# Binomial option pricing help

Binomial option pricing is a way of pricing an option contract. It’s useful because it takes into account the fact that there are two possible outcomes for any given event, which means you need to calculate both probabilities in order to find out what your expected return will be. Place your order for exemplary binomial option pricing assignment help. ORDER NOW.

Binomial model is based on assumptions about stock price volatility and time-to-expiration. This type of model can apply to many types of financial instruments including stocks, bonds or currency options. What do you think? Do these sound-like good assumptions? Let us know visiting our website for more information.

## What is an option?

An option is a contract that gives the owner of the option, known as the holder, some rights and obligations. The most important right that the holder of an option has is to buy or sell an underlying asset at a fixed price, called exercise price or strike price. This is the only thing that the holder of an option can ever does. The owner of an option may or may not have obligations linked to the holding of that option.

## Types of options

There are two types of options: a call option and a put option.

Call Option: A call option gives the holder the right to buy an underlying asset from the writer, at a certain price called exercise price or strike price. The writer has to sell their stock if he / she gets a call option.

Put Option: A put option gives the holder the right to sell an underlying asset to the writer, at a certain price called exercise price or strike price. …

Options can also be classified using time to maturity.

The two types of options are:

1 – American Options that can be exercised anytime between purchase and expiration date.

2- European Options that can only be exercised on the expiration date.

### What is the difference between European Call Option and American Call Option?

A European option can only be exercised at the expiration date, while an American option can be exercised anytime between purchase and expiration. …

### What is the difference between European Put Option and American Put Option?

A European put option can only be exercised at the expiration date, while an American put option can be exercised anytime between purchase and expiration.

The value of an option is determined by the market using some mathematical models known as Binomial Option Pricing .

## Binomial model for pricing options Model

The Binomial Option Pricing Model is a model for valuing options used in corporate finance and financial mathematics. The model was originally developed by Cox, Ross, & Rubinstein in 1979. The Binomial Option Pricing Model uses a one-period (single date as expiration) model of the option value as the combination of the underlying asset and some riskless debt. The price of each component is determined by random variables that are independent, identically distributed and follow some known probability distribution.

### Assumptions of binomial option pricing model

#### The underlying asset (stock) follows a binomial process

The price of the underlying asset will be assumed to follow a binomial process, and it represents a sequence of independent yes/no experiments in which each experiment has a certain probability of terminating in an up move.

It is assumed that the probability of success in each experiment will be constant over time, which means that the interest rate is constant during the life of the option.

Binomial Distribution: A discrete probability distribution that describes the number of successes in a sequence of independent yes/no experiments, each having success probability p, in a given total number of n trials. The trials are assumed to be statistically independent.

#### The riskless debt pays a constant interest rate

Riskless Rate: This is return provided by an investment that is totally safe. There is a constant risk free rate for borrowing and lending.

#### There is implied volatility

Implied Volatility: Implied volatility shows how much the market thinks that the underlying security should move in a period. It can be viewed as a gauge for sentiment or expected future volatility.

#### Principle of risk neutral valuation

Risk-Neutral Pricing: The risk-neutral probability of an up move is the probability that would be inferred if all future cash flows of the underlying asset were viewed as statistically independent random variables and had identical distributions.

An Example:

Suppose the binomial tree has q = 0.3, n = 50 periods with a time interval of Δt = 1/q (periods). The binomial tree is shown in the following figure. …

Let’s consider an example with n = 50, q=0.3 and Δt=1/q (periods).

The Black-Scholes model produces a price of \$11.33 for this call option whereas the Binomial Model calculates the price to be \$10.74. The Black-Scholes model gives a theoretical price which is unbiased but only accurate as the number of periods increases without limit.( The Binomial Model always gives a more accurate estimate.)

The Binomial Model has become a widely used technique for option pricing due to its speed, accuracy and relative simplicity.

– The riskless debt follows a geometric Brownian motion in the Black Scholes setting.

### Factors affecting option prices

The value of an option depends on the following factors:

#### Underlying asset price.

The higher the price, the more expensive is the option.

#### Time to expiration

The longer the time to expiration, the more valuable is the option because there are more opportunities for movements in underlying prices, and therefore a greater chance that the option will expire in-the-money.

#### Volatility of the underlying security’s price

The more volatile the price movement, the greater is the chance that the option will finish in-the-money and thus the higher is its value.The increase in volatility would cause an increase in option prices for calls and puts.

#### Riskless interest rate

The higher the assumed interest rate, the more valuable is the option because it follows a riskless debt and there exists no reinvestment risk.An increase in the interest rate causes an increase in the option prices for calls and puts.

#### Strike price of the option relative to spot price of the underlying

If the strike price is above (below) the current price, then for calls (puts) it is disadvantageous to exercise the option early because it can be more profitable to wait until expiration before making a decision. An increase in the strike price causes an increase in call prices and decrease in put prices.

#### Time to maturity

The time to expiration must be small compared with n. This assumption holds only when the interest rate is constant during the life of the option, which means that there exists no reinvestment risk.

An increase in the number of periods causes an increase in option prices for calls and puts.

### Classification of options according to strike price

Option can be classified further according to the state of the strike price of the underlying asset.

#### Type 1 options: Types of options with a known strike price

A type 1 option is an option that has a known strike price. Types of options with a known strike price are as follows:

– Call options- In this case, the value of the call is zero at expiry because there is no point in exercising it when you can sell the stock for the same price.

– Put options- In this case, the value of the put is zero at expiry because there is no point in exercising it when you can buy the stock for the same price. Types of options with a known strike price are also called conventional options.

#### Type 2 options: Types of option without a known strike price

A type 2 option is an option that has no known strike price. Types of options without a known strike price are as follows:

– Call options- In this case, the value of the call is zero at expiry because you can buy the stock for \$100 and sell it for \$200, so there is no point in exercising the option early.

– Put options- In this case, the value of the put is zero at expiry because you can sell the stock for \$100 and buy it for \$200, so there is no point in exercising the option early. Types of Options without a known strike price are also called exotic options.

### Risk management using options

In the context of finance, risk management refers to a set of techniques used to hedge funds from risk or uncertainty in order to make a profit. Options can be used for hedging against risk and uncertainty .

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