Hedging Vega Risks with Delta

Delta hedging is a risk management strategy used to neutralize the impact of price movements in the underlying asset of an option. It involves adjusting the position in the underlying asset to offset the sensitivity of the option's value, measured by its "delta."  Delta represents the rate of change in an option's price relative to changes in the price of the underlying asset. As the price of the underlying asset fluctuates, the delta also changes, requiring frequent rebalancing of the hedge.

Equity index option traders often use delta to hedge vega risks. This approach is feasible due to the strong negative correlation between the equity index and its implied volatility. Reference [1] formalized this practice by developing a so-called mean-variance (MV) delta. Essentially, the mean-variance delta is the Black-Scholes delta with an additional adjustment term. The authors pointed out,

This paper has investigated empirically the difference between the practitioner Black-Scholes delta and the minimum variance delta. The negative relation between price and volatility for equities means that the minimum variance delta is always less than the practitioner Black-Scholes delta. Traders should under-hedge equity call options and over-hedge equity put options relative to the practitioner Black-Scholes delta.

The main contribution of this paper is to show that a good estimate of the minimum variance delta can be obtained from the practitioner Black-Scholes delta and an empirical estimate of the historical relationship between implied volatilities and asset prices. We show that the expected movement in implied volatility for an option on a stock index can be approximated as a quadratic function in the option’s practitioner Black-Scholes delta divided by the square root of time. This leads to a formula for converting the practitioner Black-Scholes delta to the minimum variance delta. When the formula is tested out of sample, we obtain good results for both European and American call options on stock indices. For options on the S&P 500 we find that our model gives better results that either a stochastic volatility model or a model based on the slope of the smile.

In summary, the new delta hedging scheme using the MV delta performs well for certain underlyings, even outperforming stochastic volatility models like SABR and local volatility models.

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

References

[1] John Hull and Alan White, Optimal Delta Hedging for Options, Journal of Banking and Finance, Vol. 82, Sept 2017: 180-190

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Inventory Valuation: Definition, Methods, Meaning, Adjustment, Importance

Companies must record an accurate value for inventory in their financial statements to represent an accurate financial picture. However, this task is not straightforward due to the challenges in evaluating inventory. Therefore, it is crucial to understand what inventory valuation is and how it works.

What is Inventory Valuation?

Inventory valuation involves determining the monetary value of a company's inventory at a specific time. This valuation is crucial for financial reporting since it affects the cost of goods sold (COGS) and gross and net income. Accurate inventory valuation ensures that a company's financial statements reflect its accurate financial position and performance, providing stakeholders with essential information for decision-making.

There are several techniques for valuing inventory, each with distinct implications for financial reporting. Some common methods include First-In, First-Out (FIFO), Last-In, First-Out (LIFO), and Weighted Average Cost. Each method impacts the calculation of COGS and the valuation of ending inventory differently, influencing profitability and tax obligations.

What are the methods of Inventory Valuation?

Companies must use one of the various inventory valuation methods. The usage may differ based on policies, accounting standards, and jurisdictional limitations. Usually, the most commonly used inventory methods include the following.

First-In, First-Out (FIFO)

The FIFO method assumes that the oldest inventory items get sold first. It means that the costs associated with the oldest inventory are used to calculate the cost of goods sold (COGS). The remaining inventory gets valued at the cost of more recently acquired items. During rising prices, FIFO typically results in lower COGS and higher net income, as older, cheaper costs are matched against current revenues.

Last-In, First-Out (LIFO)

The LIFO method operates on the premise that the most recently acquired inventory items are sold first. As a result, the COGS reflects the cost of the latest inventory purchased, while older inventory remains on the balance sheet. During inflationary periods, LIFO can lead to higher COGS and lower taxable income since the more expensive, recent costs are deducted from revenues.

Weighted Average Cost

This method calculates the average cost of all inventory items available for sale during the period and applies this average cost to both COGS and ending inventory. The weighted average cost is determined by dividing the total cost of goods available for sale by the total number of units available to sell. This approach smooths out price fluctuations and provides a consistent valuation method.

