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Add UDP Receiver, Black-Litterman, and SDE Solver
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‎03_financial_engineering/portfolio_optimization/black_litterman_model.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Advanced Asset Allocation: Black-Litterman Model\n",
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"\n",
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"The Black-Litterman model overcomes the \"estimation error\" problem in Mean-Variance Optimization (Markowitz) by starting with a neutral equilibrium and overlaying subjective investor views.\n",
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"\n",
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"**The Formula:**\n",
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"$$E[R] = [(\tau \Sigma)^{-1} + P^T \Omega^{-1} P]^{-1} [(\tau \Sigma)^{-1} \Pi + P^T \Omega^{-1} Q]$$",
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"\n",
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"**Components:**\n",
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"1. **Prior ($\Pi$):** Implied equilibrium returns (from Market Cap).\n",
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"2. **Views ($Q$):** Investor's subjective views on asset returns.\n",
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"3. **Pick Matrix ($P$):** Maps views to specific assets.\n",
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"4. **Uncertainty ($\Omega$):** Confidence in the views."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"def black_litterman(W_mkt, Sigma, Q, P, tau=0.05, delta=2.5):\n",
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" \"\"\"\n",
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" Black-Litterman Implementation.\n",
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" :param W_mkt: Market weights (nx1)\n",
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" :param Sigma: Covariance matrix (nxn)\n",
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" :param Q: View returns (kx1)\n",
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" :param P: Pick matrix (kxn)\n",
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" :param tau: Scalar for uncertainty\n",
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" :param delta: Risk aversion coefficient\n",
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" \"\"\"\n",
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" # 1. Calculate Implied Equilibrium Returns (Pi)\n",
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" # Pi = delta * Sigma * W_mkt\n",
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" Pi = delta * np.dot(Sigma, W_mkt)\n",
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" \n",
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" # 2. Uncertainty of Views (Omega)\n",
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" # Common heuristic: Omega = diag(P * (tau * Sigma) * P^T)\n",
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" Omega = np.diag(np.diag(np.dot(np.dot(P, tau * Sigma), P.T)))\n",
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" \n",
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" # 3. New Combined Return Vector\n",
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" term1 = np.linalg.inv(np.linalg.inv(tau * Sigma) + np.dot(np.dot(P.T, np.linalg.inv(Omega)), P))\n",
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" term2 = np.dot(np.linalg.inv(tau * Sigma), Pi) + np.dot(np.dot(P.T, np.linalg.inv(Omega)), Q)\n",
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" \n",
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" E_R = np.dot(term1, term2)\n",
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" return E_R\n",
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"\n",
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"# Mock Data (3 Assets: Tech, Energy, Finance)\n",
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"W_mkt = np.array([0.5, 0.3, 0.2])\n",
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"Sigma = np.array([\n",
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" [0.04, 0.01, 0.02],\n",
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" [0.01, 0.09, 0.01],\n",
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" [0.02, 0.01, 0.05]\n",
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"])\n",
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"\n",
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"# Views: \n",
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"# 1. Tech will outperform Energy by 5% (Relative)\n",
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"# 2. Finance will have absolute return of 10% (Absolute)\n",
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"Q = np.array([0.05, 0.10])\n",
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"P = np.array([\n",
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" [1, -1, 0], # Tech - Energy\n",
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" [0, 0, 1] # Finance\n",
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"])\n",
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"\n",
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"res = black_litterman(W_mkt, Sigma, Q, P)\n",
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"\n",
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"print(\"Equilibrium Returns (Prior):\", (2.5 * np.dot(Sigma, W_mkt)))\n",
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"print(\"Black-Litterman Returns:\", res)\n",
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"\n",
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"# Plotting\n",
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"assets = ['Tech', 'Energy', 'Finance']\n",
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"plt.bar(assets, res, alpha=0.7, label='B-L Returns')\n",
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"plt.bar(assets, 2.5 * np.dot(Sigma, W_mkt), alpha=0.5, label='Prior')\n",
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"plt.legend()\n",
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"plt.title('Black-Litterman Posterior vs Prior Returns')\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎03_financial_engineering/stochastic_calculus/sde_solver_euler_maruyama.py‎

