Sharif Haason — Writing https://sharifhsn.dev/blog/ Sharif Haasonhttps://sharifhsn.dev 2026-04-01T14:42:17.714Z A New Chapter: Graduation and a New Role at Monarkhttps://sharifhsn.dev/blog/linkedin-2026-04-01-a-new-chapter-graduation-and-a-new-role-at-monark/2026-04-01T14:42:17.714Z2026-04-01T14:42:17.714ZSharif Haasonhttps://sharifhsn.devI'm thrilled to make two major announcements: I have completed my Master's in Financial Engineering from Stevens Institute of Technology, and I am starting a new role at Monark Mar… The December Fed Meeting: What to Watchhttps://sharifhsn.dev/blog/linkedin-2025-12-10-the-december-fed-meeting-what-to-watch/2025-12-10T11:00:16.071Z2025-12-10T11:00:16.071ZSharif Haasonhttps://sharifhsn.devThe December Fed meeting is today! Despite the worrying lack of data, the market is confident that rates will be cut by 25 bps, with the FedWatch tool giving a 87.6% chance for a c… Why 50-Year Mortgages Fall Shorthttps://sharifhsn.dev/blog/linkedin-2025-11-15-why-50-year-mortgages-fall-short/2025-11-15T14:30:01.051Z2025-11-15T14:30:01.051ZSharif Haasonhttps://sharifhsn.devFederal Housing Finance Agency director Bill Pulte recently floated a big potential change to the mortgage market: 50 year mortgages. Unfortunately, these aren’t realistic. Jefferies and First Brands: What the Trade Debt Meanshttps://sharifhsn.dev/blog/linkedin-2025-10-09-jefferies-and-first-brands-what-the-trade-debt-means/2025-10-09T14:28:33.464Z2025-10-09T14:28:33.464ZSharif Haasonhttps://sharifhsn.dev"Jefferies Fund Has $715 Million in First Brands Group, LLC’ Trade Debt"... but what does that exactly mean? Why Rate Cuts Won't Fix a Labor Supply Shockhttps://sharifhsn.dev/blog/linkedin-2025-09-09-why-rate-cuts-won-t-fix-a-labor-supply-shock/2025-09-09T19:37:25.419Z2025-09-09T19:37:25.419ZSharif Haasonhttps://sharifhsn.devInterest rate cuts won't relieve a labor supply shock: with lessons from energy and housing crises. Oil Prices and the Energy Provisions in the One Big Beautiful Billhttps://sharifhsn.dev/blog/linkedin-2025-07-03-energy-provisions-one-big-beautiful-bill/2025-07-03T18:00:26.040Z2025-07-03T18:00:26.040ZSharif Haasonhttps://sharifhsn.devGreat video about oil prices from experts in commodities. Neural Networks Aren't Impressive on Their Ownhttps://sharifhsn.dev/blog/linkedin-2025-06-07-neural-networks-aren-t-impressive-on-their-own/2025-06-07T19:26:59.305Z2025-06-07T19:26:59.305ZSharif Haasonhttps://sharifhsn.devNeural networks AREN'T impressive... The Case for Structured Errors in Rusthttps://sharifhsn.dev/blog/linkedin-2025-05-28-the-case-for-structured-errors-in-rust/2025-05-28T18:20:44.156Z2025-05-28T18:20:44.156ZSharif Haasonhttps://sharifhsn.devI found this article on structured errors insightful. Although it is focused on Rust, the explanations of the direct benefits of encoding information about the failure surface of c… Rust's `subsecond` Crate Brings Hot Reloadinghttps://sharifhsn.dev/blog/linkedin-2025-05-28-rust-s-subsecond-crate-brings-hot-reloading/2025-05-28T18:00:05.331Z2025-05-28T18:00:05.331ZSharif Haasonhttps://sharifhsn.devRust's subsecond crate is a game changer for application and game development in Rust! Its innovative hotpatching method enables hot reloading for select libraries. What a U.S. Credit Rating Downgrade Meanshttps://sharifhsn.dev/blog/linkedin-2025-05-17-what-a-u-s-credit-rating-downgrade-means/2025-05-17T15:52:46.770Z2025-05-17T15:52:46.770ZSharif Haasonhttps://sharifhsn.devMoody's has downgraded the US's credit rating from the best (Aaa) to second-best (Aa1), sending the markets into a buzz. But what does it mean to downgrade a credit rating? Rust at 10: Why I've Followed the Languagehttps://sharifhsn.dev/blog/linkedin-2025-05-16-rust-at-10-why-i-ve-followed-the-language/2025-05-16T17:38:11.094Z2025-05-16T17:38:11.094ZSharif Haasonhttps://sharifhsn.devRust turns 10! In honor of this momentous anniversary, I'd like to reflect on what Rust means to me, and why I have followed it for so long. Copulas and Portfolio Riskhttps://sharifhsn.dev/blog/computational-methods-week-14/2025-04-29T00:00:00Z2025-04-29T00:00:00ZSharif Haasonhttps://sharifhsn.devEnding early today because the Pacers are playing tonight Counterparty Risk-Weighted Assetshttps://sharifhsn.dev/blog/counterparty-risk-weighted-assets/2025-04-28T00:00:00Z2025-04-28T00:00:00ZSharif Haasonhttps://sharifhsn.devThe risk-weighted-assets notes translate counterparty exposure into a capital calculation. The exposure-at-default measure is combined with a risk weight or a model-based capital r… Multi-Name Credit Riskhttps://sharifhsn.dev/blog/advanced-derivatives-week-13/2025-04-24T00:00:00Z2025-04-24T00:00:00ZSharif Haasonhttps://sharifhsn.devThis is going to be a basic introduction, this is a complex topic to cover comprehensively. Neural Networks and Credit Ratingshttps://sharifhsn.dev/blog/computational-methods-week-13/2025-04-22T00:00:00Z2025-04-22T00:00:00ZSharif Haasonhttps://sharifhsn.devThis is an idea that was created in the 50s, exploded in the 90s, where it was called neural networks. A lot of development on the brain happened, so ANN was a term to distinguish … XVA and Counterparty Riskhttps://sharifhsn.dev/blog/xva-and-counterparty-risk/2025-04-21T00:00:00Z2025-04-21T00:00:00ZSharif Haasonhttps://sharifhsn.devThe XVA section adds counterparty and funding effects to an otherwise clean derivative value. CVA is the expected loss from counterparty default on positive exposure; FVA captures … Why Federal Reserve Independence Mattershttps://sharifhsn.dev/blog/linkedin-2025-04-18-why-federal-reserve-independence-matters/2025-04-18T16:23:13.160Z2025-04-18T16:23:13.160ZSharif