Nilay Ok Hynell

Food for thought! "The causal effect of inflation on financial stability, evidence from history" by Ugo Albertazzi, James ’t Hooft, and Lucas Ter Steege. "Our analysis demonstrates that rises in inflation cause financial instability, confirmed with multiple econometric methodologies." "One interesting finding is that inflation’s impact on crisis probability is intensified when central banks have limited independence, possibly reflecting heightened risks of de-anchoring and the related broad-based instability implications. Inflation is also particularly harmful when banks face fragile funding, larger funding gaps and higher exposure to wholesale (unstable) funding, indicating that the inflation-induced instability activates a bank-lending channel." "Overall, these findings suggest that once inflation is rising, central banks concerned with financial stability face a difficult trade-off between the destabilising effects of higher inflation on the one hand and higher interest rates on the other." https://lnkd.in/e5tPiB28

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Can complex models really outperform simple ones in finance—even with small samples? This new paper explores why the answer is yes, showing that combining diverse, intricate models leads to stronger, more stable investment strategies. A must-read for anyone exploring machine learning for return prediction: https://bit.ly/45dsduZ

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Why is a short gamma position dangerous in options trading? Say a bank sells a European call option to a client, -C. Substituting the Black–Scholes equation into C gives: -[S(t)N(d1) - Kexp(-rT)N(d2)] = Kexp(-rT)N(d2) - S(t)N(d1), where N(d2) is the probability of the option expiring in-the-money under the risk-neutral measure, and N(d1) is the option’s delta (the hedge ratio, i.e. the number of shares required to delta-hedge the option). Let's first discuss leverage. When a client buys a European call option, they pay a relatively small premium and gain synthetic delta-equivalent exposure of stock, N(d1)S(t). From the bank’s perspective, it receives only the small premium but is exposed to a much larger short delta position, -N(d1)S(t). The holding in shares, N(d1), is not fixed - it changes automatically as S moves. This is what makes options so powerful (and dangerous). Gamma tells us how much the synthetic shareholding (delta) will change for a small move in S. It is important to understand the terms "long" and "short". The option buyer is long gamma, which means their delta moves in the same direction as S: - When S goes up, delta increases (more exposure). - When S goes down, delta decreases (less exposure). The bank, on the other hand, is short gamma. To delta hedge, the bank must buy stock exposure of N(d1)S(t) to offset its short position. When S goes up, it is forced to buy shares at a higher price to hedge. When S goes down, it must sell shares at a lower price. The cycle of buying high and selling low is exactly why a short gamma position is dangerous. Follow me for more insights! #quant #options #greeks #gamma

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Building a Volatility Surface - Mathematical Explanation A volatility surface provides a three-dimensional representation of implied volatilities across different strikes and maturities Dupire Local Volatility Model In the Dupire model, we focus on the local volatility as a function of spot price and maturity , not strike . The local volatility is derived from the call price using the following PDE: (Image attached below) The formulation emphasizes that strike is not directly considered but rather the spot price . Convexity constraints are crucial to maintaining no-arbitrage conditions:(Image attached below) Sticky Strike vs. Sticky Delta Sticky Strike: The volatility surface is parameterized based on strike levels. The implied volatilities remain fixed for specific strikes even as the underlying spot price changes. Sticky Delta: The volatility surface is parameterized based on delta levels. This approach is more dynamic, adjusting volatilities based on the relative position of the strike to the spot price. Heston Stochastic Volatility Model The Heston model introduces stochastic variance, defined as: (Image attached below) The third equation representing the correlation between the two Wiener processes is essential and must be included: (Image attached below) This correlation term significantly influences the skew and curvature of the implied volatility surface. SABR Model The SABR model operates in the forward price space, not the spot price. The dynamics are given by: (Image attached below) Since the underlying modeled is the forward price , there is no drift term in the asset price equation. The implied volatility approximation in the SABR framework is: (Image attached below) Imposing Arbitrage-Free Constraints Calendar Spread Arbitrage: Implied variance must increase with maturity, ensuring (Image attached below) Butterfly Spread Arbitrage: The second derivative of the call price with respect to strike must be non-negative: Image attached below) 4. Interpolation and Smoothing Techniques Smoothing methods include cubic splines and Gaussian kernel smoothing. Extrapolation techniques for extreme strikes or maturities involve asymptotic models or log-linear interpolation. Join us for an intensive two-day workshop, with Kristopher Abdelmessih, on Options Trading in Equities and Index Options, designed to bring you from foundational principles to real-world trading insights. 📅 Date: Sunday, July 19th, 2025 ⏰ Time: 8:30 PM IST / 8:00 AM PST/ 3:00 PM GMT Register Now - https://lnkd.in/gc2reZww Use coupon code - "Option20" to get 20% off Day 1: Covers basics of index vs. equity option structures, exercise styles, ETF quirks, vol vs. funding trades, and liquidity dynamics across instruments. Day 2: Dives into real-world vol trading—dispersion, implied correlation, SPX-VIX linkages, and case studies on adapting to market shifts. (Recording of webinar will be available in case you aren't able to Join Live)

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Beyond Direction: Mastering the Hidden Risks in Your Options Portfolio with the Greeks Successful options trading requires moving beyond simple directional bets and mastering the language of risk. This post demystifies "The Greeks" (Delta, Gamma, Theta, Vega), explaining them as the dashboard for your trading portfolio. It breaks down not only what these critical metrics mean (from Chapter 7) but also how they dynamically change with shifts in price, time, and volatility (from Chapter 9). Finally, it applies these concepts to real-world strategic decisions, showing how to weigh the fundamental trade-offs between risk and reward-like the constant battle between gamma and theta-to make smarter, more resilient trading choices (from Chapter 13). A practical Python simulation is included to demonstrate how your position's delta evolves in real-time. #OptionsTrading #RiskManagement #FinancialModeling #TheGreeks #Delta #Gamma #Vega #Theta #QuantitativeFinance #Derivatives #Volatility #TradingStrategy #PortfolioManagement #SheldonNatenberg

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