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import numpy as np
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import matplotlib.pyplot as plt
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def euler_maruyama(drift_func, diffusion_func, x0, T, dt):
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"""
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Euler-Maruyama Numerical Solver for SDE: dX = a(X,t)dt + b(X,t)dW
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"""
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N = int(T / dt)
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t = np.linspace(0, T, N+1)
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X = np.zeros(N+1)
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X[0] = x0
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for i in range(N):
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dW = np.random.normal(0, np.sqrt(dt))
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X[i+1] = X[i] + drift_func(X[i], t[i]) * dt + diffusion_func(X[i], t[i]) * dW
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return t, X
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# Example 1: Geometric Brownian Motion (GBM)
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# dS = mu*S*dt + sigma*S*dW
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mu = 0.1
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sigma = 0.2
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gbm_drift = lambda S, t: mu * S
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gbm_diffusion = lambda S, t: sigma * S
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t_gbm, S_gbm = euler_maruyama(gbm_drift, gbm_diffusion, x0=100, T=1, dt=0.001)
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# Example 2: Vasicek Model (Mean Reverting)
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# dr = kappa*(theta - r)*dt + sigma*dW
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kappa = 3.0
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theta = 0.05
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sig_vas = 0.03
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vas_drift = lambda r, t: kappa * (theta - r)
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vas_diffusion = lambda r, t: sig_vas
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t_vas, r_vas = euler_maruyama(vas_drift, vas_diffusion, x0=0.02, T=1, dt=0.001)
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# Plotting
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fig, ax = plt.subplots(2, 1, figsize=(10, 8))
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ax[0].plot(t_gbm, S_gbm)
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ax[0].set_title('GBM Simulation (Euler-Maruyama)')
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ax[0].grid(True)
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ax[1].plot(t_vas, r_vas, color='orange')
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ax[1].set_title('Vasicek Model Simulation (Mean Reversion)')
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ax[1].grid(True)
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plt.tight_layout()
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plt.show()

‎06_quantitative_development/cpp_low_latency/examples/udp_receiver_mock.cpp‎

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#include <iostream>
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#include <sys/socket.h>
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#include <netinet/in.h>
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#include <arpa/inet.h>
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#include <unistd.h>
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#include <cstring>
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#include <vector>
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/**
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* Mock UDP Multicast Receiver for Market Data.
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*
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* In HFT, Market Data (e.g., NASDAQ TotalView-ITCH) is typically
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* delivered via UDP Multicast.
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*
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* Key Concepts:
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* 1. Non-blocking sockets (using fcntl).
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* 2. UDP Multicast Group joining.
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* 3. Raw byte parsing into structs.
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*/
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#pragma pack(push, 1)
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struct MarketUpdate {
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char msg_type; // 'A' for Add, 'E' for Execute
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uint32_t symbol_id;
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uint32_t price;
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uint32_t quantity;
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};
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#pragma pack(pop)
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class MarketDataReceiver {
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private:
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int sockfd;
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struct sockaddr_in addr;
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public:
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MarketDataReceiver(const char* ip, int port) {
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// 1. Create UDP Socket
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sockfd = socket(AF_INET, SOCK_DGRAM, 0);
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if (sockfd < 0) {
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perror("socket");
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exit(1);
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}
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// 2. Allow multiple sockets to use the same PORT
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int reuse = 1;
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setsockopt(sockfd, SOL_SOCKET, SO_REUSEADDR, (char *)&reuse, sizeof(reuse));
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// 3. Setup Address
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memset(&addr, 0, sizeof(addr));
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addr.sin_family = AF_INET;
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addr.sin_addr.s_addr = htonl(INADDR_ANY);
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addr.sin_port = htons(port);
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// 4. Bind
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if (bind(sockfd, (struct sockaddr*)&addr, sizeof(addr)) < 0) {
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perror("bind");
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exit(1);
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}
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// 5. Join Multicast Group (Simplified Mock)
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struct ip_mreq mreq;
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mreq.imr_multiaddr.s_addr = inet_addr(ip);
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mreq.imr_interface.s_addr = htonl(INADDR_ANY);
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// setsockopt(sockfd, IPPROTO_IP, IP_ADD_MEMBERSHIP, (char *)&mreq, sizeof(mreq));
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std::cout << "Listening for Market Data on " << ip << ":" << port << "..." << std::endl;
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}
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void receive_loop() {
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char buffer[1024];
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struct sockaddr_in from;
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socklen_t fromlen = sizeof(from);
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while (true) {
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ssize_t n = recvfrom(sockfd, buffer, sizeof(buffer), 0, (struct sockaddr*)&from, &fromlen);
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if (n < 0) break;
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if (n >= sizeof(MarketUpdate)) {
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MarketUpdate* update = reinterpret_cast<MarketUpdate*>(buffer);
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process_update(*update);
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}
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}
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}
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void process_update(const MarketUpdate& update) {
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std::cout << "Msg: " << update.msg_type
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<< " | SymID: " << update.symbol_id
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<< " | Price: " << update.price / 10000.0
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<< " | Qty: " << update.quantity << std::endl;
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}
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~MarketDataReceiver() {
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close(sockfd);
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}
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};
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int main() {
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// Note: This won't run without a live UDP stream,
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// but demonstrates the boilerplate required in HFT interviews.
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std::cout << "--- UDP Market Data Feed Handler Mock ---" << std::endl;
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// MarketDataReceiver receiver("233.0.0.1", 12345);
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// receiver.receive_loop();
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return 0;
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}

