How To Calculate Put Option In Excel

Calculate put option prices using the Black-Scholes model with parameters you can export to Excel

Comprehensive Guide: How to Calculate Put Options in Excel

Put options are financial derivatives that give the holder the right, but not the obligation, to sell a stock at a predetermined price (strike price) by a specific date. Calculating put option prices manually can be complex, but Excel provides powerful tools to model these calculations using the Black-Scholes formula or binomial trees.

Understanding Put Option Basics

Before diving into calculations, it’s essential to understand key components:

• Strike Price (K): The price at which the option holder can sell the stock
• Current Stock Price (S): The market price of the underlying stock
• Time to Expiration (T): Time remaining until the option expires
• Volatility (σ): Measure of how much the stock price fluctuates
• Risk-Free Rate (r): Theoretical return of an investment with zero risk
• Dividend Yield (q): Expected dividend payments during the option’s life

The Black-Scholes Model for Put Options

The Black-Scholes formula for put options is:

P = Ke^-rTN(-d₂) – Se^-(q)TN(-d₁)

Where:

• d₁ = [ln(S/K) + (r – q + σ²/2)T] / (σ√T)
• d₂ = d₁ – σ√T
• N(x) = Cumulative standard normal distribution function

Step-by-Step Excel Implementation

1. Set Up Your Inputs: Create cells for all required parameters (S, K, T, r, σ, q)
2. Calculate d₁ and d₂:
   • d1 = (LN(stock_price/strike_price) + (risk_free_rate – dividend_yield + volatility^2/2)*time_to_expiry) / (volatility*SQRT(time_to_expiry))
   • d2 = d1 – volatility*SQRT(time_to_expiry)
3. Calculate N(d₁) and N(d₂): Use Excel’s NORM.S.DIST function:
   • =NORM.S.DIST(d1, TRUE) for N(d₁)
   • =NORM.S.DIST(d2, TRUE) for N(d₂)
4. Calculate Put Price:

   =EXP(-risk_free_rate*time_to_expiry)*strike_price*NORM.S.DIST(-d2, TRUE) – EXP(-dividend_yield*time_to_expiry)*stock_price*NORM.S.DIST(-d1, TRUE)

Excel Functions Breakdown

Function	Purpose	Example
LN()	Natural logarithm	=LN(150/145)
SQRT()	Square root	=SQRT(0.25)
EXP()	Exponential function	=EXP(-0.015*0.25)
NORM.S.DIST()	Standard normal cumulative distribution	=NORM.S.DIST(0.5, TRUE)
POWER()	Raises number to a power	=POWER(0.25, 2)

Practical Example in Excel

Let’s calculate a put option with these parameters:

• Stock Price (S) = $150
• Strike Price (K) = $145
• Time to Expiry (T) = 90 days (0.2466 years)
• Risk-Free Rate (r) = 1.5%
• Volatility (σ) = 25%
• Dividend Yield (q) = 1.2%

Cell	Formula	Result
A1	150 (Stock Price)	150
A2	145 (Strike Price)	145
A3	0.2466 (Time in years)	0.2466
A4	0.015 (Risk-Free Rate)	0.015
A5	0.25 (Volatility)	0.25
A6	0.012 (Dividend Yield)	0.012
A7	=LN(A1/A2)+(A4-A6+A5^2/2)*A3)/(A5*SQRT(A3))	0.3481 (d1)
A8	=A7-A5*SQRT(A3)	0.1981 (d2)
A9	=EXP(-A4*A3)*A2*NORM.S.DIST(-A8,TRUE)-EXP(-A6*A3)*A1*NORM.S.DIST(-A7,TRUE)	$4.82 (Put Price)

Advanced Excel Techniques

For more sophisticated analysis:

1. Data Tables: Create sensitivity tables to see how option prices change with different inputs
2. Goal Seek: Find the implied volatility that makes the model price equal to the market price
3. Monte Carlo Simulation: Model potential price paths using random number generation
4. VBA Macros: Automate complex calculations with Visual Basic for Applications

Common Mistakes to Avoid

• Time Unit Mismatch: Ensure all time units are consistent (days vs. years)
• Volatility Input: Volatility should be entered as a decimal (0.25 for 25%), not percentage
• Dividend Omission: Forgetting to account for dividends can significantly affect results
• Negative Time Values: Time to expiry must be positive
• Incorrect Normal Distribution: Using NORM.DIST instead of NORM.S.DIST for standard normal

Alternative Models in Excel

While Black-Scholes is standard, other models can be implemented:

Model	When to Use	Excel Implementation
Binomial Tree	American options, dividends, early exercise	Complex nested IF statements or VBA
Monte Carlo	Complex path-dependent options	RAND(), AVERAGE(), and iterative calculations
Black-76	Futures options	Modified Black-Scholes with futures price
Bjerksund-Stensland	American options approximation	Complex formula with multiple components

Verifying Your Calculations

To ensure accuracy:

1. Compare with online calculators like the CBOE Options Calculator
2. Check boundary conditions (when T=0, put price should equal max(K-S, 0))
3. Verify that put-call parity holds: C – P = S – Ke^-rT
4. Test with known values from finance textbooks

Excel Template Download

For a ready-to-use template, you can download this Put Option Calculator Excel Template that includes all the formulas pre-built. The template features:

• Automatic calculations with data validation
• Dynamic charts showing price sensitivity
• Greeks calculation (Delta, Gamma, Vega, Theta, Rho)
• Comparison with call option prices

Academic Resources

For deeper understanding, consult these authoritative sources:

• Federal Reserve: What is the Black-Scholes Model?
• Corporate Finance Institute: Black-Scholes Model Guide
• Investopedia: Black-Scholes Model Explained
• NYU Stern: Options and Derivatives Valuation

Excel Shortcuts for Option Calculations

Speed up your workflow with these keyboard shortcuts:

Shortcut	Action
F4	Toggle absolute/relative references
Ctrl+Shift+Enter	Enter array formula (for complex calculations)
Alt+=	Quick sum (useful for totaling sensitivity tables)
Ctrl+1	Format cells (for currency, percentage formatting)
Ctrl+D	Fill down (copy formulas quickly)

Limitations of Excel for Option Pricing

While Excel is powerful, be aware of its limitations:

• Performance: Complex models with many iterations can slow down
• Precision: Excel uses 15-digit precision which may affect very sensitive calculations
• Real-time Data: Requires manual updates or API connections for live prices
• Complex Options: Exotic options may require specialized software
• Error Handling: Need to build robust error checking for invalid inputs

Professional Applications

Put option calculations in Excel are used by:

• Portfolio Managers: For hedging strategies and risk management
• Traders: To identify mispriced options in the market
• Financial Analysts: For valuation models and scenario analysis
• Academics: For teaching finance concepts and testing theories
• Corporate Finance: For employee stock option valuation

Future Developments in Option Pricing

Emerging trends that may affect Excel implementations:

• Machine Learning: AI models that can predict volatility more accurately
• Blockchain: Smart contracts that automate option execution
• Quantum Computing: Potential to solve complex pricing models instantly
• Cloud Computing: Excel Online with enhanced calculation power
• Big Data: Incorporating more market data points in real-time