Excel Option Pricing Models: Mastering Black-Scholes and Binomial Trees with Rust

Option Pricing in Excel with Black-Scholes and Binomial Trees 🚀

This guide explores implementing option pricing models in Excel, focusing on Black-Scholes and Binomial Trees, enhanced with Rust for performance.

Black-Scholes Model in Excel 📝

The Black-Scholes model is a widely used option pricing formula. Here's how to implement it in Excel:

1. Gather Inputs: Stock price, strike price, time to expiration, risk-free rate, and volatility.
2. Calculate d1 and d2: These are intermediate variables in the formula.
3. Apply the Formula: Calculate the call and put option prices.

Here's the Black-Scholes formula:

Call Option Price: $C = S * N(d1) - X * e^{-rT} * N(d2)$

Put Option Price: $P = X * e^{-rT} * N(-d2) - S * N(-d1)$

Where:

• $S$ = Current stock price
• $X$ = Strike price
• $r$ = Risk-free interest rate
• $T$ = Time to expiration (in years)
• $N(x)$ = Cumulative standard normal distribution function
• $e$ = Base of the natural logarithm

Excel implementation:

# d1 = (LN(S/X) + (r + (σ^2)/2)*T) / (σ*SQRT(T))
# d2 = d1 - σ*SQRT(T)
# Call Option Price = S*NORMSDIST(d1) - X*EXP(-r*T)*NORMSDIST(d2)
# Put Option Price = X*EXP(-r*T)*NORMSDIST(-d2) - S*NORMSDIST(-d1)

Binomial Tree Model in Excel 🌳

The Binomial Tree model is a numerical method for option pricing, especially useful for American options.

1. Set up the Tree: Create a tree representing possible stock price movements over time.
2. Calculate Option Values at Expiration: Determine the option value at each terminal node.
3. Backward Induction: Work backward through the tree to calculate the option value at each node.

Excel implementation involves creating columns representing time steps and rows representing possible stock prices. Formulas are used to calculate the option values at each node.

Enhancing Performance with Rust 🦀

Rust can significantly improve the performance of option pricing calculations, especially for complex models or large datasets. Here's how to integrate Rust with Excel:

1. Write Rust Code: Implement the Black-Scholes or Binomial Tree model in Rust.
2. Compile to DLL: Compile the Rust code into a Dynamic Link Library (DLL).
3. Call DLL from Excel: Use Excel's VBA to call the Rust DLL.

Example Rust code (simplified Black-Scholes):

// src/lib.rs
#[no_mangle]
pub extern "C" fn black_scholes(s: f64, x: f64, r: f64, t: f64, sigma: f64) -> f64 {
    let d1 = (s.ln() - x.ln() + (r + sigma.powi(2) / 2.0) * t) / (sigma * t.sqrt());
    let d2 = d1 - sigma * t.sqrt();
    let nd1 = 0.5 * (1.0 + (d1 / 2.0_f64.sqrt()).erf());
    let nd2 = 0.5 * (1.0 + (d2 / 2.0_f64.sqrt()).erf());
    let call_price = s * nd1 - x * (-r * t).exp() * nd2;
    call_price
}

Compile to DLL:

cargo build --release

Excel VBA to call the Rust DLL:

'VBA Module
Declare Function black_scholes Lib "path/to/your/dll.dll" (ByVal s As Double, ByVal x As Double, ByVal r As Double, ByVal t As Double, ByVal sigma As Double) As Double

Sub TestBlackScholes()
    Dim S As Double, X As Double, r As Double, T As Double, sigma As Double
    S = Range("A1").Value 'Stock Price
    X = Range("A2").Value 'Strike Price
    r = Range("A3").Value 'Risk-free Rate
    T = Range("A4").Value 'Time to Expiration
    sigma = Range("A5").Value 'Volatility
    
    Dim callPrice As Double
    callPrice = black_scholes(S, X, r, T, sigma)
    
    Range("B1").Value = callPrice 'Output
End Sub

This approach allows you to leverage Rust's performance for computationally intensive tasks while using Excel for data management and presentation.