Haasonhttps://sharifhsn.devTrump is threatening the independence of the Federal Reserve. But why does this even matter? And what does the Fed even do? Dependence and Copulashttps://sharifhsn.dev/blog/advanced-derivatives-week-12/2025-04-17T00:00:00Z2025-04-17T00:00:00ZSharif Haasonhttps://sharifhsn.devRelevant variables for these credits Euler–Milstein and Monte Carlo Extensionshttps://sharifhsn.dev/blog/computational-methods-week-12/2025-04-15T00:00:00Z2025-04-15T00:00:00ZSharif Haasonhttps://sharifhsn.devWe will expand on the variance reduction techniques, we will repeat a couple things from last week. Vietnam and the Tariff Shockhttps://sharifhsn.dev/blog/linkedin-2025-04-14-vietnam-and-the-tariff-shock/2025-04-14T15:40:44.045Z2025-04-14T15:40:44.045ZSharif Haasonhttps://sharifhsn.devThe biggest loser of the tariffs, the tragedy of the "miracle on the Mekong": Vietnam 🇻🇳 The Big Short and the Boring Cause of the 2008 Crisishttps://sharifhsn.dev/blog/linkedin-2025-04-12-the-big-short-and-the-boring-cause-of-the-2008-crisis/2025-04-12T18:25:14.194Z2025-04-12T18:25:14.194ZSharif Haasonhttps://sharifhsn.devI rewatched The Big Short last night, and realized that they sensationalized a pretty boring reason that the 2008 crisis happened. Romania's Export-Driven Debt Strategy as a Warninghttps://sharifhsn.dev/blog/linkedin-2025-04-11-romania-s-export-driven-debt-strategy-as-a-warning/2025-04-11T15:38:23.906Z2025-04-11T15:38:23.906ZSharif Haasonhttps://sharifhsn.devTrump's policy of reducing the national debt through an export-driven economy has parallels to 1980s Romania—and it doesn't end well. China's Tariff Strategy and the One-Punch Proverbhttps://sharifhsn.dev/blog/linkedin-2025-04-10-china-s-tariff-strategy-and-the-one-punch-proverb/2025-04-10T13:30:12.308Z2025-04-10T13:30:12.308ZSharif Haasonhttps://sharifhsn.devAn old Chinese proverb contains the key to understanding their tariff strategy: 打得一拳开 免得百拳来 Structured Credit and CDOshttps://sharifhsn.dev/blog/advanced-derivatives-week-11/2025-04-10T00:00:00Z2025-04-10T00:00:00ZSharif Haasonhttps://sharifhsn.devLast day of class is Thursday, May 8\. Why Crashing the Economy Won't Workhttps://sharifhsn.dev/blog/linkedin-2025-04-09-why-crashing-the-economy-won-t-work/2025-04-09T01:35:45.991Z2025-04-09T01:35:45.991ZSharif Haasonhttps://sharifhsn.devThe secret plan behind crashing the economy—and why it can’t work 😴 Monte Carlo and Variance Reductionhttps://sharifhsn.dev/blog/computational-methods-week-11/2025-04-08T00:00:00Z2025-04-08T00:00:00ZSharif Haasonhttps://sharifhsn.devWe will cover this stuff in two different lectures. Today is Monte Carlo 1. Misinformation in Volatile Marketshttps://sharifhsn.dev/blog/linkedin-2025-04-07-misinformation-in-volatile-markets/2025-04-07T19:31:32.998Z2025-04-07T19:31:32.998ZSharif Haasonhttps://sharifhsn.devMisinformation becomes especially dangerous in volatile markets... 😱 Documentation Is the Key to Vibe Codinghttps://sharifhsn.dev/blog/linkedin-2025-04-05-documentation-is-the-key-to-vibe-coding/2025-04-05T19:46:48.390Z2025-04-05T19:46:48.390ZSharif Haasonhttps://sharifhsn.devDocumentation is the key to vibe coding success! Rust 1.86: `get_disjoint_mut`https://sharifhsn.dev/blog/linkedin-2025-04-03-rust-1-86-get-disjoint-mut/2025-04-03T18:41:40.946Z2025-04-03T18:41:40.946ZSharif Haasonhttps://sharifhsn.devRust 1.86.0 has been released, with a very nice ergonomic feature to get around the borrow checker: get_disjoint_mut Credit Default Swap Valuationhttps://sharifhsn.dev/blog/advanced-derivatives-week-10/2025-04-03T00:00:00Z2025-04-03T00:00:00ZSharif Haasonhttps://sharifhsn.devWe discussed the mechanics of CDS a bit, and then started on the valuation. So let’s discuss the valuation in more details. Calibration and SDE Parameter Estimationhttps://sharifhsn.dev/blog/computational-methods-week-10/2025-04-01T00:00:00Z2025-04-01T00:00:00ZSharif Haasonhttps://sharifhsn.devParameter estimation for stochastic differential equations. CDS and Credit Marketshttps://sharifhsn.dev/blog/cds-and-credit-markets/2025-03-31T00:00:00Z2025-03-31T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-635 syllabus turns to credit as a traded asset through credit default swaps. A CDS exchanges a premium leg for protection against a defined credit event. The buyer pays the … The Cost of AI-Generated Imageshttps://sharifhsn.dev/blog/linkedin-2025-03-28-the-cost-of-ai-generated-images/2025-03-28T13:00:08.066Z2025-03-28T13:00:08.066ZSharif Haasonhttps://sharifhsn.devNew AI images stun the world 🤯 but are they worth the cost? 🤔 Hazard Rates and Credit Default Swapshttps://sharifhsn.dev/blog/advanced-derivatives-week-09/2025-03-27T00:00:00Z2025-03-27T00:00:00ZSharif Haasonhttps://sharifhsn.devLambda hazard rate is convenient to work with. Midterm Cheat Sheethttps://sharifhsn.dev/blog/computational-methods-midterm-cheat-sheet/2025-03-25T00:00:00Z2025-03-25T00:00:00ZSharif Haasonhttps://sharifhsn.devHandwritten midterm reference for quadrature and Black-Scholes notation; several formulas are unclear in the source render. GARCH Risk Statisticshttps://sharifhsn.dev/blog/garch-risk-statistics/2025-03-24T00:00:00Z2025-03-24T00:00:00ZSharif Haasonhttps://sharifhsn.devThe risk-statistics portion of FE-635 introduces GARCH as a way to model time-varying volatility. Returns may have little serial correlation while their squared returns cluster: ca… LIBOR Market Model and Hazard Rateshttps://sharifhsn.dev/blog/advanced-derivatives-week-08/2025-03-20T00:00:00Z2025-03-20T00:00:00ZSharif Haasonhttps://sharifhsn.devThe LIBOR Market Model (or Brace-Gatarek-Musiela Model) Stochastic Volatility, Jumps, and Fourier