What is the importance of Inventory Valuation?

Inventory valuation is essential for several reasons, particularly its impact on financial reporting and tax implications. Accurate inventory valuation directly influences the cost of goods sold (COGS), which affects gross profit and net income on financial statements. This accuracy enables stakeholders, including investors and creditors, to assess the company's financial health effectively.

Additionally, the chosen valuation method can significantly impact tax liabilities; for example, using the Last-In, First-Out (LIFO) method during inflation can lead to lower taxable income and improved cash flow, making strategic inventory valuation crucial for financial planning. Moreover, effective inventory valuation is critical for efficient inventory management and performance measurement.

Conclusion

Inventory valuation is a technique that helps derive inventory value at a specific time. While it may sound straightforward, companies face several challenges during the process. Companies use one of the three prominent methods to evaluate inventory, including FIFO, LIFO, and weight average cost. Each of these methods has its advantages and disadvantages.

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No-arbitrage Model for Pricing CAT Bonds

Catastrophe bonds, or CAT bonds, are a type of risk-linked security designed to transfer the financial risk of natural disasters from insurers to investors. These bonds are typically issued by insurance or reinsurance companies to cover significant losses caused by events such as hurricanes, earthquakes, or floods. Investors in CAT bonds receive higher yields compared to traditional bonds, but they risk losing part or all of their principal if a specified catastrophe occurs during the bond's term.

Pricing models for catastrophic risk-linked securities have primarily followed two methodologies: the theory of equilibrium pricing and the no-arbitrage valuation framework. Reference [1] proposed a pricing approach based on the no-arbitrage framework, offering valuable insights into how CAT bonds are priced.

In their model, the authors utilize the CIR stochastic process model for interest rates and the jump-diffusion stochastic process model for losses. They pointed out,

In this paper, we first discussed the notions of CAT bonds, then described how these bonds were modeled using mathematical concepts of finance and then derived a PIDE and a first-order differential equation through the semi-discretization approach. In this equation, one of the components connected with these securities, the market price of risk of damage, is unavailable; a quadratic term was built using market ask and bid prices to determine this variable. This quadratic equation was improperly formulated; thus, we used the Tikhonov regularization to transform it into a near-initial problem. Then, using the Euler-Lagrange equation, we obtained a Poisson PDE equation. Finally, we provided an approach and numerical findings for determining the market price of risk.

We find the stochastic model, equation (1), to be particularly insightful and effective in describing catastrophic losses.

This year has witnessed numerous hurricanes across Asia, Europe, and America, leading to significant claims for insurers. This paper represents a contribution to advancing risk-sharing practices in the insurance industry.

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

References

[1] S. Pourmohammad Azizi & Abdolsadeh Neisy, Inverse Problems to Estimate Market Price of Risk in Catastrophe Bonds, Mathematical Methods of Statistics, Vol. 33 No. 3 2024

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Financial Guarantee: Definition, Types, Meaning, Importance, Example

Borrowing and lending can be confusing - however, it's one of the main forces of the economy.

Without borrowing or lending, many people would not be able to afford big purchases like a house or car, and businesses would struggle to grow and expand.

However, with borrowing and lending comes risk - both for the borrower and lender. This is where financial guarantees come in and understanding it is crucial for any individual or business looking to take on a loan.

What is a Financial Guarantee?

When people or businesses take out a loan, they may be asked to provide a financial guarantee as security for the lender.

A financial guarantee is basically a promise made by a third party (usually a bank or insurance company) to pay off the borrower's debt if they are unable to do so.

This gives the lender assurance that their money will be repaid, even if the borrower defaults on their loan.

It's a very common practice in the financial world, and it can come in different forms such as a letter of credit, deposit account, or even a cash collateral.

By understanding how it works, borrowers can improve their chances of getting loans approved and lenders can mitigate the risk of losing money.

Importance of Financial Guarantee

Financial guarantees play a crucial role in the financial world - here are some of the key reasons.

