Finding Undervalued/Overvalued SPX Options: An In-Depth Guide with Calculation Examples
Let's explore various ways to derive the theoretical fair value of SPX options. While no single method perfectly predicts the 'true value', understanding these calculations provides a solid foundation for identifying potential mispricings.
Step 1: Option Pricing Models
The Black-Scholes Model: This remains the most widely used model. Remember its key inputs:
Spot Price (S)
Strike Price (X)
Time to Expiration (T)
Risk-Free Interest Rate (r)
Implied Volatility (IV)
Example 1: Pricing a Call Option
Let's assume the following:
SPX Current Price (S): 4,000
Strike Price (X): 4,100
Time to Expiration (T): 1 month (expressed as 1/12 of a year)
Risk-Free Rate (r): 2%
Implied Volatility (IV): 20%
Plugging these values into a Black-Scholes calculator gives us a theoretical call option price of approximately $25.50
Example 2: Pricing a Put Option
Using the same inputs, but for a put option with a 4,100 strike price, the Black-Scholes model gives us a theoretical price of around $51.
Step 2: Limitations of Black-Scholes
The Black-Scholes model makes simplifying assumptions that don't always hold in real-world markets. Key limitations include:
Constant Volatility: The model assumes IV remains unchanged over the option's life, which rarely happens.
Lognormal Returns: It assumes stock prices move in a lognormal distribution, which doesn't fully account for extreme price jumps or crashes.
No Dividends: Relevant for stock options, but not for SPX options.
Step 3: Alternative Models and Adjustments
Binomial Tree Model: This model accounts for potential changes in volatility and more accurately reflects the reality of early exercise for American-style options.
Monte Carlo Simulations: These simulations generate thousands of potential price paths for the underlying assets to derive a more robust estimate of option prices.
Adjusting for Skew: Analyze the IV skew (how IV changes with strike price) and adjust your option pricing model's volatility input to create a more accurate valuation.
Step 4: Determining Undervaluation/Overvaluation
Once you have a theoretical fair value:
Compare to Market Price: If the option's actual market price is significantly lower than its theoretical value, it might be considered undervalued. Conversely, a market price well above the fair value might indicate overvaluation.
Relative Valuation: Compare the option's pricing to options with similar characteristics (strike, expiration) to identify discrepancies.
Important Considerations
Market Sentiment: Fear and uncertainty can drive up implied volatility and inflate option prices beyond their theoretical values.
Supply and Demand: A surge in demand for an option can drive its price significantly higher regardless of its theoretical valuation.
Step 5: Charting
Visualize option price behavior alongside the SPX's price movement for further insights into potential mispricings. Also, chart the implied volatility across different strikes and expirations to analyze the volatility skew.
Step 6: Risk Management
Always prioritize risk management. Position sizing, the use of spreads, and strategic hedges will mitigate the risks inherent in options trading, especially when targeting potentially undervalued options.