Transformshttps://sharifhsn.dev/blog/computational-methods-week-09/2025-03-18T00:00:00Z2025-03-18T00:00:00ZSharif Haasonhttps://sharifhsn.devTheoretical transformations, very technical Short-Rate Calibration and HJMhttps://sharifhsn.dev/blog/advanced-derivatives-week-07/2025-03-13T00:00:00Z2025-03-13T00:00:00ZSharif Haasonhttps://sharifhsn.devWe’ll look specifically at Vasicek and CIR. Then we will make some remarks on the Hull-White two factor model, then some more complex model. American Options and Cubic Splineshttps://sharifhsn.dev/blog/computational-methods-week-07/2025-03-11T00:00:00Z2025-03-11T00:00:00ZSharif Haasonhttps://sharifhsn.devCubic Splines, you solve something that is like a tridiagonal system FX Volatility Smiles and Uncertaintyhttps://sharifhsn.dev/blog/fx-volatility-smiles-and-uncertainty/2025-03-10T00:00:00Z2025-03-10T00:00:00ZSharif Haasonhttps://sharifhsn.devThe next FE-635 notes explain why a single Black–Scholes volatility is not enough for an FX market. Discrete hedging creates P&L even when the model's inputs are correct, and volat… Hull–White Interest Rate Treeshttps://sharifhsn.dev/blog/advanced-derivatives-week-06/2025-03-06T00:00:00Z2025-03-06T00:00:00ZSharif Haasonhttps://sharifhsn.devThis will be focused on numerical methods, next week we will have more examples. Crank–Nicolson and the Heston Modelhttps://sharifhsn.dev/blog/computational-methods-week-06/2025-03-04T00:00:00Z2025-03-04T00:00:00ZSharif Haasonhttps://sharifhsn.devDon’t use AI, you won’t learn anything. Finite-Difference Sketcheshttps://sharifhsn.dev/blog/computational-methods-finite-difference-sketches/2025-03-04T00:00:00Z2025-03-04T00:00:00ZSharif Haasonhttps://sharifhsn.devA handwritten finite-difference sketch with A/B/C labels; surrounding equation notation is unclear in the source render. FX Discrete Hedging and Greekshttps://sharifhsn.dev/blog/fx-discrete-hedging-and-greeks/2025-03-03T00:00:00Z2025-03-03T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-635 notes move from an ideal continuous hedge to the discrete hedges used in practice. A delta hedge removes the first-order response to an FX move at one instant; between r… Constant Maturity Swaps and Short-Rate Modelshttps://sharifhsn.dev/blog/advanced-derivatives-week-05/2025-02-27T00:00:00Z2025-02-27T00:00:00ZSharif Haasonhttps://sharifhsn.devTiming and quanto adjustments, we also looked at nonstandard swaps, LIBOR for LES? Another kind of nonstandard swap is… Differential Equations and PDE Methodshttps://sharifhsn.dev/blog/computational-methods-week-05/2025-02-25T00:00:00Z2025-02-25T00:00:00ZSharif Haasonhttps://sharifhsn.devFinite difference methods to approximate PDEs this week Black–Scholes Pricing for FXhttps://sharifhsn.dev/blog/fx-black-scholes-pricing/2025-02-24T00:00:00Z2025-02-24T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-635 workbook implements Black–Scholes-style pricing for calls, puts, forwards, and deposits. Its inputs separate the domestic discount rate from the foreign rate, because an… Interest Rate Adjustments and Currency Swapshttps://sharifhsn.dev/blog/advanced-derivatives-week-04/2025-02-20T00:00:00Z2025-02-20T00:00:00ZSharif Haasonhttps://sharifhsn.devWe may have to make some adjustments when we value interest rate derivatives. These are convexity, timing, and quant adjustments. We will see when it is appropriate to make these a… PBMs Under Fire: What CVS's Response Leaves Outhttps://sharifhsn.dev/blog/linkedin-2025-02-18-pbms-under-fire-what-cvs-s-response-leaves-out/2025-02-18T16:47:24.726Z2025-02-18T16:47:24.726ZSharif Haasonhttps://sharifhsn.devTrump has taken aim at pharmacy benefit managers, and the response from the industry seems to be… duck and cover. Prem Shah, executive VP at CVS, responded to skepticism on #Bloomb… Trinomial Trees, Dividends, and Greekshttps://sharifhsn.dev/blog/computational-methods-week-04/2025-02-18T00:00:00Z2025-02-18T00:00:00ZSharif Haasonhttps://sharifhsn.devI posted an assignment, this assignment is due this week on Sunday. Let’s just talk about the homework. Bond Options, Caps, Floors, and Swaptionshttps://sharifhsn.dev/blog/advanced-derivatives-week-03/2025-02-13T00:00:00Z2025-02-13T00:00:00ZSharif Haasonhttps://sharifhsn.devWe’re going to look at bond options, caps and floors, and everything about swaptions. Depending on time, we may go forward. Tree Approximation and American Optionshttps://sharifhsn.dev/blog/computational-methods-week-03/2025-02-11T00:00:00Z2025-02-11T00:00:00ZSharif Haasonhttps://sharifhsn.devWe’re not going to use the arbitrage method, we are going to use the forest methods. FX Parity and Forward Tradinghttps://sharifhsn.dev/blog/fx-parity-and-forward-trading/2025-02-10T00:00:00Z2025-02-10T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-635 notes begin with the distinction between spot and forward FX. The forward rate is the exchange rate implied by borrowing in one currency, lending in the other, and carry… Yield Curves and Bootstrappinghttps://sharifhsn.dev/blog/advanced-derivatives-week-02/2025-02-06T00:00:00Z2025-02-06T00:00:00ZSharif Haasonhttps://sharifhsn.devWe started to look at interest rates. In the first part we’re going to discuss various interpolation methods, functions that are useful for modeling the yield curve. Black–Scholes, Calibration, and Implied Volatilityhttps://sharifhsn.dev/blog/computational-methods-week-02/2025-02-04T00:00:00Z2025-02-04T00:00:00ZSharif Haasonhttps://sharifhsn.devHanlon 2 is occupied by the system administrator, Zheng Xing. He will move his class so that we can occupy there. They will need to remote desktop into the lab. Bond Pricing, Duration, and