##
Binary option pricing

The payoff of binary options differ from those of regular options. Binary options either have a positive payoff or none. In the example of a binary call, if the price at a certain date,

**Southward**

_{
T
},_{}

is larger than or equal to a strike cost

**G**, it will generate a payoff

**Q**. Notice, that information technology does not matter whether the hereafter stock price only equals the strike, is somewhat larger or a lot larger. Thus as long as the stock price is larger than or equal to K, the payoff of a binary does not change.

The same holds in the instance of a binary put. Of course, this pick only generates a payoff

**Q**, if the stock price

**S**

_{
T
},_{
}is smaller than the strike cost

**1000**.

##
Binary option pricing: simulation ingredients

The most straightforward manner in pricing a binary option is done through a simulation experiment. In many simulation exercises, the geometric Brownian motion, as shown below, can be used to model the underlying stock behaviour. In this formula**S** equals the price of the stock,

**μ** equals the stock’s render,

**σ** equals the stock’s volatility and

**Δt**

equals ane time footstep. Another possibility to value binary options is the construction of a multi-step binomial model.

In order to implement the stock price evolution in Excel this has to be restated as follows:

With an uncertainty parameter**ε**generated by a certain distribution, often just a normal distribution.

##
Binary selection pricing: simulation implementation

The value of a Binary choice can be calculated based on the following method:

Footstep 1: Decide the return**μ**, the volatility**
σ**, the risk free rate

**the time horizon**

r,

r,

T

T

and the time stride

**Δt**

Stride two: Generate using the formula a price sequence

Step iii: Calculate the payoff of the binary telephone call and, or put and shop it

Pace 4: Apply step ii and 3 N times (e.1000. 10000)

Step 5: Calculate the average of all the stored payoffs

Pace 6: Discount this value back to today

##
Summary

Binary options either generate in the future a sure payoff as specified by the contract or none at all. Binary option pricing can be done through a Monte Carlo simulation experiment. Because of its fixed payoff and its resemblence to sport betting, binary option trading is oftentimes seem as pure speculation or gambling.

**Source: https://breakingdownfinance.com/finance-topics/derivative-valuation/option-valuation/binary-option-pricing/**