You are here

20banner.png?itok=oRphv0VF /%

The Binomial Option Pricing Model is an options valuation method developed by Cox in 1979.  It is a very simple model that uses an iterative procedure to price options, allowing for the specification of nodes, or points in time, during the time span between the valuation date and the options expiration date. When compared to the Black Scholes model and other complex models, the binomial option pricing model is mathematically simple and easy to use.

The model  lowers the possibilities of price changes and is based on the concept of no arbitrage, it assumes a perfectly efficient market, and shortens the duration of the option. Under these simplifications, it is able to provide a mathematical valuation of the option at each node specified.

Binomial Option pricing model is an important topic for the FRM Part 1 exam. There are both conceptual and numerical questions in the exam to test this topic. Here, we will discuss various concepts related to binomial option pricing model.

Assumptions in Binomial Option Pricing Model

One simplifying assumption that the Binomial Option Pricing Model makes is that over a certain time period, the underlying can only do one of two things: go up, or go down

In detail, the assumptions in binomial option pricing models are as follows:

1. There are only two possible prices for the underlying asset on the next day. From this assumption, this model has got its name as Binomial option pricing model (Bi means two)
2.  The two possible prices are the up-price and down-price
3. The underlying asset does not pay any dividends
4. The rate of interest (r) is constant throughout the life of the option
5. Markets are frictionless i.e. there are no taxes and no transaction cost
6. Investors are risk neutral i.e. investors are indifferent towards risk

Binomial option model building process

Let us consider that we have a share of a company whose current value is S₀. Now in the next month, the price of this share is going to increase by u% (up state) or it is going to go down by d% (down state). No other outcome of price is possible for this stock in next month. Let p be the probability of up state. Therefore the probability of down state is 1-p.

Now let us assume that call option exists for this stock which matures at the end of the month. Let the strike price of the call option be X. Now in case, the option holder decides to exercise the call option at the end of month, what will be the payoffs?

The payoffs are given in the diagram below

Now, the expected payoff using the probabilities of up state and down state. From the above diagram, the expected value of payoff is

Once the expected value of the payoff is calculated, this expected value of payoff has to be discounted by risk free rate to get the arbitrage free price of call option. Use continuous discounting for discounting the expected value of the payoff. FRM Part 1 uses continuous compounding and discounting for all numerical problems on derivatives.

In some questions, the probability of up state is not given. In such a case, probability of up state can be calculated with the formula

Where;

p = up state probability

r = risk free rate

d = Down state factor

u = Up state factor

Using the above the model building process, similar model can be build for multi period options and also for put options.

Binomial Option Pricing Model Advantages

Binomial Option Pricing Model Limitations