1. Reduces Risk for Lenders: Lending money always comes with risk. By requiring a financial guarantee, lenders have a safety net in case the borrower is unable to make their loan payments.
2. Increases Borrowing Power: Having a financial guarantee can strengthen an individual or business's creditworthiness. This means they are seen as less risky by lenders, which can increase their chances of getting approved for loans and potentially at more favorable terms.
3. Boosts Confidence in Investments: Financial guarantees are often used in investment transactions such as bonds or stocks, giving investors added protection that their investments will be repaid with interest.
4. Ensures Fulfillment of Obligations: In some cases, a company may be required to provide a financial guarantee to fulfill obligations under a contract. This can help build trust and reassurance in business relationships.
5. Mitigates Risk for Borrowers: While it may seem like financial guarantees only benefit lenders, they can also protect borrowers from having their assets seized or credit damaged if they are unable to make loan payments.

Different Types of Financial Guarantees

There are various types of financial guarantees, each serving a specific purpose. However, we can categorize them into two different groups

1. Personal Financial Guarantees

This is basically when people borrow money for personal reasons, such as buying a home or financing education, and need someone to co-sign the loan.

The cosigner provides a financial guarantee that they will cover the borrower's payments if they are unable to do so. A common example would be when students need a cosigner for their student loans.

2. Corporate Financial Guarantees

Another type of financial guarantee is when a company guarantees the obligations of another company, usually one within the same corporate group.

This can be seen when a parent company provides a financial guarantee for its subsidiary or when one company guarantees the debts of another to secure better loan terms.

It's a common practice in the business world, especially when companies want to expand or take on new projects that require significant financing.

Conclusion

Financial guarantees are very common in both personal and business financing. They provide assurance to lenders, help mitigate risk for borrowers, and come in various forms depending on the specific situation. It's important to understand the different types of financial guarantees and their implications before entering into any agreements involving them. It's advisable to talk to a professional who knows the ins and outs of a financial guarantee.

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Examining the Causal Relationship Between S&P 500 and VIX Futures

It’s well-known that there is a strong negative correlation between the S&P 500 index and the VIX. But what exactly is the causal relationship between them? In the financial media, we often see analysts using the VIX as an indicator to time and predict market direction. Is this approach valid?

Reference [1] addresses these questions by studying the causal relationship between the E-mini S&P 500 and VIX futures. The authors pointed out,

In this paper, we investigate the contemporaneous relation between returns of the VIX futures and the E-mini S&P 500 futures with the aim of examining the driving force behind the negative relation between stock returns and implied volatility… We use the method of identification through heteroskedasticity to capitalize on the intraday shifts in the covariance of the VIX futures and the E-mini S&P 500 futures at times when the variance of their innovations increases. This method accounts for the simultaneity of the relation between returns in the two futures markets.

Our results consistently show that causality in the contemporaneous relation between VIX futures and E-mini S&P 500 futures is largely from E-mini S&P 500 futures to VIX futures, suggesting that stock returns cause changes in expectations of implied volatility. New information causes stock prices to change. This changes the expectation of future return volatility, and VIX futures prices also change to reflect this revision in expectations. Our results also imply that the leverage and volatility feedback effects are not the key explanations for this relation. In essence, the strong wind in the sails of the contemporaneous relation between VIX futures and E-mini S&P 500 futures blows forcefully from E-mini S&P 500 futures to VIX futures.

In short, it’s actually the S&P 500 futures that cause changes in the expectations of implied volatility.

This study has significant implications for portfolio and risk managers, as they should use the signals from the S&P 500 to manage volatility exposure, not the other way around. Let us know what you think in the comments below or in the discussion forum.

This article provides an academic perspective; in the next post, I’ll present a practitioner’s view.

References

[1] Ekow A. Aikins and Alexander Kurov, Which Way Does the Wind Blow Between SPX Futures and VIX Futures?, 2024, SSRN, Journal of Futures Markets, Forthcoming

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The Going Concern Principle: Definition, Assumptions, Meaning, Importance, Example

Companies use the going concern principle when preparing financial statements. In its absence, these statements may look very different. Therefore, it is crucial to discuss it.

