There are no PFE option models. The contest is $1K to anyone who can tell the class what's wrong with existing option pricing models (model indy, as a whole)?
Parkinson's High-Low Range σ² = (1 / (4n × ln(2))) × Σ[ln(High_i/Low_i)]² Where: σ² is the variance (volatility squared) n is the number of days in the sample High_i is the highest price on day i Low_i is the lowest price on day i
Last try Garman-Klass volatility estimation σ² = (1/n) × Σ[0.5 × (ln(High_i/Low_i))² - (2ln(2)-1) × (ln(Close_i/Open_i))²] Where: σ² is the variance (volatility squared) n is the number of days in the sample High_i, Low_i, Open_i, Close_i are the respective prices for day i (2ln(2)-1) is approximately 0.383
Fundamental Flaws in Existing Option Pricing Models Option pricing models, such as Black-Scholes, Binomial, and Monte Carlo, are foundational tools in financial markets for valuing options and informing trading strategies. While these models have revolutionized derivatives pricing, they suffer from several critical flaws that limit their accuracy and applicability in real-world trading scenarios. Below, I outline the primary issues with these models as a collective framework, emphasizing their theoretical and practical shortcomings. Unrealistic Assumptions About Market Dynamics Existing option pricing models rely on simplifying assumptions that often diverge from actual market behavior. For instance, many models assume continuous price movements, constant volatility, and no transaction costs, which are unrealistic in dynamic markets. They typically presume that asset prices follow a log-normal distribution, ignoring the fat-tailed distributions and sudden jumps (e.g., due to news or liquidity shocks) that characterize real price action. These assumptions lead to mispriced options, particularly for out-of-the-money or exotic options, where extreme price movements are more likely. Traders relying on these models may underestimate tail risks, resulting in suboptimal hedging or pricing decisions. Inadequate Handling of Volatility Volatility is a central input in option pricing models, yet these models often mishandle it. Most assume volatility is constant or follows a predictable pattern, whereas markets exhibit stochastic and clustering volatility, with periods of calm followed by sharp spikes. Even models that incorporate time-varying volatility (e.g., stochastic volatility models) struggle to capture the full complexity of volatility surfaces, particularly during high-impact events. This leads to inaccurate option valuations, as implied volatility (derived from market prices) frequently deviates from model assumptions, forcing traders to manually adjust inputs, undermining the models’ predictive power. Neglect of Market Microstructure and Liquidity Option pricing models generally overlook market microstructure factors, such as liquidity constraints, bid-ask spreads, and order book dynamics. They assume frictionless trading with infinite liquidity, which is far from reality, especially in less liquid options markets or during volatile periods. Wide spreads or thin order books can significantly affect option prices, yet models fail to account for these costs, leading to theoretical valuations that don’t reflect executable prices. For traders, this disconnect can result in overpaying for options or misjudging risk, particularly in fast-moving markets where liquidity dries up. Limited Adaptability to Non-Standard Instruments While effective for vanilla options (e.g., European calls/puts), existing models struggle with exotic or path-dependent options (e.g., Asian, barrier, or lookback options). Models like Black-Scholes are tailored to specific payoff structures and struggle to generalize, requiring complex modifications or computationally intensive methods (e.g., Monte Carlo simulations) that are impractical for real-time trading. This lack of flexibility limits their utility for pricing bespoke derivatives or structured products, forcing traders to rely on approximations that may not capture the instrument’s true risk profile. Failure to Incorporate Behavioral and Sentiment Factors Option pricing models are rooted in mathematical assumptions about rational market behavior, ignoring the psychological and sentiment-driven actions of market participants. Factors like fear, greed, or herding behavior—evident in volatility skews or option demand spikes during market stress—are not modeled, leading to discrepancies between theoretical and market prices. This behavioral disconnect means models often undervalue or overvalue options in emotionally charged markets, reducing their reliability for traders navigating real-world conditions. Conclusion In summary, existing option pricing models, while groundbreaking, are hampered by unrealistic assumptions, inadequate volatility modeling, neglect of market microstructure, limited adaptability to complex instruments, and failure to account for behavioral factors. These flaws result in valuations that frequently diverge from actual market prices, posing challenges for traders seeking accurate pricing and risk management. While no model can fully capture the market’s complexity, addressing these limitations—through dynamic volatility inputs, microstructure adjustments, or behavioral considerations—would enhance their practical utility, offering traders a more robust framework for decision-making in the options market.
Some kind of Montecarlo would be truly model independent Code: 1. Collect price data at the highest available frequency 2. Create N bootstrap samples of the price path 3. For each sample, record the maximum range 4. Calculate the interquartile range (IQR) of these maximums 5. Derive empirical scaling factors across different time horizons 6. Report the final volatility as the IQR of maximum ranges scaled to the desired time frame