DV01https://sharifhsn.dev/blog/advanced-derivatives-week-01/2025-01-30T00:00:00Z2025-01-30T00:00:00ZSharif Haasonhttps://sharifhsn.devTake-home exam format, 24/48 hours, lots of writing code, during finals week. The Cost of Transit Delayshttps://sharifhsn.dev/blog/linkedin-2025-01-28-the-cost-of-transit-delays/2025-01-28T14:46:42.541Z2025-01-28T14:46:42.541ZSharif Haasonhttps://sharifhsn.devAs a frequent user of public transit, I know how impactful delays are both on my productivity and my mental health. Being stuck in Secaucus Junction because of some nonsense happen… Stochastic Processes and Computational Pricinghttps://sharifhsn.dev/blog/computational-methods-week-01/2025-01-28T00:00:00Z2025-01-28T00:00:00ZSharif Haasonhttps://sharifhsn.devI’m out on vacation this week, so I watched the recording Rust 1.84: Three Infrastructure Changeshttps://sharifhsn.dev/blog/linkedin-2025-01-10-rust-1-84-three-infrastructure-changes/2025-01-10T13:25:09.372Z2025-01-10T13:25:09.372ZSharif Haasonhttps://sharifhsn.devA new version of the Rust language has been released: Rust 1.84.0! Exotic Optionshttps://sharifhsn.dev/blog/exotic-options/2024-12-12T00:00:00Z2024-12-12T00:00:00ZSharif Haasonhttps://sharifhsn.devThe final FE-610 notes apply the earlier stopping-time and maximum results to path-dependent payoffs. A barrier option depends on whether the underlying crosses a level before expi… Options and Volatilityhttps://sharifhsn.dev/blog/options-and-volatility/2024-12-12T00:00:00Z2024-12-12T00:00:00ZSharif Haasonhttps://sharifhsn.devThe final FE-535 notes turn to nonlinear risk through options. An option's payoff is convex, so a small change in the underlying can have a different effect depending on where the … Default Fields in Rust Structshttps://sharifhsn.dev/blog/linkedin-2024-12-08-default-fields-in-rust-structs/2024-12-08T16:50:39.228Z2024-12-08T16:50:39.228ZSharif Haasonhttps://sharifhsn.devA recent RFC (request for comment) for the Rust language has divided the community: default fields in structs. Hedging Bondshttps://sharifhsn.dev/blog/bond-hedging/2024-12-05T00:00:00Z2024-12-05T00:00:00ZSharif Haasonhttps://sharifhsn.devThe bond-hedging lab combines duration, futures, and forward positions. A portfolio can be made locally insensitive to a yield move by matching its dollar duration with an offsetti… Rust 1.83 Brings More `const`https://sharifhsn.dev/blog/linkedin-2024-11-28-rust-1-83-brings-more-const/2024-11-28T16:16:30.611Z2024-11-28T16:16:30.611ZSharif Haasonhttps://sharifhsn.devA happy Thanksgiving to all! Today, in addition to my loved ones, I'm grateful for a brand-new version of Rust, now with more const! const evaluation is one of the most important s… Poisson Processeshttps://sharifhsn.dev/blog/poisson-processes/2024-11-28T00:00:00Z2024-11-28T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-610 notes introduce Poisson processes as counting processes with independent increments and a constant arrival intensity. For a rate \(\lambda\), the number of arrivals by t… Linear Hedginghttps://sharifhsn.dev/blog/linear-hedging/2024-11-21T00:00:00Z2024-11-21T00:00:00ZSharif Haasonhttps://sharifhsn.devThe linear-risk notes approximate a portfolio's change by its sensitivities to risk factors. A hedge chooses positions whose factor exposures offset the portfolio's exposures, ofte… Stochastic Differential Equationshttps://sharifhsn.dev/blog/stochastic-differential-equations/2024-11-21T00:00:00Z2024-11-21T00:00:00ZSharif Haasonhttps://sharifhsn.devThe SDE section writes a state process as a drift plus a diffusion term, Multidimensional Market Modelshttps://sharifhsn.dev/blog/multidimensional-market-models/2024-11-14T00:00:00Z2024-11-14T00:00:00ZSharif Haasonhttps://sharifhsn.devThe multidimensional market model in the FE-610 notes has several stocks driven by several Brownian factors. Prices, drifts, volatilities, and correlations become vectors and matri… Risk-Neutral Valuation and Interest Rate Parityhttps://sharifhsn.dev/blog/risk-neutral-valuation-and-parity/2024-11-14T00:00:00Z2024-11-14T00:00:00ZSharif Haasonhttps://sharifhsn.devThe risk-neutral valuation notes use a pricing measure under which discounted tradable prices are martingales. The expected payoff is discounted at the funding rate rather than for… Joint and Conditional Distributionshttps://sharifhsn.dev/blog/joint-and-conditional-distributions/2024-11-11T00:00:00Z2024-11-11T00:00:00ZSharif Haasonhttps://sharifhsn.devThe final FE-540 notes work with a joint law rather than treating each variable in isolation. A conditional density is obtained by normalizing the joint density with the relevant m… Forward Contractshttps://sharifhsn.dev/blog/forward-contracts/2024-11-07T00:00:00Z2024-11-07T00:00:00ZSharif Haasonhttps://sharifhsn.devThe forward-contract notes build value from replication. A forward fixes the delivery price today, while the underlying can be financed or invested until maturity. The forward pric… Risk-Neutral Measureshttps://sharifhsn.dev/blog/risk-neutral-measures/2024-11-07T00:00:00Z2024-11-07T00:00:00ZSharif Haasonhttps://sharifhsn.devThe risk-neutral section motivates a change of measure rather than assuming investors literally expect the risk-free rate. Discounted tradable prices should be martingales under a … A Rainbow on Election Dayhttps://sharifhsn.dev/blog/linkedin-2024-11-06-a-rainbow-on-election-day/2024-11-06T19:56:37.382Z2024-11-06T19:56:37.382ZSharif Haasonhttps://sharifhsn.devA brief pause from election-day politics to notice an unexpected rainbow. Random Vectors and Independencehttps://sharifhsn.dev/blog/random-vectors-and-independence/2024-11-04T00:00:00Z2024-11-04T00:00:00ZSharif Haasonhttps://sharifhsn.devThe