What is the Going Concern Principle in accounting?

The going concern principle is a foundational accounting concept that assumes a business will continue to operate for the foreseeable future, typically at least the next 12 months. This assumption allows for the deferral of certain expenses and the recognition of revenue over time, which are essential for presenting an accurate picture of a company's financial position and performance.

Management plays a crucial role in assessing the company's ability to continue as a going concern. If there are significant doubts about the company's future operations, management must disclose them in the financial statements. Nonetheless, the going concern principle is vital for ensuring the integrity of financial reporting and the proper management of a company's resources.

How does the Going Concern Principle work?

The going concern principle provides a framework for financial reporting that assumes a business will continue its operations for at least the next 12 months. This assumption is crucial for how assets and liabilities are valued and reported. Under this principle, assets are recorded at their historical cost rather than their liquidation value, allowing companies to defer recognizing potential losses associated with asset impairment.

Additionally, liabilities are classified based on their expected settlement during normal operations, with current liabilities due within a year and long-term liabilities anticipated to be paid off over time. External auditors also evaluate the appropriateness of this assumption during their assessments. If they find substantial doubts, they may require additional disclosures to inform stakeholders about potential risks.

What is the importance of the Going Concern Principle?

The going concern principle is crucial for ensuring accurate financial reporting. This assumption allows companies to record assets at historical cost rather than liquidation value, providing a more realistic picture of their financial health. By reflecting the true economic value of the business, the going concern principle fosters confidence among stakeholders, including investors and creditors.

Additionally, the going concern principle encourages management to adopt long-term strategies focused on sustainability and growth. It compels businesses to regularly assess their financial health and potential risks, enabling them to identify and address issues that could threaten their continuity. Compliance with accounting standards such as GAAP and IFRS further underscores the principle's importance to ensure that financial statements are credible and trustworthy.

What are the limitations of the Going Concern Principle?

The going concern principle has several limitations that can impact its reliability in financial reporting. One concern is that assessments of a company's ability to continue operating depend on management's subjective judgment and estimates, causing inconsistencies and inaccuracies. Furthermore, the principle may not adequately account for sudden changes in market conditions or external factors.

Another limitation is the typical time horizon of the going concern assumption, which generally extends only 12 months into the future. This narrow focus may overlook longer-term risks that could threaten a company's sustainability beyond this period. Lastly, management may sometimes display over-optimism in their evaluations, which could lead to inadequate risk recognition and misleading financial statements regarding the company's actual stability.

Conclusion

The going concern principle in accounting assumes that companies will continue to operate for the next 12 months or the foreseeable future. This assumption allows companies to present a more accurate financial picture. The going concern principle requires companies to record assets at cost and liabilities at the settlement value. In its absence, the same methods will not apply.

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Is the Put-Call Ratio a Reliable Indicator?

The put-call ratio (PCR) is a popular indicator used in financial markets to gauge investor sentiment. It is calculated by dividing the number of traded put options by the number of traded call options over a specific period.

The put-call ratio is often promoted and utilized by market analysts for making predictions. A high put-call ratio typically suggests that investors are buying more puts than calls, indicating a bearish sentiment, as investors might be seeking downside protection or speculating on declines. Conversely, a low put-call ratio reflects bullish sentiment, with more investors buying calls in anticipation of rising prices. Traders and analysts often use this ratio to identify potential reversals or confirm existing trends, interpreting extreme levels as signs of overbought or oversold conditions.

Reference [1] studied the predictability of the PCR, specifically utilizing the PCR based on traded volume and open interests. The authors pointed out,

In our study, we aimed to find whether our independent variables of Option Volume traded and Option Open Interest can be used to predict the Underlying return for an index-Bank Nifty Index for our present study. The major findings of our study have been two found. Firstly, we find that our independent variables do have a strong relationship with our dependent variable. This corroborates with the other major studies as covered in our literature review. Secondly, we find that the linear regression predictability for our underlying returns is only accounted for up to 50% by our independent variable. This once again follows on the significant researchers found during our study of literature. Thirdly, the predictability powers of our independent variables are significantly lesser than as propagated in the literature.

