Crypto Treasury Models: Balance Sheet Risk and Bitcoin Price Dependency

As crypto currencies gain broader acceptance, some corporations have begun including crypto in their balance sheets, forming new "crypto treasury" models. However, these models entail significant financial risks. Digital asset price volatility can translate into earnings variability and elevated refinancing risk—effects that are amplified when acquisitions are debt-financed.

Reference [1] investigates the relationship between Bitcoin (BTC) and equity markets, focusing on firms that have adopted BTC as part of their corporate treasury strategy. The study uses a dataset of 39 publicly listed BTC-holding companies from 2017 to 2025. The author applies correlation analysis, single-factor return models, and transfer entropy methods to quantify both linear and nonlinear dependencies.

Of particular interest is the use of Transfer Entropy, an extension of Wiener-Granger causality, which can identify the causal direction of dependency. The authors pointed out,

This study offers a detailed empirical assessment of the evolving link between Bitcoin (BTC) and equity markets in the context of corporate treasury strategies centered on digital assets. Focusing on Strategy (MSTR), the largest public holder of BTC, we combine correlation analysis, single factor models, and transfer entropy (TE) techniques to quantify the direction and dynamics of informational dependence between BTC and MSTR equity returns

Our findings consistently indicate that BTC serves as the dominant source in the information flow. On average, TE_BTC→MST R is higher than in the reverse direction, and statistically significant directional dependence from BTC to MSTR is more frequent and persistent. These asymmetries become particularly pronounced during market-wide events. In contrast, TEMST R→BT C peaks are rare, localized, and confined mainly to firm-specific actions such as convertible bond issuances or balance sheet disclosures.

…Rolling TE reveals a richer structure, characterized by intermittent bursts of significant influence and prolonged periods of near-random noise. This calls into question the reliability of static hedge ratios and highlights the need for adaptive quantitative strategies and risk management approaches that respond to changing market conditions.

In short, there is a strong relationship between BTC prices and the stock prices of firms that adopted crypto treasury models. However, this relationship is mostly unidirectional, flowing from BTC to equity prices.

The article also points out that the relationship is not stable and can appear random for prolonged periods. This characteristic must be considered when designing hedging strategies.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Sabrina Aufiero, Antonio Briola, Tesfaye Salarin, Fabio Caccioli, Silvia Bartolucci, Tomaso Aste, Cryptocurrencies in the Balance Sheet: Insights from (Micro)Strategy -- Bitcoin Interactions, arXiv:2505.14655

Post Source Here: Crypto Treasury Models: Balance Sheet Risk and Bitcoin Price Dependency

source https://harbourfronts.com/crypto-treasury-models-balance-sheet-risk-bitcoin-price-dependency/

Risk, Timing, and Strategy: Key Differences in 0DTE Options Trading Styles

We have discussed the impact of 0DTE options on the market, drawing from both practitioner insights and academic literature. Both sources point to the conclusion that 0DTE options have little or almost no impact on the market; they do not increase market volatility, contrary to what many investors have argued.

The CBOE recently updated its report with new data, which briefly reconfirmed that 0DTE options have little or no impact,

High volume doesn’t equal high risk. What matters for determining the potential impact of market maker gamma hedging activity is the balance of the volume between buys vs. sells, not the notional size. And what’s remarkable about SPX 0DTE flow is how balanced it is between buyers and sellers, puts and calls. As we outlined above, both institutional and retail investors use these options for a range of purposes – from tactical bets to systematic yield harvesting. This is why the put/call ratio for SPX 0DTE options have consistently hovered around one, in sharp contrast to non-0DTE options (where the primary use case is hedging). This is also why the net gamma exposure (or market maker positioning) of 0DTE options have been so minimal.

The report also compares retail and institutional traders, offering several useful insights.

• Both groups use similar strategies, with just over half of opening customer trades in outright puts and calls, and the remainder in multi-leg strategies. Institutional investors show a slightly higher preference for vertical spreads, while retail traders are more active in complex strategies like iron condors and butterflies.
• Institutional investors tend to initiate positions early in the trading day and leave them open longer—likely due to higher risk tolerance or the availability of alternative hedging methods. In contrast, retail traders are active both at the open and close of the trading session.
• Retail traders frequently initiate and unwind positions throughout the day, suggesting more hands-on risk management and a lower tolerance for risk.

The report highlights that while the strategies are broadly similar, the approach to timing and risk management differs meaningfully between the two groups.

Let us know what you think in the comments below or in the discussion forum.

