Derivatives Trading Basics

A detailed intuitive and mathematical explanation of Hedging with Implied vs. Actual Volatility *Implied Volatility: Represents the market's expectation of how volatile the stock will be in the future. Derived from the market price of options. It is forward-looking and reflects market sentiment. Traders hedge using implied vol when they trust the market’s view on future volatility. * Actual Volatility Represents the historical volatility of the stock over a past period. Backward-looking and reflects actual price movements. Traders hedge using actual vol when they have confidence in their own forecasts of future volatility based on historical data. *Hedging with Implied Vol: Pros: It provides smoother P&L (Profit and loss) since it aligns with market prices. Easy to observe and obtain from market prices. Profitable if the actual volatility turns out to be higher than implied when buying options, or lower when selling options. Cons: Uncertainty about the actual amount of profit. It can be less accurate if the market's volatility forecast is incorrect. *Hedging with Actual Vol Pros: Predictable profit at expiration No standard deviation in final profit if the forecasted actual vol is accurate Cons Significant P&L fluctuations during the life of the option Relies heavily on the accuracy of the vol forecast *Mathematical Explanation *Expected Profit and Standard Deviation 1. Expected Profit: The profit from hedging an option is influenced by the difference between the actual and implied vol. The formula for expected profit when buying an at-the-money straddle (image attached below) Where: σ = Actual volatility σ~ = Implied volatility S = Current stock price T = Time to expiration t = Current time *Standard Deviation of Profit: The risk associated with the profit is given by the standard deviation of the profit. The formula for the standard deviation of the profit: (Image attached below) This depends on the actual vol and not on the implied vol *Hedging with Different Volatilities *Actual Vol = Implied Vol: When hedging with the same volatility as the market price, the standard deviation of profit is zero. The expected profit is small relative to the market price of the option. *Actual Vol > Implied Vol: Hedging with actual volatility higher than implied can result in expected profit, but also brings a higher standard deviation of profit. The risk of loss exists if hedging is not accurately aligned with actual volatility. *Actual Vol < Implied Vol: When actual volatility is less than implied, hedging with lower volatility ensures no loss until a certain point of underestimation. This scenario tends to have a more dramatic downside compared to the upside. Hedging with implied vol is generally more aligned with market expectations and tends to provide smoother P&L. Hedging with actual vol provides more predictable results at expiration but with higher risk and P&L fluctuations during the life of the option

Dynamic Delta Hedging vs. Static Delta Hedging Dynamic Delta Hedging and Static Delta Hedging are strategies used to manage the risk associated with holding options. These strategies involve using the option's Delta, which measures the sensitivity of the option's price to changes in the price of the underlying asset. Dynamic Delta Hedging involves continuously adjusting the hedge position to maintain a delta-neutral portfolio. This means that as the underlying asset's price changes, the position is frequently rebalanced to keep the portfolio's delta at zero. The goal is to offset the changes in the value of the option with opposite changes in the value of the hedge position. Advantages - Provides more accurate hedging by constantly adjusting for changes in the underlying asset's price. - Better suited for volatile markets where the underlying asset's price can change rapidly. Disadvantages - Higher transaction costs due to frequent rebalancing. - Requires constant monitoring and trading, which can be resource-intensive. Application - Used by market makers and institutional investors who need to manage large and complex portfolios. - American Options: More suitable due to the possibility of early exercise, requiring constant adjustments to accurately hedge the position. Static Delta Hedging involves setting up a hedge at the beginning and making minimal adjustments throughout the life of the option. This strategy relies on an initial hedge that is intended to remain effective without frequent rebalancing. Advantages: - Lower transaction costs due to fewer trades. - Simpler to implement and manage, requiring less monitoring and trading. Disadvantages - Less accurate hedging as it does not adjust for changes in the underlying asset's price. - Can be ineffective in volatile markets where the underlying asset's price changes significantly. Application - Often used by investors with smaller portfolios or those who prefer a more passive approach. - European Options: More suitable as the option can only be exercised at expiration, allowing the static hedge to remain relatively effective without frequent adjustments. European vs. American Options European Options Exercise: This can only be exercised at expiration. Dynamic Delta Hedging: Still effective, providing precise risk management up to the expiration date. Static Delta Hedging: This can be more effective due to the predictability of the exercise date and the lack of need to manage early exercise risk. American Options Exercise: Can be exercised at any time before expiration. Dynamic Delta Hedging: Necessary due to the possibility of early exercise, requiring continuous adjustments to accurately manage the option's risk. Static Delta Hedging: Less suitable as it does not account for the possibility of early exercise, which can lead to significant risk if the underlying asset's price changes substantially.

