Janitha Meedeniya

The FRTB SA Formula In statistics, the variance of two variables X and Y, say people’s height and weight, can be summed to get the variance of the combined (X+Y) variable. The formula is Var(X + Y) = Var(X) + Var(Y) + 2.Cov(X,Y) where Cov(X,Y) describes how the two variables move together or covary. If there is no relationship btw height and weight, then Cov(X,Y) would be zero and the combined variance would just be sum of the two variances. But there is a +ve correlation btw height & weight so the Cov(X,Y) term adds to the overall variance. If the correlation was negative then Cov(X,Y) would subtract from it. In the 1950s Harry Markowitz applied variance-covariance techniques to movements of stock prices in a portfolio. The analysis was groundbreaking at the time. The variance, or risk, of a portfolio, he argued, was higher if there was +ve correlation btw the movements of two stocks in the portfolio. A matrix containing variances and covariances, calculated from historical time series of price movements across all stock pairs, defined the risk of the portfolio. In the 1990s market risk teams in banks started using Markowitz’s theory for another objective: to measure the value-at-risk (VaR) of their trading books. The total VaR, say in a trading book containing IR exposures with tenor buckets per Table 1 in the diagram below, is not just the sum of the individual risk-weighted exposures. If it were, then +ve exposure buckets could be directly offset with negative exposure buckets. The total capital charge is higher than the sum of the weighted exposures because the underlying tenor rates are highly +vely correlated. In the FRTB SA capital charge formula below, the risk weights Wi are analogous to the variances in Markowitz. However, instead of being set directly = to the variances of the IR variables, e.g. the variance of the 1Y rate, the risk weights are calibrated to the 97.5th percentile of a time-series of 10-day market moves of the rate. Table 1 shows the risk-weights provided in the FRTB document post-calibration. The document doesn’t provide any evidence of the calibration. It just states the 97.5th percentile calibration assumption. The risk sensitivities Si in the formula are analogous to asset weights in Markowitz. E.g., the sensitivity in the 1Y bucket is an exposure to a 1bp move in the 1Y rate. A high sensitivity => a large position => a high weighting will be applied to the 1Y risk weight of 2.25% obtained from Table 1. The correlations from the FRTB SA formula below are obtained from a correlation matrix provided in the FRTB document. They are analogous to Markowitz asset correlations. Because interest rates for tenors on the yield curve typically move up and down in parallel with each other, the correlations used in the IR FRTB SA formula will be high – leading to a higher capital charge. Per Markowitz, high +ve correlations lead to higher portfolio risk.

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Buy side Quant Jobs Advice by Head of Quantitative Research at BAM, Ex-Quant Risk Head HRT, Millennium and Quant Analytics Head, Citadel - Giuseppe Paleologo A lot of you have asked us about the Quant Recruiting at Top Quant Prop shops and Hedge Funds. Here's a doc written by Giuseppe Paleologo, who has 20+ years of Quant experience mainly in the buy side. It covers goldmine information related to the Quant industry, Life as a Quant, Interview Prep for Quant roles, Quant firms and other do's and don'ts which will be useful for students and early professionals alike. Here's the latest version of the pdf at the permanent link tinyurl.com/quantadvice2. Hope it helps! Do share with your network. --------------------------- Join us for an exclusive webinar with Dr. Rob Navin – Founder & CEO of Real Time Risk Systems – where he reveals - How a Unified Overnight Grid Architecture Delivers Microsecond Derivatives Pricing speed Time -7:30 PM IST/2:00 PM GMT/ 10:00 AM EST Date - 24h August 2025 Register Now - https://lnkd.in/gKamMDnn Use the Coupon code "RTRS20" to get a 20% early bird off. About the Speaker Rob Navin is the Founder & CEO of Real Time Risk Systems and had co-founded an alternative asset fund that grew from $150M to $1.1B AUM. A Ph.D. in Theoretical Particle Physics from Caltech. Key takeaways you’ll get: How overnight grid computation can power real-time intraday pricing Using vector-valued Taylor series expansions for speed and accuracy Keeping “architecture purity” to avoid performance bottlenecks Why this approach lets quants innovate without slowing down production Real-world examples, including complex instruments like convertible bonds ➡ Kickstart your Quant Interview Prep ↗ ‘Interview Byte’ contains 500+ Interview questions (https://lnkd.in/gkqcrrKf) ↗ Quant Insider Project Handbook has 21 industry-oriented projects, which include 10 industry-oriented projects based on challenges conducted by Top HFT's and Hedge Funds. (https://lnkd.in/gWBEn78U) ↗ Check out Quant Insider Stack - https://lnkd.in/gcfdUEfg A Bundle of Interview Byte and Project Handbook Machine Learning for Finance course- Designed by Industry Veterans Hariom Tatsat, CQF, FRM with years of working at Wallstreet - https://lnkd.in/gtJDWcus Use Coupon code - "EARLYBIRD20" for 20% off on the ML for Finance course ↗ATC - Algorithmic Trading Certificate (ATC): A Practitioner’s Guide, taught by Ex-Citadel Director Nick Firoozye - https://lnkd.in/gkMfXVP2 Follow us on Twitter - https://lnkd.in/ggsyM4sr Subscribe to Quant Insider's new YouTube channel -https://lnkd.in/gT4vGZAh For more quant finance memes, follow us on Instagram - Quant Insider (https://lnkd.in/gfjc4hBu)

