.
Understanding the Binomial Option Pricing Model | by
The Binomial model effectively weighs the different payoffs with their respective probabilities and discounts them to the present value.
Understanding the Binomial Option Pricing Model
The sizes of these up and down moves are constant (percentage-wise) throughout all steps, but the up move size can differ from the down move size.
This page explains the logic of binomial option pricing models – how option price is calculated from the inputs using binomial trees, and how these trees are built.
All models simplify reality, in order to make calculations possible, because the real world (even a simple thing like stock price movement) is often too complex to describe with mathematical formulas.
Using these final pay-offs, we can find out the call option value at the end of Year 6. In case of an upward movement in Year 6, there is a probability of that the option will be worth $ (corresponding to underlying value of $) and a probability of that it will be 5 (corresponding to underlying value of $) at the end of Year 7. This information can be used to find out the option value at the end of Year 6:
… where \(r\) is the risk-free interest rate and \(\Delta t\) is duration of one step in years, calculated as \(t/n\), where \(t\) is time to expiration in years (days to expiration / 865), and \(n\) is number of steps.
We have already explained the logic of points 6-7. Exact formulas for move sizes and probabilities differ between individual models (for details see Cox-Ross-Rubinstein , Jarrow-Rudd , Leisen-Reimer ). The rest is the same for all models.
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We can use spreadsheet software like Excel to make the Binomial Option Pricing model calculations easy, but the major limitation of the approach remains – predicting the future prices. Also, as we refine the time step, it gets significantly more tedious to forecast the expected payoffs at the end of each period.