Subject:

## Binary option pricing: simulation ingredients

The most straightforward way 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 return, **σ** equals the stock’s volatility and **Δt** equals 1 time step. 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 option pricing: simulation implementation

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

Step 1: Determine the return **μ**, the volatility** σ**, the risk free rate** r, **the time horizon** T** and the time step** Δt**

Step 2: Generate using the formula a price sequence

Step 3: Calculate the payoff of the binary call and, or put and store it

Step 4: Apply step 2 and 3 N times (e.g.

## Exotic options: binary (aka, digital) option (FRM T3-44)

10000)

Step 5: Calculate the average of all the stored payoffs

Step 6: Discount this value back to today