Understanding the Receive and Pay Legs of a Swap: Key Components in Risk Management In the world of derivatives, particularly interest rate swaps, the terms "receive leg" and "pay leg" are fundamental concepts that treasury professionals must understand. These two components form the basis of how a swap functions and are crucial in managing financial risks effectively. A swap is a contractual agreement between two parties to exchange cash flows based on different financial instruments. In an interest rate swap, one party agrees to pay a fixed interest rate on a notional amount, while the other party agrees to pay a floating interest rate on the same notional amount. The "receive leg" refers to the cash flows that a party receives, while the "pay leg" refers to the cash flows that the party pays. For example, if a company enters into a swap where it pays a fixed rate and receives a floating rate, the fixed rate payment is the "pay leg," and the floating rate payment is the "receive leg." The purpose of such a swap is typically to hedge against interest rate risk, allowing the company to stabilise its cash flows by locking in a fixed rate while benefiting from potential declines in floating rates. Understanding these legs is essential for treasury managers, as the structure of the swap determines the impact on the company’s financials. The receive leg can provide a hedge against rising costs or falling income, while the pay leg represents the cost of the hedge. By carefully analysing these components, institutions can craft strategies that align with their risk management goals. In summary, the receive and pay legs of a swap are the mechanisms through which risks are managed and financial outcomes are shaped. Mastery of these concepts is vital for anyone involved in treasury management, as they enable the effective use of swaps to protect against market uncertainties and support financial stability.

Good morning. One theme I have followed closely this year is how funding decisions evolve when politics, pricing and liquidity all start pulling in different directions. Borrowers usually remain loyal to a single currency unless the economics give them a clear reason to move. When that pattern changes, it is worth looking at what is happening in the deeper structure of global credit. The chart below is a good illustration. It shows that several large Asian firms now secure a lower all-in cost by issuing in euros and swapping the proceeds back into their home currency than by issuing in dollars. DBJ, NTT, SoftBank, DBS and KOLAHO are aligned on this point. Euro spreads have tightened enough and the swap back into local currency is inexpensive enough that the final cost undercuts the dollar alternative. Once you see that, the larger picture starts to come into focus. Four elements stand out. • European investors have become a more influential part of Asian primary markets. They are seeking diversified credit exposure and have been willing to take tighter pricing on well-known Asian names. • Cross-currency basis conditions now favour euro funding. Swapping euro proceeds back into local currency is efficient, which removes one of the main advantages of the dollar market. • Asian treasurers are adjusting to a more complicated external environment. Tariffs, US policy uncertainty and a softer dollar are all encouraging borrowers to broaden their funding channels. • Pricing is driving the shift. When the post-swap cost in euros is lower, the choice becomes straightforward and orderbooks in Europe are deep enough to take the supply. For me, the value of this chart lies in how clearly it captures the quiet adjustments reshaping global funding flows. Capital gravitates toward the combination of cost, liquidity and predictability that best fits the moment. At the margin, that combination is increasingly pointing issuers toward Europe. I will be watching whether this is a temporary window created by favourable swap levels or the beginning of a more durable division of funding between New York and Europe. The early signs suggest the transition is already underway.

