Understanding Binary Options in Excel

Binary option is a type of trading that involves predicting whether the price of an underlying asset will go up or down within a certain time period. The trader can choose to buy or sell the option, depending on their expectation of the market movement. The trader receives a fixed payout if the option expires in the money, meaning that the price of the asset was higher than the strike price at the expiration time. The trader loses their entire investment if the option expires out of the money, meaning that the price of the asset was lower than or equal to the strike price at the expiration time.

Binary option is different from other types of options, such as vanilla options, which give the holder the right to buy or sell an underlying asset at a specified price on or before a certain date. Vanilla options allow traders to take a position in the underlying asset and benefit from its price fluctuations. Binary options do not give traders any ownership or exposure to the underlying asset, and they only depend on whether their prediction is correct or not.

Binary option is also different from other types of trading, such as spot trading, futures trading, or forex trading, which involve buying and selling assets at their current market prices. Binary option involves betting on whether an asset will be above or below a certain level at a certain time. Binary option has a fixed expiry time and a fixed payout rate, which are determined by the broker and agreed upon by both parties before placing an order.

Binary option is considered a high-risk and unpredictable investment option by many regulators and authorities around the world. It is prone to fraud and scams by unlicensed brokers who may manipulate prices, misrepresent information, or disappear with traders’ money. It is also banned by some countries, such as Australia, Israel, and Indonesia, as it may pose legal and ethical issues for investors.

Basic Theory

A binary option is a financial instrument with only two possible outcomes: a fixed payout or nothing at all. Traders predict whether the price of an underlying asset will be above or below a predetermined strike price at the option’s expiration. If the prediction is correct, the trader receives a fixed payout; otherwise, they lose the initial investment.

Procedures

Define Variables:
- Underlying Asset Price (S)
- Strike Price (K)
- Time to Expiration (T)
- Volatility (σ)
- Risk-Free Rate (r)
- Binary Option Type (Call/Put)
Use Black-Scholes Formula:The Black-Scholes formula is commonly used to calculate the theoretical price of European-style binary options. For a Call option:
$C = e^{-rT} \cdot N(d_2)$

For a Put option:

$P = e^{-rT} \cdot N(-d_2)$

Where:
- $d_2 = \frac{{\ln(S/K) + (r - \frac{{\sigma^2}}{2})T}}{{\sigma \sqrt{T}}}$
- $N(x)$ is the cumulative distribution function of the standard normal distribution.
Construct an Excel Table:Create a table with columns for the variables (S, K, T, σ, r) and calculated values (d2, Call Price, Put Price).

Scenario with Real Numbers

Let’s consider a scenario with the following values:

Underlying Asset Price ( $S = 100$ )
Strike Price ( $K = 105$ )
Time to Expiration ( $T = 1$ year)
Volatility ( $σ = 0.2$ )
Risk-Free Rate ( $r = 0.05$ )
Call Option

Enter these values into an Excel table.
Calculate $d_2$ using the formula mentioned earlier.
Use $d_2$ to calculate the Call option price using the Black-Scholes formula.
Display the results in the Excel table.

Result

For the given scenario, the calculated Call option price is $0.2824.

Other Approaches

Binomial Model: Use a binomial tree to approximate option prices at different nodes.
Monte Carlo Simulation: Simulate random price movements to estimate option prices.

These alternative approaches provide flexibility and can be implemented in Excel using appropriate formulas and simulations.