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)
Step 5: Calculate the average of all the stored payoffs
Step 6: Discount this value back to today