later FE-540 notes package several random variables into a random vector, such as \(X=(X_1,X_2)\). The joint distribution records probability over rectangles and more general s… Derivatives and Clearinghouseshttps://sharifhsn.dev/blog/derivatives-and-clearinghouses/2024-10-31T00:00:00Z2024-10-31T00:00:00ZSharif Haasonhttps://sharifhsn.devThe derivatives notes frame a contract as a way to move or reshape risk. Futures and standardized options trade through a clearinghouse, while bilateral contracts expose each party… Stochastic Calculus Reviewhttps://sharifhsn.dev/blog/stochastic-calculus-review/2024-10-31T00:00:00Z2024-10-31T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-610 review consolidates the first half of the course: probability spaces and filtrations, martingales, Brownian motion, quadratic variation, the Itô integral, Itô's formula,… Student's t and Heavy-Tailed Distributionshttps://sharifhsn.dev/blog/student-t-and-heavy-tailed-distributions/2024-10-28T00:00:00Z2024-10-28T00:00:00ZSharif Haasonhttps://sharifhsn.devAfter the gamma and beta families, the FE-540 notes turn to Student's \(t\) distribution and other shapes used when observations are more extreme than a Gaussian model suggests. St… Remembering the Boarding-School Historyhttps://sharifhsn.dev/blog/linkedin-2024-10-27-remembering-the-boarding-school-history/2024-10-27T15:20:30.081Z2024-10-27T15:20:30.081ZSharif Haasonhttps://sharifhsn.devA reflection on President Biden's apology for federal Indian boarding schools. Interest Rate Risk and Durationhttps://sharifhsn.dev/blog/interest-rate-risk-and-duration/2024-10-24T00:00:00Z2024-10-24T00:00:00ZSharif Haasonhttps://sharifhsn.devThe interest-rate-risk notes approximate how a bond portfolio changes when yields move. Duration is the first-order sensitivity of price to yield; convexity captures the curvature … Multidimensional Itô Calculushttps://sharifhsn.dev/blog/multidimensional-ito-calculus/2024-10-24T00:00:00Z2024-10-24T00:00:00ZSharif Haasonhttps://sharifhsn.devWhen several state variables move together, the FE-610 notes replace the scalar Itô formula with its multidimensional version. The Hessian term contains both variances and cross-va… Gamma, Beta, and Chi-Squared Distributionshttps://sharifhsn.dev/blog/gamma-beta-and-chi-squared-distributions/2024-10-21T00:00:00Z2024-10-21T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-540 distribution notes connect several continuous families through the gamma function. The chi-squared family is a gamma distribution with parameters \(n/2\) and \(1/2\), wh… Black–Scholeshttps://sharifhsn.dev/blog/black-scholes/2024-10-17T00:00:00Z2024-10-17T00:00:00ZSharif Haasonhttps://sharifhsn.devThe Black–Scholes notes start with a stock following geometric Brownian motion, Probability and Regression Reviewhttps://sharifhsn.dev/blog/probability-and-regression-review/2024-10-17T00:00:00Z2024-10-17T00:00:00ZSharif Haasonhttps://sharifhsn.devThe first-exam review returns to probability, conditional expectation, and regression. A risk estimate is a conditional statement: it depends on the information set, the horizon, a… Continuous Random Variables and Transformationshttps://sharifhsn.dev/blog/continuous-random-variables-and-transformations/2024-10-14T00:00:00Z2024-10-14T00:00:00ZSharif Haasonhttps://sharifhsn.devThe continuous part of the FE-540 notes replaces sums with integrals. If \(X\) has density \(f_X\), then Bonds and the Time Value of Moneyhttps://sharifhsn.dev/blog/bonds-and-time-value-of-money/2024-10-10T00:00:00Z2024-10-10T00:00:00ZSharif Haasonhttps://sharifhsn.devThe bond material in the FE-535 notes treats a fixed-coupon bond as a stream of future cash flows. Discounting those cash flows gives its present value, and the yield is the consta… Itô Calculushttps://sharifhsn.dev/blog/ito-calculus/2024-10-10T00:00:00Z2024-10-10T00:00:00ZSharif Haasonhttps://sharifhsn.devItô's formula is the stochastic analogue of the multivariable chain rule. If Minneapolis Housing and Zoninghttps://sharifhsn.dev/blog/linkedin-2024-10-08-minneapolis-housing-and-zoning/2024-10-08T21:50:44.977Z2024-10-08T21:50:44.977ZSharif Haasonhttps://sharifhsn.devWhat Minneapolis changed in its zoning rules, and what happened to housing and rents. Stochastic Integralshttps://sharifhsn.dev/blog/stochastic-integrals/2024-10-03T00:00:00Z2024-10-03T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-610 notes define an integral such as \(\int_0^T\Delta_t\,dW_t\) by starting with simple adapted processes. On each partition interval, the position \(\Delta_t\) is chosen fr… A CUPS Vulnerability Explainedhttps://sharifhsn.dev/blog/linkedin-2024-09-27-cups-linux-vulnerability/2024-09-27T11:29:52.298Z2024-09-27T11:29:52.298ZSharif Haasonhttps://sharifhsn.devAn overview of the 2024 CUPS printer-discovery vulnerability and its risk. Brownian Motionhttps://sharifhsn.dev/blog/brownian-motion/2024-09-26T00:00:00Z2024-09-26T00:00:00ZSharif Haasonhttps://sharifhsn.devBrownian motion is the continuous limit of a scaled symmetric random walk. Its increments are independent and normally distributed, with \(W_t-W_s\sim N(0,t-s)\). It is a martingal… Brownian Motion and Geometric Growthhttps://sharifhsn.dev/blog/brownian-motion-risk-models/2024-09-26T00:00:00Z2024-09-26T00:00:00ZSharif Haasonhttps://sharifhsn.devThe stochastic-process notes move from a random walk to Brownian motion and then to geometric Brownian motion. Brownian increments are normally distributed with variance proportion… How rustc_codegen_clr Connects Rust to .NEThttps://sharifhsn.dev/blog/linkedin-2024-09-23-rust-mir-to-dotnet/2024-09-23T11:47:41.887Z2024-09-23T11:47:41.887ZSharif