An Intuitive Approach to Implied Volatility Implied volatility is usually introduced through models. Black–Scholes as the benchmark, extended by local volatility, stochastic volatility, jump-diffusion frameworks, or full surface calibrations. These approaches are powerful and necessary — but they are not the most intuitive way to think about option prices. There is a much simpler perspective: Imagine you are the only market maker for options on a completely exotic underlying: Gizmos. There is no option market yet, no implied volatility surface to look at. Clients call you and ask for prices. What volatility would you use? The natural starting point is obvious: you look at the current realized volatility of Gizmos. This is the best empirical estimate of how the underlying behaves right now. From there, you add a risk premium: - Time to maturity: the longer the option’s life, the more uncertainty you need to warehouse. - Known price-relevant events during the life of the option: scheduled announcements, decisions, or structural changes. - Unknown risks: regime shifts, tail events, and shocks that cannot be timed or modeled, but must be priced. This simple logic already explains much of what we observe in real markets: Longer maturities embed more uncertainty → term structure of implied volatility. Downside options require more compensation due to asymmetric and hard-to-hedge risks → volatility skew. One could add that competition, balance sheet constraints, and hedging costs refine these premiums — but they do not change the core intuition. The key point is this: Despite the apparent complexity and the multitude of models, option prices are fundamentally intuitive. Implied volatility is simply the level at which risk is willingly transferred, given observable behavior and unobservable uncertainty. In that sense, options markets are not only sophisticated — they are remarkably efficient. #options #volatility #investing

Here's the full video interview with the founding partners of The Ambrus Group, unveiling a groundbreaking strategy that is redefining tail risk hedging. Unlike traditional approaches that bleed investor capital during normal market conditions, Ambrus has developed an innovative, carry-neutral model that aims to provide robust protection against market crashes without depleting capital in the interim. Kris Sidial, William W., and Sal Abbasi, whose experience spans across prestigious firms like Morgan Stanley and Citadel, are leveraging deep expertise in proprietary trading to actively manage the "bleed" associated with traditional tail risk strategies. By separating their portfolio into two uncorrelated buckets - one focused on convex protection and the other on alpha-generating trades - Ambrus focuses to self-fund the cost of hedging, effectively delivering crash protection at zero net cost to investors. This approach allows them to capitalize on market dislocations without subjecting clients to the painful drawdowns that plague many tail risk funds. In this video, you will learn: - Chapter 1 at 01:20 (min:sec): Carry-neutral tail risk hedging: Protection against market crashes without losing capital in the interim How short term proprietary trading pays for the bleed that comes with being long volatility - Chapter 2 at 03:32: Team Backgrounds & Expertise - Chapter 3 at 05:29: The Ambrus Group’s two bucket portfolio - Chapter 4 at 07:28: Simplicity is key: Making tail risk strategies really work #tailrisk #hedging #hedgefund #assetprotection #familyoffice