In short, the authors showed that the predictability of the PCR is less reliable than often suggested in financial media. Additionally, they found that predictability is weaker for index options than for single-name stock options.

This study has limitations, as it uses only one year of data and focuses on the Indian market. However, it should serve as a caution that we should conduct our own analysis in the markets we trade and that the predictability of the PCR might not be as strong as popular financial media suggests.

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

References

[1] L. G. Honey Singh and Amar Kumar Chaudhary, Option Volume and Open Interest for Predicting Underlying Return—A Study of Index Option in Indian Stock Market, in Financial Markets and Corporate Finance 5th International Conference on FMCF (ICFMCF2023), IIT Delhi, India, July 6–8

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Demonetization: Definition, Examples in India, Advantages, Disadvantages, Meaning

Demonetization is all about taking away the value of certain currency notes to tackle problems like black money and counterfeit cash.

By pulling specific notes from circulation, the government shifts the economy towards greater transparency and accountability.

It's a powerful tool that can reshape monetary habits and impact various sectors, making it crucial for maintaining a balanced and robust economic environment.

What is Demonetization?

Demonetization is when the government decides to take certain currency notes out of circulation, making them no longer valid as money.

This happens during changes in the national currency system. The old notes and coins are removed from everyday use, often replaced by new ones.

Sometimes, the change is so significant that an entirely new currency is introduced, replacing the old one completely.

This process is a way to refresh the financial system and adapt to evolving economic needs, impacting how money is handled in daily transactions.

How Demonetization Works

Demonetization happens when a government decides to shake up the currency scene by removing certain bills or coins from circulation.

The process begins with an official announcement, where the authorities declare specific currency units invalid for transactions. This move aims to tackle issues like counterfeit money, and black money or to transition towards a digital economy.

Banks play a crucial role by accepting old notes and exchanging them for new ones. People are encouraged to deposit their outdated currency into bank accounts within a set timeframe.

This changeover often includes the release of fresh currency designs or even entirely new denominations.

Demonetization shakes up cash flow to boost financial transparency and encourages people to try out different payment methods, changing the economic landscape.

Pros and Cons of Demonetization

There are both benefits and drawbacks of demonetization, which vary depending on the country's unique circumstances.

Pros

• Eliminates counterfeit money from circulation, leading to a more secure financial system.
• Discourages illegal activities like tax evasion and money laundering.
• Encourages the adoption of digital payment methods, reducing reliance on physical cash.

Cons

• Can cause temporary disruption in daily transactions and businesses that rely heavily on cash flow.
• May negatively impact low-income individuals who have limited access to banking services or rely on cash for their livelihoods.
• Implementation costs can be significant, with potential economic repercussions if not executed effectively.

Real-Life Examples

• In 2016, India implemented demonetization of the 500 and 1000 rupee notes, affecting over 80% of the country's currency in circulation. It aimed to combat corruption, black money, and tax evasion, but its impact on the economy was debatable.
• In 2015, Zimbabwe started using the USD as its official currency because hyperinflation made their own money practically worthless. This shift helped stabilize the economy, but it also created some challenges for low-income folks dealing with USD exchange rates.

Conclusion

Demonetization is a financial tool that can bring significant changes to a country's economic landscape. While it has its pros and cons, it can be a useful tool when implemented thoughtfully and strategically. Individuals and businesses should be aware of the potential effects and adapt accordingly. In the end, a properly executed demonetization can help create a more transparent, efficient, and secure financial system.

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Causal Relationship Between VIX ETPs and Futures in Low- and High-Volatility Regimes

VIX Exchange-Traded Products (ETPs) are financial instruments designed to provide exposure to the CBOE Volatility Index (VIX), which measures the market's expectation of 30-day forward-looking volatility derived from S&P 500 options. VIX ETPs, such as ETFs and ETNs, allow investors to gain exposure to volatility without directly trading options or futures on the VIX. These products often use VIX futures contracts to simulate exposure to the VIX index, with strategies ranging from short-term to mid-term volatility.