Haasonhttps://sharifhsn.devA short guide to Rust's compiler pipeline and a backend that targets .NET. Discrete Distributions and Momentshttps://sharifhsn.dev/blog/discrete-distributions-and-moments/2024-09-23T00:00:00Z2024-09-23T00:00:00ZSharif Haasonhttps://sharifhsn.devFor a discrete random variable, the probability mass function gives the mass at each possible value: Martingales and Random Walkshttps://sharifhsn.dev/blog/martingales-and-random-walks/2024-09-19T00:00:00Z2024-09-19T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-610 notes describe a martingale as an adapted process whose conditional expected future value equals its current value: Monte Carlo Risk Simulationhttps://sharifhsn.dev/blog/monte-carlo-risk-simulation/2024-09-19T00:00:00Z2024-09-19T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-535 lab notes use Monte Carlo methods to turn a model for returns into a distribution of portfolio outcomes. Simulate the relevant risk factors, revalue the portfolio on eac… Random Variables and CDFshttps://sharifhsn.dev/blog/random-variables-and-cdfs/2024-09-16T00:00:00Z2024-09-16T00:00:00ZSharif Haasonhttps://sharifhsn.devThe FE-540 notes define a random variable as a measurable function from the original sample space to the real line. Measurability means that inverse images of Borel sets are events… What Washing Machines Can Teach Us About Tariffshttps://sharifhsn.dev/blog/linkedin-2024-09-12-washing-machine-tariffs/2024-09-12T11:54:43.644Z2024-09-12T11:54:43.644ZSharif Haasonhttps://sharifhsn.devA look at the 2018 washing-machine tariffs, consumer costs, and U.S. manufacturing. Probability Spaces and Filtrationshttps://sharifhsn.dev/blog/probability-spaces-and-filtrations/2024-09-12T00:00:00Z2024-09-12T00:00:00ZSharif Haasonhttps://sharifhsn.devFE-610 begins with the probability-space machinery needed for continuous-time finance. The notes revisit sigma-algebras and probability measures, then add a filtration \((\mathcal … Risk-Adjusted Performancehttps://sharifhsn.dev/blog/risk-adjusted-performance/2024-09-12T00:00:00Z2024-09-12T00:00:00ZSharif Haasonhttps://sharifhsn.devThe performance notes compare return with the risk taken to earn it. The Sharpe ratio uses excess return divided by volatility, while beta measures sensitivity to a common market f… NVIDIA, Cisco, and Market Euphoriahttps://sharifhsn.dev/blog/linkedin-2024-09-10-nvidia-and-the-cisco-bubble/2024-09-10T13:30:09.913Z2024-09-10T13:30:09.913ZSharif Haasonhttps://sharifhsn.devBill Smead compares current enthusiasm for AI with the dot-com era's Cisco boom. Probability Measures and Bayes' Rulehttps://sharifhsn.dev/blog/probability-measures-and-bayes-rule/2024-09-09T00:00:00Z2024-09-09T00:00:00ZSharif Haasonhttps://sharifhsn.devA probability measure \(\mathbb P\) assigns a number in \([0,1]\) to every event in \(\mathcal F\). The notes begin with \(\mathbb P(\Omega)=1\) and countable additivity for disjoi… Bessent on Tariffs and the Deficithttps://sharifhsn.dev/blog/linkedin-2024-09-05-bessent-tariffs-and-deficits/2024-09-05T11:41:31.361Z2024-09-05T11:41:31.361ZSharif Haasonhttps://sharifhsn.devA response to Scott Bessent's arguments about tariffs, inflation, and fiscal policy. Risk Measurement and Portfolio Constructionhttps://sharifhsn.dev/blog/risk-measurement-and-portfolio-construction/2024-09-05T00:00:00Z2024-09-05T00:00:00ZSharif Haasonhttps://sharifhsn.devFE-535 opens by separating the risk-management process from a single risk number: identify exposures, measure them, evaluate the result, and decide how the portfolio should be cons… Probability Spaceshttps://sharifhsn.dev/blog/probability-spaces/2024-09-02T00:00:00Z2024-09-02T00:00:00ZSharif Haasonhttps://sharifhsn.devThe first step in the FE-540 notes is to give random experiments a mathematical home. A probability space is a triple \((\Omega,\mathcal F,\mathbb P)\): \(\Omega\) is the sample sp… What the Price Gouging Prevention Act Sayshttps://sharifhsn.dev/blog/linkedin-2024-08-27-price-gouging-prevention-act/2024-08-27T18:32:34.267Z2024-08-27T18:32:34.267ZSharif Haasonhttps://sharifhsn.devA summary of the 2024 bill's price-gouging language, defenses, and penalties. Floating Point Architecturehttps://sharifhsn.dev/blog/floating-point-architecture/2022-05-31T00:00:00Z2022-05-31T00:00:00ZSharif Haasonhttps://sharifhsn.devFloating point numbers are complicated enough in the abstract. How do systems programmers and hardware designers cope with the complexity of floating point? IEEE-754https://sharifhsn.dev/blog/ieee-754/2022-05-31T00:00:00Z2022-05-31T00:00:00ZSharif Haasonhttps://sharifhsn.devIEEE-754 is the standard for floating point computation around the world. Thus, any real-world discussion of floating point must include it. Floating Pointhttps://sharifhsn.dev/blog/floating-point/2022-05-28T00:00:00Z2022-05-28T00:00:00ZSharif Haasonhttps://sharifhsn.devFloating point representation is a complex topic full of nuance. To understand it, we must focus on the abstract method used to represent non-integer numbers. Network Securityhttps://sharifhsn.dev/blog/network-security/2022-04-22T00:00:00Z2022-04-22T00:00:00ZSharif Haasonhttps://sharifhsn.devThe internet has taken over the world, but with it have come malicious actors. People want to spy on you, scam you, steal from you, or harm you through the internet. Through networ… A Crash Course in Pythonhttps://sharifhsn.dev/blog/python-crash-course/2022-04-14T00:00:00Z2022-04-14T00:00:00ZSharif Haasonhttps://sharifhsn.devPython is a powerful jack-of-all-trades language that is much less limited than OCaml. Diskshttps://sharifhsn.dev/blog/disks/2022-04-14T00:00:00Z2022-04-14T00:00:00ZSharif