The binomial tree model is a commonly used approach for pricing derivatives, such as options. The basic idea behind the model is to create a tree of possible stock prices over time, based on a set of input parameters
The binomial tree model is a commonly used approach for pricing derivatives, such as options. The basic idea behind the model is to create a tree of possible stock prices over time, based on a set of input parameters. By working backwards through the tree, we can calculate the fair value of the derivative at each node, and ultimately arrive at a price for the derivative at the current time.
The key inputs to the binomial tree model are:
The up factor (u) is calculated as e^(σ * sqrt(dt)), where dt = T/n The down factor (d) is calculated as 1/u The probability of an up move (p) is calculated as (e^(r*dt) - d) / (u - d) The probability of a down move (1-p) is simply 1-p Once we have constructed the binomial tree, we can work backwards through the tree to calculate the fair value of the derivative at each node, using the following formulas:
For a call option, the option value at a given node is Max(S-K, 0) For a put option, the option value at a given node is Max(K-S, 0) The option value at a given node is then discounted to the current time using the risk-free rate and the time to that node. By working backwards through the tree in this way, we can calculate the fair value of the derivative at the current time, which is the price we would expect to pay to enter into the derivative contract.
Overall, the binomial tree model provides a relatively simple and intuitive way to price derivatives, and can be extended to handle more complex instruments, such as American options, which can be exercised at any point prior to expiration.