References

[1] 0DTEs Decoded: Positioning, Trends, and Market Impact, CBOE, May 2025

Originally Published Here: Risk, Timing, and Strategy: Key Differences in 0DTE Options Trading Styles

source https://harbourfronts.com/risk-timing-strategy-key-differences-0dte-options-trading-styles/

Market Regimes and Strike Selection: A Case Study on the Call Condor

Parameter optimization is a technique used in trading strategy design. It is used to identify the best set of parameters for maximizing performance and to study the strategy dynamics in order to gain insights. However, while this technique is frequently applied to linear instruments, it is used less often on non-linear instruments, such as options. This is likely due to the complexities involved in modeling non-linear instruments.

Reference [1] attempts to optimize the parameters of a popular options strategy, the call condor. The authors studied strike selection within the context of a specific market regime. They pointed out,

Next, the study examines how market scenarios impact the results mentioned above. As shown in Pane A of Figure 4, widening outside ranges is more feasible for the neutral market than for the bullish and bearish markets. Three curves represent the dynamics of fair value for the LCC strategy over the widths of the outside ranges given three market scenarios. The fair values gradually increase over the widths of the outside ranges for all market scenarios. However, a wider range of outside strikes can boost profits more in the neutral market scenario because the future market price is more likely to fall in the range. Our findings suggest that a wider range of outside strikes is more appropriate for the neutral market.

Although a wider inside range (K3 – K2) of strike prices can yield a lower fair value for the LCC strategy, the trader obtains relatively lower profits in both bearish and bullish markets and higher profits in the neutral market. The economic implication is that strategy traders can achieve greater profits by choosing an exact portfolio of options with a narrower range of strikes to capture specific market scenarios. Suppose the strategy traders remain in a bullish or bearish market. In that case, they should adjust their choice of inside ranges to align closer with the prevailing bullish or bearish market conditions, respectively.

In short, by analyzing the optimal parameters, the authors identified the most favorable market environment for each strike selection.

Note that the study was conducted using theoretical option prices rather than traded prices, but it still offers valuable insights. Portfolio and risk managers can benefit from this type of simulated study to enhance their understanding of strategy and decision-making.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Jin-Ray Lu, Motsa Zandile Tema, Evaluating the Choices of Strike Ranges for the Long Call Condor Strategy, International Review of Accounting, Banking and Finance, Vol 17, No. 1, Spring, 2025, Pages 42-56

Article Source Here: Market Regimes and Strike Selection: A Case Study on the Call Condor

source https://harbourfronts.com/market-regimes-strike-selection-case-study-call-condor/

Trend vs. Mean Reversion: A Statistical Physics Approach to Financial Markets

Trend and mean reversion are two prevalent forces in financial markets. Studying their interplay is important, as it provides clues for developing accurate timing models. Reference [1] formally examines the relationship between trend and mean reversion in financial markets, across timeframes ranging from intraday to monthly, and spanning over 300 years.

The authors propose a lattice gas model of financial markets, where the lattice represents the social network of investors, and the gas molecules represent shares of an asset. Mathematically, for a given market and time horizon, they define the strength ϕ of a trend using its t-statistic. They find that tomorrow’s return, 𝑅(𝑡+1) (normalized to have variance 1), is well modeled by a cubic polynomial of today’s trend strength,

R(t + 1) = a + b · ϕ(t) + c · ϕ(t)^3 + ϵ(t)

• …trends tend to revert before they become statistically strongly significant. In other words, by the time a trend has become so obvious that everybody can see it in a price chart, it is already over. This is consistent with the hypothesis that any obvious market inefficiency is quickly eliminated by investors.
• The parameters b, c are universal in the sense that they seem to be the same for all assets within the limits of statistical significance. This is in line with the fact that many successful trend-followers use the same systematic trading strategy for all assets.
• c is negative and does not seem to depend much on the trend’s time horizon T. However, b depends on the horizon: it peaks at T ∼ 3-12 months, which is in line with the time scales on which trend followers typically operate. b decays for longer or shorter horizons and appears to become negative for T < 1 day or T > several years.
• While c has been fairly stable over time, b appears to have vanished over the decades. This is in line with the fact that trendfollowing no longer works as well today as it did in the 1990’s. Markets seem to have become quite efficient with respect to trends.

In short, the authors develop an interesting model of the financial market and conclude that markets tend to be in a trending regime over time scales from a few hours to a few years while exhibiting mean reversion over shorter and longer horizons. In the trending regime, weak trends tend to persist, whereas in the reversion regime, weak trends tend to reverse.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Sara A. Safari, Christof Schmidhuber, Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades, https://ift.tt/mjHlSqe

Post Source Here: Trend vs. Mean Reversion: A Statistical Physics Approach to Financial Markets

source https://harbourfronts.com/trend-vs-mean-reversion-statistical-physics-approach-financial-markets/

Forecasting Volatility in Digital Assets: A Comparative Study

Modeling the volatility of cryptocurrencies is important for understanding and managing risk in these markets. Reference [1] provides a literature review of various volatility prediction approaches and evaluates three models: GARCH, EGARCH, and EWMA.