Haasonhttps://sharifhsn.devPersistent storage is essential to every system that we can think of, and we can hardly think of a computer without it. However, managing disks is not as simple as it might appear … Particleshttps://sharifhsn.dev/blog/particles/2022-04-12T00:00:00Z2022-04-12T00:00:00ZSharif Haasonhttps://sharifhsn.devTiny particles are affected in different ways than we are by waves. There are several different effects that must be discussed. Multimedia Networkinghttps://sharifhsn.dev/blog/multimedia/2022-04-07T00:00:00Z2022-04-07T00:00:00ZSharif Haasonhttps://sharifhsn.devStreaming multimedia is a relatively new concept in internet technology, but now has become central to the daily media consumption of people around the world. Control in Prologhttps://sharifhsn.dev/blog/prolog-control/2022-04-05T00:00:00Z2022-04-05T00:00:00ZSharif Haasonhttps://sharifhsn.devConditional statements are very powerful and are in used in almost every language. How does Prolog implement the same idea? Special Relativityhttps://sharifhsn.dev/blog/special-relativity/2022-04-05T00:00:00Z2022-04-05T00:00:00ZSharif Haasonhttps://sharifhsn.devAlbert Einstein revolutionized the world of physics when he discovered the special theory of relativity. It is only possible due to his contributions that valuable technologies lik… Waveshttps://sharifhsn.dev/blog/waves/2022-03-29T00:00:00Z2022-03-29T00:00:00ZSharif Haasonhttps://sharifhsn.devLight is curious because it is both a particle and a wave, which makes it behave strangely in certain contexts. When projected through a slit, some strange fringes will appear, whi… The Link Layerhttps://sharifhsn.dev/blog/link-layer/2022-03-28T00:00:00Z2022-03-28T00:00:00ZSharif Haasonhttps://sharifhsn.devThrough all the layers of the internet, the most essential is the link layer: converting bits to and from signals, detecting errors, flow control, and addressing. Prologhttps://sharifhsn.dev/blog/prolog/2022-03-24T00:00:00Z2022-03-24T00:00:00ZSharif Haasonhttps://sharifhsn.devProlog is a special programming language that is not like many others. It exemplifies the paradigm of logic programming. Threadshttps://sharifhsn.dev/blog/threads/2022-03-23T00:00:00Z2022-03-23T00:00:00ZSharif Haasonhttps://sharifhsn.devConcurrency is a powerful tool to increase performance in applications. This is usually accomplished using threads. Routing Algorithmshttps://sharifhsn.dev/blog/routing-algorithms/2022-03-21T00:00:00Z2022-03-21T00:00:00ZSharif Haasonhttps://sharifhsn.devWhen a host needs to find the best destination/prefix to another host, what routing algorithm does it use? We can use either intra or inter domain. Swappinghttps://sharifhsn.dev/blog/swapping/2022-03-21T00:00:00Z2022-03-21T00:00:00ZSharif Haasonhttps://sharifhsn.devSometimes we don't have a lot of memory to access. In those cases, we need a place to put our data. The natural solution is to put data in the disk, which has very high storage. Th… Routershttps://sharifhsn.dev/blog/routers/2022-03-10T00:00:00Z2022-03-10T00:00:00ZSharif Haasonhttps://sharifhsn.devEveryone nowadays gets the Internet through the router in their home. But what is a router? Mirrorshttps://sharifhsn.dev/blog/mirrors/2022-03-08T00:00:00Z2022-03-08T00:00:00ZSharif Haasonhttps://sharifhsn.devMirrors can interact with light in interesting ways. In fact, reflection and refraction are probably most people's engagement with laws of physics surrounding light in their daily … Lambda Calculushttps://sharifhsn.dev/blog/lambda-calculus/2022-03-03T00:00:00Z2022-03-03T00:00:00ZSharif Haasonhttps://sharifhsn.devWhen we discuss the principles of programming languages, lambda calculus is the bedrock of our discussion. It is the most abstract, formal way to describe functions and application… More Internet Protocolshttps://sharifhsn.dev/blog/other-protocols/2022-03-03T00:00:00Z2022-03-03T00:00:00ZSharif Haasonhttps://sharifhsn.devBesides the primary Internet protocols, there are some others to learn about, like DHCP, NAT, IPv6, etc. Electromagnetic Waveshttps://sharifhsn.dev/blog/electromagnetic-waves/2022-03-01T00:00:00Z2022-03-01T00:00:00ZSharif Haasonhttps://sharifhsn.devWe have discussed electric fields and magnetic fields, and the way that they change and interact. The full interaction of these fields will create electromagnetic waves, the study … ISP Addressinghttps://sharifhsn.dev/blog/isp-addressing/2022-02-28T00:00:00Z2022-02-28T00:00:00ZSharif Haasonhttps://sharifhsn.devHow does an ISP assign IP addresses to its customers? Making a Website with Zola, Github Pages, and Github Actionshttps://sharifhsn.dev/blog/making-a-website/2022-02-26T00:00:00Z2022-02-26T00:00:00ZSharif Haasonhttps://sharifhsn.devMaking a website in the modern era is not easy to do for free. I did it using Zola, Github Pages, and Github Actions. I've always wanted to have a personal website where I can uplo… Currying Arguments in a Functionhttps://sharifhsn.dev/blog/curry/2022-02-21T00:00:00Z2022-02-21T00:00:00ZSharif Haasonhttps://sharifhsn.devCurrying is the concept of having multiple arguments in a function. OCaml defaults to currying its functions. int - int - int is a function that takes two ints and returns an int. HTTP Explainedhttps://sharifhsn.dev/blog/http/2022-02-20T00:00:00Z2022-02-20T00:00:00ZSharif Haasonhttps://sharifhsn.devHTTP is probably the most visible Internet protocol to end users. It appears (as well as its cousin, HTTPS) at the beginning of every URL we use to access the internet. But how doe… Paginghttps://sharifhsn.dev/blog/paging/2022-02-20T00:00:00Z2022-02-20T00:00:00ZSharif Haasonhttps://sharifhsn.devThe main problem that