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Top 10 Must-Read Resources on E-FX, forex & Market Microstructure 👇 From HFT strategies to liquidity dynamics and interbank operations … >>> 1. Agency Execution vs. Principal Trading in FX - https://lnkd.in/eBw92fHb >>> 2. Understanding FX Market Fragmentation & Execution - https://lnkd.in/eKKAzpDX >>> 3. How Liquidity Aggregation Works in FX Markets - https://lnkd.in/eirhE6M5 >>> 4. HFT Infrastructure for FX: A Deep Dive - https://lnkd.in/egyfywjj >>> 5. The Core of FX Market Microstructure: Order Flow & Price Formation - https://lnkd.in/eh_xh9qy >>> 6. E-FX Trading: The Shift from Voice to Automation - https://lnkd.in/eb9VHvT7 >>> 7. FX Liquidity Providers & Market Making Strategies - https://lnkd.in/ec_iDq8s >>> 8. How the Forex Interbank Market Operates - https://lnkd.in/e7CtiBgx >>> 9. Building a Quantitative HFT Strategy for FX - https://lnkd.in/exgecgPQ >>> 10. FX Markets & Treasury Management Insights - https://lnkd.in/en3g3KR7 Is there anything else I can add to this list? #efx #forex #high-frequencytrading #hft #quantitative #finance

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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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Excellent New CME Trading Platform and Simulator - Released Today! The new CME Trading Simulator offers a professional, risk-free environment to practice trading futures and options using real market data across all seven asset classes. With a customizable workspace, users can drag and drop widgets, analyze charts, monitor market depth with the Price Ladder, and manage positions in real time. The simulator supports both standard and micro-sized contracts, allowing traders to test and refine strategies without risking capital. Additional features include watchlists, a trade plan tool to set objectives and manage risk, and an options grid for deeper market insights—all designed to help users build trading confidence and expertise Link - CME Trading Tools https://lnkd.in/d6iaZyEY Link - Userguide https://lnkd.in/e8pFHuGA #quant #finance #trading #simulator #cme #pricing #risk

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Learning Quantitative Trading: Estimating ATM Option Prices - Simple Math for Faster Trades 🚀 Sometimes the best trading tools aren’t complicated models — they’re quick rules of thumb you can use on the fly. A classic approximation (Brenner & Subrahmanyan, 1988) shows that the at-the-money (ATM) option price can be estimated without the full Black–Scholes model: 👉 C ≈ P ≈ 0.4 × S × σ × √T Where: • S = stock price • σ = volatility (annualized) • T = time to expiry (in years) 🔹 Quick Derivation • Start from Black–Scholes at ATM: C = S[N(d₁) – N(d₂)], with d₁ = 0.5σ√T, d₂ = –d₁ • Use Taylor expansion near 0: N(x) ≈ 0.5 + 0.4x ⇒ N(d₁) – N(d₂) ≈ 0.8 d₁ • Plug back: C ≈ 0.4 S σ √T 📊 Example: Apple ≈ $175, σ = 20%, T ≈ 1 week → √T ≈ 0.14 → C ≈ $1.95 (Market ≈ $1.86) Pretty close for “back of the envelope” math. 💡 Practical Use for Traders • 📈 Volatility check → Spot overpriced/underpriced implied vol instantly. • ⚡ Quick sizing → Estimate hedging cost for short-dated ATM options. • ⏱ Execution edge → Decide fast if a quote looks “fair” in live markets. ✅ Takeaway: This formula is a trader’s compass for ATM option valuation when speed matters. 🤔 What other quick rules of thumb or formulas do YOU use on your desk? 👇 Drop them in the comments — let’s build a quant & trader cheat sheet together.

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