𝐔𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐂𝐮𝐫𝐫𝐞𝐧𝐜𝐲 𝐒𝐰𝐚𝐩𝐬   A Currency Swap is a financial arrangement between two parties involving the exchange of one currency for another, aiming to optimize borrowing costs and mitigate exchange rate risks in cross-border transactions.    The agreement can include fixed or floating interest rates.   Let's break it down with an example!   𝐖𝐞 𝐡𝐚𝐯𝐞 𝟑 𝐩𝐚𝐫𝐭𝐢𝐞𝐬 👉 Company US  👉 Company Fr 👉 Swap Bank   Company US wants to finance a €40 million expansion of their plant in France   Should Company US discover a French MNC with corresponding financing needs, both parties could gain advantages through a swap.   It finds Company Fr, a French company seeking to finance $60 million in the US   They enter a Currency Swap, where the EUR/USD spot exchange rate is 1.5 (you need 1.5 USD to buy 1 Euro)   𝐏𝐫𝐞𝐯𝐚𝐥𝐞𝐧𝐭 𝐑𝐚𝐭𝐞𝐬: Company US can borrow at an 8% rate in the US (local) market or can borrow at a 7% rate in Euros  Company Fr can borrow at a 9% rate in the US market and can borrow at a 6% rate in Euros (local market)   𝐓𝐡𝐞 𝐒𝐰𝐚𝐩 𝐂𝐨𝐧𝐭𝐫𝐚𝐜𝐭: ⏩ Company US borrows $60 million at 8% locally. ⏩ Company Fr borrows €40 million at 6% locally. They exchange these interest amounts through a Swap Bank.   The principal amounts of $60 million and €40 million are exchanged at the beginning   ⏩ Company US pays 6% on €40 million to the Swap Bank, which passes it to Company Fr. ⏩ Company Fr pays 8% on $60 million to the Swap Bank, which passes it to Company US.   𝐀𝐬 𝐚 𝐫𝐞𝐬𝐮𝐥𝐭: Company US's payment of 8% on $60 million is cancelled out as it is being paid by Co. Fr in a Swap exchange. Similarly, Company Fr's payment of 6% on €40 million is cancelled out as it is being paid by Company US in a Swap exchange.   ⏩ Company US effectively pays a 6% Euro rate (€2.4 million). ⏩ Company Fr effectively pays an 8% Dollar rate ($4.8 million).   𝐇𝐨𝐰 𝐝𝐨𝐞𝐬 𝐢𝐭 𝐛𝐞𝐧𝐞𝐟𝐢𝐭 𝐞𝐢𝐭𝐡𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞 𝐩𝐚𝐫𝐭𝐢𝐞𝐬?   Both companies save 1% in interest rates compared to prevailing market rates.   From the prevalent rates, we know Company US could borrow Euros at 7%, but post the swap it borrowed Euros at 6%   Similarly, Company Fr could borrow Dollars at 9% but post the swap it borrowed Dollars at 8%   P.S - the Swap Bank does charge some interest

Cross Currency Swap Theory & Practice - An Illustrated Step-by-Step Guide of How to Price Cross Currency Swaps with an Excel pricing workbook example. A Cross Currency Swap (CCS) is a financial instrument that allows investors to exchange a set of cashflow liabilities for an equivalent set in another currency, often USD. Investors trade CCS to secure cheaper funding, hedge FX exposures, manage liquidity risk and of course for speculative purposes. In this paper we review the CCS product, its features and risks. We show how to price CCS and provide the mathematical formulae with examples & illustrations. Furthermore we outline how to calculate the CCS Basis Spread, which is how CCS are quoted in the financial marketplace. The article comes with an Excel pricing workbook. Cross Currency Swap Pricing https://lnkd.in/dtbzT5eW Excel Workbook https://lnkd.in/dPcf24Tt #quant #finance #trading #pricing #risk #crosscurrency #swaps #basis #spread