segments have introduced to managing memory space is that their variable size wastes memory through fragmentation. Fixed-size pieces that are easier to handle… TCP Explainedhttps://sharifhsn.dev/blog/tcp/2022-02-20T00:00:00Z2022-02-20T00:00:00ZSharif Haasonhttps://sharifhsn.devTCP is the well-known protocol for reliable transfer of data. But how does it actually work? Electromagnetic Inductionhttps://sharifhsn.dev/blog/induction/2022-02-18T00:00:00Z2022-02-18T00:00:00ZSharif Haasonhttps://sharifhsn.devThe final piece to the puzzle of electromagnetism here is electromagnetic induction, where we use magnets to create current. Data Types in OCamlhttps://sharifhsn.dev/blog/data-types/2022-02-17T00:00:00Z2022-02-17T00:00:00ZSharif Haasonhttps://sharifhsn.devWhen we make our programs more and more complex, we need more complex data types as well. We have only used OCaml's built-in data types, how can we construct our own data types? Operational Semanticshttps://sharifhsn.dev/blog/operational-semantics/2022-02-17T00:00:00Z2022-02-17T00:00:00ZSharif Haasonhttps://sharifhsn.devWhat are the formal semantics of how a programming language works, mathematically? That's a broad topic. Operational semantics, which are how programs execute, are narrow enough fo… Tail Recursion in OCamlhttps://sharifhsn.dev/blog/tail-recursion/2022-02-15T00:00:00Z2022-02-15T00:00:00ZSharif Haasonhttps://sharifhsn.devRecursion in many languages can cause significant overhead. It might seem that the excess amount of recursion in OCaml would decrease its performance. But it actually doesn't, and … UDP Explainedhttps://sharifhsn.dev/blog/udp/2022-02-14T00:00:00Z2022-02-14T00:00:00ZSharif Haasonhttps://sharifhsn.devThe simplest transport protocol that is used communicate between sockets is known as UDP, the User Datagram Protocol. Magnetshttps://sharifhsn.dev/blog/magnets/2022-02-11T00:00:00Z2022-02-11T00:00:00ZSharif Haasonhttps://sharifhsn.devThe question of how magnets work has [long puzzled many](https://www.youtube.com/shorts/8bhYMnHb5JY). We will endeavor to answer all of those questions today. SMTP Explainedhttps://sharifhsn.dev/blog/smtp/2022-02-10T00:00:00Z2022-02-10T00:00:00ZSharif Haasonhttps://sharifhsn.devEmail is the most popular way in the world to send large messages. This is a complicated process which requires its own protocol: SMTP. Higher Order Functions in OCamlhttps://sharifhsn.dev/blog/higher-order-functions/2022-02-08T00:00:00Z2022-02-08T00:00:00ZSharif Haasonhttps://sharifhsn.devWe can do a lot of cool things with functions besides calling them in OCaml. FTP Explainedhttps://sharifhsn.dev/blog/ftp/2022-02-07T00:00:00Z2022-02-07T00:00:00ZSharif Haasonhttps://sharifhsn.devBefore we had Google Drive, users needed a way to access files from other people quickly and easily. The method for that was FTP. Memory Virtualizationhttps://sharifhsn.dev/blog/memory-virtualization/2022-02-07T00:00:00Z2022-02-07T00:00:00ZSharif Haasonhttps://sharifhsn.devAccessing physical memory can cause big issues if we do it directly. How can we virtualize the memory like the CPU so we can use it efficiently and safely? Lets, Tuples, and Records in OCamlhttps://sharifhsn.dev/blog/lets-tuples-records/2022-02-03T00:00:00Z2022-02-03T00:00:00ZSharif Haasonhttps://sharifhsn.devLists are the most basic data structure in OCaml, but there are others that we need to be aware of. Circuitshttps://sharifhsn.dev/blog/circuits/2022-02-01T00:00:00Z2022-02-01T00:00:00ZSharif Haasonhttps://sharifhsn.devCircuits are the method by which all electricity travels throughout the world and power every single device in existence. It is therefore crucial to understand them while understan… DNS Explainedhttps://sharifhsn.dev/blog/dns/2022-01-31T00:00:00Z2022-01-31T00:00:00ZSharif Haasonhttps://sharifhsn.devWe need protocols to define the way that messages are interpreted. Packet Switching vs Message Switchinghttps://sharifhsn.dev/blog/packet-switching/2022-01-31T00:00:00Z2022-01-31T00:00:00ZSharif Haasonhttps://sharifhsn.devHow do we get the best performance in sending information over the internet? What is packet switching and how can it help? Performance is bottlenecked by propagation delay and tran… Schedulinghttps://sharifhsn.dev/blog/schedulers/2022-01-31T00:00:00Z2022-01-31T00:00:00ZSharif Haasonhttps://sharifhsn.devThe way that the operating system decides which processes to run and when is a complicated process known as scheduling. This is how it works. Lists in OCamlhttps://sharifhsn.dev/blog/lists/2022-01-27T00:00:00Z2022-01-27T00:00:00ZSharif Haasonhttps://sharifhsn.devLists are the most basic data structure in OCaml. The most analoguous structure is a vector in C++ or Rust. Lists are homogenous and of arbitrary length. Electric Potentialhttps://sharifhsn.dev/blog/electric-potential/2022-01-25T00:00:00Z2022-01-25T00:00:00ZSharif Haasonhttps://sharifhsn.devBesides electrical charge and field, there's another force that is relevant to electricity: electric potential. Functions in OCamlhttps://sharifhsn.dev/blog/functions/2022-01-25T00:00:00Z2022-01-25T00:00:00ZSharif Haasonhttps://sharifhsn.devA function takes arguments, performs operations using them, and returns a value. In OCaml, we can write functions like so Electrostaticshttps://sharifhsn.dev/blog/electrostatics/2022-01-18T00:00:00Z2022-01-18T00:00:00ZSharif Haasonhttps://sharifhsn.devWhat is electricity, and how does it work? CPU Virtualizationhttps://sharifhsn.dev/blog/cpu-virtualization/2022-01-04T00:00:00Z2022-01-04T00:00:00ZSharif Haasonhttps://sharifhsn.devWe need a way to map on to the physical CPU through our operating system. We do this through virtualization.