Research has focused on examining the lead-lag relationship between VIX ETPs and VIX futures. Reference [1] similarly investigates this relationship but goes further by examining the causal relationship across different regimes. Specifically, it categorizes the market into two regimes: regime 1, classified as low-mean, low-volatility, and regime 2, classified as high-mean, high-volatility. The authors pointed out,

Cointegration tests reveal unique stable long-run equilibrium relations between VIX ETPs and Futures. Regime shifting models demonstrate the time variation in causation with the volatility of volatility, in particular highlighting different causal relations between ETFs versus ETNs, with causality more stable between high and low volatility regimes for ETFs. In our models, regime 1 is classified as low-mean low-volatile, while regime 2 is classified as high-mean high-volatile, with about 25 times larger volatility than regime 1. Markets return to equilibrium more swiftly regime 1 compared to 2.

We observe time variation in causality with the volatility of volatility. In particular, demand pressures for VIX ETNs and futures can change in different regimes. For example, SPVXSTR sensitive to VXX in regime 1 than regime 2, and XIV is substantially more sensitive to TVIX in regime 2 than 1. On the other hand, we observe very little variation in causality between regimes 1 and 2 for the corresponding ETFs.

In summary, for VIX Exchange-Traded Notes (ETNs), which are unsecured, the study observes a time variation in causality influenced by the volatility of volatility. Specifically, SPVXSTR is more sensitive to VXX in regime 1 than in regime 2, while XIV is significantly more sensitive to TVIX in regime 2 than in regime 1. For Exchange-Traded Funds (ETFs), which hold the underlying assets they track, the study finds very little variation in causality between regimes 1 and 2.

This research contributes additional granularity to the literature on VIX ETPs and futures.

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

References

[1] Michael O’Neill and Gulasekaran Rajaguru, On the analysis of time-varying causality between VIX exchange-traded products and VIX futures contracts in high and low volatility regimes, Journal of Accounting Literature, 2024

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Term Structure of VIX Futures

VIX futures are financial derivatives that allow traders to speculate on or hedge against future volatility in the stock market, specifically the S&P 500 index. They are based on the CBOE Volatility Index (VIX), which measures market expectations of near-term volatility. Unlike spot VIX, which reflects current market volatility, VIX futures reflect market expectations of volatility at different points in the future. This often leads to a term structure where VIX futures prices can be in contango or backwardation.

Reference [1] proposed a framework to price VIX futures. Essentially, the authors break down the factors affecting VIX futures term structures into two key components: demand and variance risks. They pointed out,

… shocks to the variance and demand factors alter the term structure of VIX futures differently. Assessing the implications of the shocks is useful for exploring risk management strategies based on VIX futures. For instance, a positive shock to the variance factor increases economic uncertainty, and leads investors to expect the impact of the shock to be large but short-lived. Hence, investors tend to hold more short-term VIX futures to hedge against these volatility risks. In contrast, a positive shock to the demand factor directly reduces investor demand for VIX futures, leading futures prices to fall. When investors realize that the demand shock is sustained, they reduce their investment in long-term VIX futures and short long-term VIX futures to deal with the demand risk.

… We find that the jump risk contributes to explaining the conditional mean, variance, and higher-order moments of VIX futures. The parameters pertaining to the investors’ demand and arbitrageurs’ risk aversion are nontrivial in terms of pricing futures and fitting the term structure. We compare the variance and demand factors and find that the former is more important in pricing short-term futures, whereas the latter has a greater effect on long-term futures. In addition, the impulse response analysis suggests that shocks to the variance factor dissipate more quickly over the horizons than shocks to the demand factor.

In short, the VIX futures term structures can be influenced by these demand and variance risks.

This is an important contribution to the research on the pricing of VIX futures as it could help explain why, recently, short-dated VIX futures are in backwardation, while the spot VIX is in contango.

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

References

[1] Yang X. & Huang J., Demand Risks and Term Structure of Volatility Index Futures, Journal of Management Science and Engineering, 2024

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