The EGARCH model is an extension of the GARCH model that accounts for the asymmetric impact of positive and negative shocks on volatility. It reflects the common belief that bad news tends to cause larger market reactions than equally sized good news. The authors pointed out,

The EGARCH (1,1) volatility estimation model demonstrated superior performance. This finding aligns with the outcomes of a study conducted by Alexander and Dakos (2023), Ngunyi et al. (2019), and Naimy and Hayek (2018) demonstrating that the asymmetric GARCH model exhibited superior performance across several cryptocurrencies. Further, Bergsli et al. (2022) found that the EGARCH and APARCH model exhibited superior performance compared to other GARCH models. According to the findings of the aforementioned study, the GARCH (1,1), EGARCH (1,1), and EWMA volatility estimation model exhibited limitations in capturing high volatility fluctuations and demonstrate improved accuracy when the observed daily volatility is at a lower level. However, it is crucial to acknowledge that the aforementioned discoveries are only relevant to Bitcoin and Ethereum. The maximum threshold of high volatility is expected to be linked to the degree of uncertainty. This finding might assist investors and prospective investors in evaluating the risks and rewards associated with the Bitcoin and Ethereum.

In short, the EGARCH(1,1) model performs the best for both Bitcoin and Ethereum.

This article is important because it highlights effective tools for forecasting crypto market volatility. It also discusses the weaknesses of these forecast models, notably their limitations in capturing periods of high volatility, while showing improved accuracy when daily volatility is relatively low.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Irawan, Andree and Utam, Wiwik, Modelling cryptocurrency price volatility through the GARCH and EWMA model, Management & Accounting Review (MAR), 24 (1): 6. pp. 153-179.

Article Source Here: Forecasting Volatility in Digital Assets: A Comparative Study

source https://harbourfronts.com/forecasting-volatility-digital-assets-comparative-study/

Joint Calibration of SPX and VIX Options Using the Willow Tree Method

The willow tree method is a powerful technique with many applications in derivative pricing. We have discussed how it can be used to determine the implied volatilities of American options. It can also be applied to price convertible bonds by simultaneously [glossary_exclude]accounting [/glossary_exclude]for equity and credit risks. In addition, it is useful for calculating the value of complex path‐dependent derivatives and associated risk measures, such as Asian options and American moving average barrier options. Reference [1] proposed using the willow tree method to build a model that describes the volatility dynamics of both SPX and VIX options concurrently.

Among the methods commonly used to jointly calibrate SPX and VIX options, the non-parametric approach typically reconstructs the risk‐neutral density (RND) using only SPX option prices. The authors employed the implied willow tree (IWT) method to extract the RND of both SPX and VIX options, thereby accommodating both sets of market-observed option prices effectively. They pointed out,

In this study, we propose a novel nonparametric discrete‐time model called the joint implied willow tree (JIWT) approach to tackle the joint calibration challenge. The JIWT method bypasses the need for model‐based simulation techniques by using discrete‐time nonparametric methods to derive the risk‐neutral probabilities from observable SPX and VIX option prices. Our method offers three primary contributions. First, we delve into the conditional probability distributions between two maturities using both SPX and VIX option prices. While solely SPX option prices provide insight into SPX unconditional RNDs, they offer limited information on conditional densities. Leveraging the VIX definition (1) grounded in the SPX, we can identify conditional densities that align with VIX and its options prices. It enables us to capture the volatility smile in both the SPX and VIX markets, especially for short‐term maturity. Second, our JIWT method is simpler, more straightforward to implement, and efficiently extends to multiple maturities of SPX and VIX options as compared with the nonparametric discrete‐time model proposed by Guyon (2023)… Third, our JIWT method operates without the need for any prespecified mathematical model for SPX. Instead, it extracts the entire RNP directly from market‐observable option prices, making it both model‐free and data‐driven.

In short, this paper proposed a nonparametric method for calibrating SPX and VIX option prices simultaneously. The method has proven successful in addressing the joint calibration challenge of the SPX and VIX markets. As a result, it will enable risk and portfolio managers to identify new opportunities and manage risks more effectively.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Bing Dong, Wei Xu, Zhenyu Cui, Joint Implied Willow Tree: An Approach for Joint S&P 500/VIX Calibration, Journal of Futures Markets, 2025; 1–22

Post Source Here: Joint Calibration of SPX and VIX Options Using the Willow Tree Method

source https://harbourfronts.com/joint-calibration-spx-vix-options-using-willow-tree-method/

The Bitcoin-Gold Ratio as a Predictor of Stock Market Returns

The ratio of gold prices to other asset classes has been shown to be a useful predictor of stock market returns. We previously discussed how the gold-oil ratio serves as one such indicator.