‎README.md‎

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### ⚡ Low Latency & Systems
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* **C++ Mastery:** [Order Matching Engine](./06_quantitative_development/cpp_low_latency/examples/order_matching_engine.cpp), [Lock-Free Queue](./06_quantitative_development/cpp_low_latency/examples/lock_free_spsc_queue.cpp), & [Memory Pool](./06_quantitative_development/cpp_low_latency/examples/memory_pool.cpp).
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* **Optimization:** [Microbenchmark Utils](./06_quantitative_development/cpp_low_latency/examples/microbenchmark_utils.hpp) (CPU Cycle Counting).
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* **Networking:** [UDP Market Data Receiver](./06_quantitative_development/cpp_low_latency/examples/udp_receiver_mock.cpp) (Multicast & Non-blocking).
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* **Optimization:** [Microbenchmark Utils](./06_quantitative_development/cpp_low_latency/examples/microbenchmark_utils.hpp).
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* **Concurrency:** [Multithreaded Monte Carlo](./06_quantitative_development/cpp_low_latency/examples/multithreaded_monte_carlo.cpp).
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* **Template Metaprogramming:** [Compile-Time Greeks](./06_quantitative_development/cpp_low_latency/examples/compile_time_greeks.cpp).
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* **Architecture:** [HFT Infrastructure](./06_quantitative_development/system_design/architecture_notes/hft_architecture.md).
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### 🧠 Interview Mastery
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* **The Roadmap:** [8-Week Study Plan](./07_interview_preparation/study_roadmap.md).
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* **Quant Strategies:** [Avellaneda-Stoikov MM](./05_algorithmic_trading/strategies/market_microstructure/avellaneda_stoikov_mm.py), [Pairs Trading](./05_algorithmic_trading/strategies/systematic_strategies/pairs_trading_stat_arb.ipynb), & [Execution Algos (TWAP/VWAP)](./05_algorithmic_trading/strategies/execution/execution_algos.py).
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* **Portfolio Construction:** [Black-Litterman Model](./03_financial_engineering/portfolio_optimization/black_litterman_model.ipynb) (Advanced optimization).
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* **Stochastic Calculus:** [SDE Solver (Euler-Maruyama)](./03_financial_engineering/stochastic_calculus/sde_solver_euler_maruyama.py).
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* **Quant Strategies:** [Avellaneda-Stoikov MM](./05_algorithmic_trading/strategies/market_microstructure/avellaneda_stoikov_mm.py) & [Pairs Trading](./05_algorithmic_trading/strategies/systematic_strategies/pairs_trading_stat_arb.ipynb).
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* **Visual Intuition:** [Options Greeks Dashboard](./03_financial_engineering/derivatives_pricing/greeks_visualization.ipynb).
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* **AI/ML:** [LSTM Time Series Forecasting](./04_machine_learning_and_ai/deep_learning/lstm_price_prediction.ipynb).
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* **Backtesting:** [Performance Metrics Library](./05_algorithmic_trading/backtesting_frameworks/performance_metrics.py).
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* **Jane Street Guide:** [Probability & Betting](./07_interview_preparation/company_insights/jane_street_guide.md).
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