Question

Introduce the binomial model of option pricing and describe its design and underlying assumptions. Make sure you consider both the one-step and the two-step tree

Answer 1

Binomial option pricing model:

It is a model that is used to price options. When compared with black scholes model, it is mathematically easy to use. The model is based on the concept of arbitrage.

Assumptions under binomial option pricing model:

• There are only two possible prices for the underlying asset on the next day. It is from this assumption that it got the name binomial option model (bi means two).
• There could be two possible prices namely up & down price.
• It is assumed that the underlying asset doesn’t pay any dividends.
• The rate of interest is assumed to be constant throughout the life of the option.
• It is assumed that there are no taxes & transaction costs.
• Investors are indifferent towards the risk.

One step binomial model:

If there is a price of the stock S0, If we want to derive current price of European call option on the stock, if the option lasts for time t & during the life of the option, the price can either move from S0 to new level or down from S0 to new level. Thus movement of stock price can be described as one step binomial tree.

Two step binomial tree:

The above analysis can be extended when the movement of the stock price can be described by a two step binomial tree. The stock price is initially S0. During each time it either moves up to u times the previous price or moves down to d times the previous price. The option on the stock matures at t & the length of each time step is t/2. The value of the option after two down movements is denoted by fdd