Continuing this line of inquiry, Reference [1] examines the informational value of the Bitcoin-gold (BG) price ratio. The logic behind this metric is that Bitcoin represents a high-risk asset, whereas gold is traditionally viewed as a safe haven. Therefore, a rising BG ratio may signal increased investor risk appetite. It may also reflect growing optimism and interest in technological innovation, which boosts demand for Bitcoin. As a result, a higher BG ratio can indicate a tech-driven risk appetite that translates into stronger stock returns.

The authors pointed out,

…we show that the BG ratio has a positive effect on U.S. stock market returns across various market conditions during the pandemic and in the post-pandemic periods. This result holds with the inclusion of various financial and economic control variables. Our main result is robust to the use of Ethereum instead of Bitcoin, underlining the impact of the cryptocurrency-to-gold ratio on stock market returns. It generally holds when considering the European stock market, suggesting the impact of BG and EG ratios is not limited to the U.S. stock market.

We further show that the positive impact of the BG ratio on stock returns stems from the channel of risk aversion. Thus, the changes in the BG ratio manifest risk aversion or, in other words, risk appetite, which is new to the related literature and draws important implications for investors and policy-makers.

Changes in the BG ratio can serve as a potential indicator of risk appetite in both Europe and the U.S. Thus, investors could consider incorporating this metric into their portfolio strategies to adjust their exposure to equities under different market conditions…

In summary, the authors show that the Bitcoin-gold ratio is positively correlated with U.S. stock market returns.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Elie Bouri, Ender Demir, Bitcoin-to-gold ratio and stock market returns, Finance Research Letters (2025) 107456

Post Source Here: The Bitcoin-Gold Ratio as a Predictor of Stock Market Returns

source https://harbourfronts.com/bitcoin-gold-ratio-predictor-stock-market-returns/

VIX vs. SPX Options: Skewness, Term Structure, and Hedging Implications

VIX index options have become the second most traded contracts on the CBOE, surpassed only by S&P 500 (SPX) options. However, unlike SPX options, where the term structure of volatility has been extensively studied, the volatility term structure of VIX options has received far less attention. Reference [1] fills this gap by examining the term structure of VIX options and their role in hedging.

The authors pointed out,

In equity and variance swap options, it is well known that implied volatilities exhibit convexity (i.e., smile) over strikes. In our VIX option data, the smile is actually a concave frown for the most part of our sample, and particularly so when VIX is low. When VIX is high, it surprisingly changes to a convex smile. Even more surprisingly, our model replicates this empirical phenomenon.

We show that VIX options variations are not necessarily spanned by SPX options as a PCA decomposition shows that VIX options returns contain variation not seen in SPX options. The model also replicates the time-varying nature of the hedging relationship between SPX options, the underlying SPX index, VIX futures, and VIX options. In regressing SPX put option changes onto changes in these variables, we find that VIX options are nearly uncorrelated with SPX options in low volatility periods while the correlation spikes in high volatility periods. Our model explains this through essentially time varying factor loadings: when volatility is low, ATM SPX options depend primarily on cash flow news, while ATM VIX options depend on volatility and jump arrival intensity. In high volatility periods, the correlations increase, and VIX call options can serve as important hedging instruments for SPX puts.

In summary, some notable features of VIX options are,

• While the implied Black-Scholes volatility for SPX options is always a convex function of strike, VIX options behave differently, their shape shifts from concave in normal times to convex during high-volatility periods.
• The distribution of VIX returns is also markedly different from that of equities: VIX exhibits a strong right skew, far more pronounced than the left skew typically seen in SPX returns.
• VIX options display a downward-sloping term structure, i.e. longer-dated contracts have lower implied volatilities than shorter ones.
• Shocks to the implied volatility of volatility (VVIX) are positively, but not perfectly, correlated with VIX itself, suggesting that VIX option prices include components beyond just the VIX level.
• During calm markets, VIX calls don’t show a meaningful correlation with SPX puts and offer limited value for hedging. However, in turbulent times, VIX calls significantly reduce hedging errors, highlighting how VIX options (or SPX puts) can become valuable hedging instruments during periods of market stress.

This is a very important contribution, as it helps better understand the relationships within the SPX and VIX complex.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Eraker, B., and A. Yang. 2022. The Price of Higher Order Catastrophe Insurance: The Case of VIX Options. Journal of Finance 77, no. 6: 3289–3337.

Originally Published Here: VIX vs. SPX Options: Skewness, Term Structure, and Hedging Implications

source https://harbourfronts.com/vix-vs-spx-options-skewness-term-structure-hedging-implications/