Understanding Volatility Surfaces in Quantitative Finance In quantitative finance, pricing derivatives accurately hinges on more than just a simple volatility number. Market-implied volatility is not constant across strikes and maturities — it bends, twists, and reshapes. This non-uniformity gives rise to the volatility surface, a foundational concept for modern pricing, risk, and hedging models. 1. What is a Volatility Surface? ➤ A volatility surface maps implied volatility across strike prices (moneyness) and time to maturity ➤ Rather than assuming volatility is fixed (as in Black-Scholes), the market provides different volatilities for each option, leading to complex, 3D surfaces ➤ These surfaces evolve over time and reflect market sentiment, supply-demand imbalances, and expectations of future uncertainty 2. Why is it Crucial in Quantitative Finance? ➤ Risk-Neutral Pricing: Derivative prices must be consistent with observed market quotes. Vol surfaces allow models to reproduce current option prices precisely ➤ Dynamic Hedging: Changes in volatility skew/smile impact hedging portfolios — traders calibrate models daily to the surface to remain delta/gamma/vega neutral ➤ Stress Testing: Shifts or distortions in surfaces help quantify the PnL impact under market stress scenarios 3. Key Modeling Approaches ➤ Local Volatility Models (e.g., Dupire) → Assume volatility is a function of strike and time, producing path-dependent dynamics → Common in equity derivatives where volatility smile is pronounced ➤ Stochastic Volatility Models (e.g., Heston) → Treat volatility itself as a random process, introducing correlation with the asset → Captures volatility clustering and mean reversion — relevant in FX and commodities ➤ SABR Model → Widely used in interest rate derivatives → Accurately models volatility smile for swaptions and bond options ➤ LV-LSV Hybrids → Combine local and stochastic frameworks to better reflect complex dynamics, particularly in exotic option pricing 4. Where Does This Matter in Industry? ➤ Equity desks calibrate surfaces daily to quote volatility for exotic structures (barriers, autocallables) ➤ FX markets use surfaces for dual digitals, touch/no-touch options, and structured forwards ➤ Interest rate desks model swaption vol cubes and collars using SABR-based interpolation ➤ Model risk teams monitor surface arbitrage violations — ensuring prices are free from butterfly/calendar spread inconsistencies Volatility surfaces are not just about smoothing market quotes — they’re blueprints of risk perception, tools for calibration, and the canvas on which almost every pricing model is painted. In practice, they separate theoretical elegance from operational robustness. #QuantitativeFinance #VolatilitySurface #LocalVolatility #StochasticVolatility #SABR #OptionsPricing #MarketRisk #QuantResearch #Derivatives #RiskManagement

💱 What is a Currency Swap? A currency swap is a financial derivative contract in which two parties exchange principal and interest payments in different currencies The swap typically involves: 1️⃣ Initial exchange of principal amounts in different currencies 2️⃣ Periodic exchange of interest payments (which can be fixed or floating) 3️⃣ Final re-exchange of the principal amounts at the end of the swap term 🔁 Purpose of a Currency Swap Currency swaps are used by: 🔅 Corporates: To hedge against foreign currency debt 🔅 Governments: To manage foreign reserves or funding costs 🔅 Investors and banks: To gain access to cheaper foreign funding or exposure Imagine 💡 1️⃣ A Sri Lankan company (Company A) has a loan in USD but earns in LKR 2️⃣ A U.S. company (Company B) has a loan in LKR (perhaps via a local subsidiary) but earns in USD They can enter a currency swap to exchange their obligations and reduce foreign exchange risk 🔄 Step-by-Step: How a Currency Swap Works 👥 Parties: Company A (Sri Lanka): Needs USD Company B (USA): Needs LKR Step 1️⃣ : Initial Principal Exchange 🔹 Company A gives LKR 32 million (at LKR 320/USD) 🔹Company B gives USD 100,000 This allows each party to access the currency they need without going to the forex market Step 2️⃣ : Periodic Interest Payments (e.g., annually) Let’s assume a 3-year swap: 🔹 Company A pays interest on USD 100,000 at 5% annually → USD 5,000 🔹 Company B pays interest on LKR 32 million at 12% annually → LKR 3.84 million Each party pays interest in the currency it originally received. Step 3️⃣ : Final Re-exchange of Principal At the end of 3 years: 🔹 Company A returns USD 100,000 🔹 Company B returns LKR 32 million This protects both companies from exchange rate volatility during the contract period 🧠Currency swaps are a useful tool for multinational companies to manage foreign currency liabilities, reduce financing costs, and hedge long-term FX risk But they must be entered with clear legal agreements and understanding of counterparties #RiskManagement #CorporateFinance #FinancialStrategy #TreasuryManagement #DerivativeMarkets #CurrencyTrading #HedgingStrategies #ForeignExchangeRisk #OptionsTrading #FinancialMarkets #CFRM #SL02