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Delete main.zig
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// M3g -- Market microstructure sims
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// Language: Zig (tick-level latency, deterministic memory layout)
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// Protocol: line-delimited JSON on stdin/stdout to hub.tcl
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const std = @import("std");
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const math = std.math;
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// -- Hyperbolic functions --------------------------------------------------
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fn sinh(x: f64) f64 {
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return (@exp(x) - @exp(-x)) / 2.0;
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}
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fn cosh(x: f64) f64 {
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return (@exp(x) + @exp(-x)) / 2.0;
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}
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fn tanh(x: f64) f64 {
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return sinh(x) / cosh(x);
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}
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// -- BoundedPrediction (L2: every output has explicit bounds) -------------
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const BoundedPrediction = struct {
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value: f64,
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lower_bound: f64,
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upper_bound: f64,
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confidence: f64,
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time_horizon: []const u8,
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sim_type: []const u8 = "market_microstructure",
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fn init(value: f64, lower: f64, upper: f64, confidence: f64, horizon: []const u8) !BoundedPrediction {
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if (lower > value or value > upper)
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return error.BoundsViolation;
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if (confidence < 0.0 or confidence > 10.0)
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return error.ConfidenceOutOfRange;
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return .{
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.value = value,
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.lower_bound = lower,
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.upper_bound = upper,
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.confidence = confidence,
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.time_horizon = horizon,
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};
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}
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};
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// -- Order book -----------------------------------------------------------
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const Side = enum { bid, ask };
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const Order = struct {
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price: f64,
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quantity: f64,
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side: Side,
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id: u64,
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};
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const MAX_LEVELS: usize = 256;
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const OrderBook = struct {
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bids: [MAX_LEVELS]Order,
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asks: [MAX_LEVELS]Order,
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n_bids: usize,
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n_asks: usize,
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mid_price: f64,
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fn init() OrderBook {
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return .{
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.bids = undefined,
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.asks = undefined,
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.n_bids = 0,
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.n_asks = 0,
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.mid_price = 0.0,
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};
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}
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fn addOrder(self: *OrderBook, order: Order) void {
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switch (order.side) {
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.bid => {
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if (self.n_bids < MAX_LEVELS) {
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self.bids[self.n_bids] = order;
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self.n_bids += 1;
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}
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},
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.ask => {
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if (self.n_asks < MAX_LEVELS) {
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self.asks[self.n_asks] = order;
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self.n_asks += 1;
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}
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},
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}
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self.updateMid();
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}
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fn bestBid(self: *const OrderBook) f64 {
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if (self.n_bids == 0) return 0.0;
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var best: f64 = 0.0;
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for (self.bids[0..self.n_bids]) |b| {
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if (b.price > best) best = b.price;
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}
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return best;
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}
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fn bestAsk(self: *const OrderBook) f64 {
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if (self.n_asks == 0) return math.inf(f64);
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var best: f64 = math.inf(f64);
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for (self.asks[0..self.n_asks]) |a| {
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if (a.price < best) best = a.price;
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}
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return best;
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}
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fn spread(self: *const OrderBook) f64 {
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return self.bestAsk() - self.bestBid();
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}
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fn updateMid(self: *OrderBook) void {
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const bb = self.bestBid();
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const ba = self.bestAsk();
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if (bb > 0.0 and ba < math.inf(f64)) {
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self.mid_price = (bb + ba) / 2.0;
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}
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}
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// L2: slippage is a function of order size and current depth (non-linear)
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fn estimateSlippage(self: *const OrderBook, size: f64, side: Side) f64 {
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var remaining = size;
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var cost: f64 = 0.0;
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const ref_price = self.mid_price;
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switch (side) {
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.bid => {
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// Buying: walk up the ask side
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var i: usize = 0;
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while (i < self.n_asks and remaining > 0.0) : (i += 1) {
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const fill = @min(remaining, self.asks[i].quantity);
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cost += fill * self.asks[i].price;
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remaining -= fill;
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}
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},
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.ask => {
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// Selling: walk down the bid side
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var i: usize = 0;
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while (i < self.n_bids and remaining > 0.0) : (i += 1) {
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const fill = @min(remaining, self.bids[i].quantity);
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cost += fill * self.bids[i].price;
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remaining -= fill;
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}
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},
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}
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if (size <= remaining) return 0.0;
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const avg_price = cost / (size - remaining);
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return @abs(avg_price - ref_price) / ref_price;
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}
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};
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// -- Almgren-Chriss optimal execution -------------------------------------
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// min integral [lambda * x(t) * dx/dt + eta * (dx/dt)^2] dt
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// Solution via Riccati: x(t) = X * sinh(kappa*(T-t)) / sinh(kappa*T)
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// kappa = sqrt(lambda / eta)
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const AlmgrenChriss = struct {
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lambda: f64, // permanent impact
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eta: f64, // temporary impact
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sigma: f64, // volatility (for timing risk)
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risk_aversion: f64,
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fn optimalTrajectory(self: *const AlmgrenChriss, total_shares: f64, T: f64, n_buckets: usize, schedule: []f64) void {
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const kappa = @sqrt(self.risk_aversion * self.sigma * self.sigma / self.eta);
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const sinh_kT = sinh(kappa * T);
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const dt = T / @as(f64, @floatFromInt(n_buckets));
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var prev_x = total_shares;
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for (0..n_buckets) |i| {
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const t = @as(f64, @floatFromInt(i + 1)) * dt;
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const x_t = total_shares * sinh(kappa * (T - t)) / sinh_kT;
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schedule[i] = (prev_x - x_t) / total_shares;
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prev_x = x_t;
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}
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}
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fn executionCost(self: *const AlmgrenChriss, total_shares: f64, T: f64) f64 {
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const kappa = @sqrt(self.risk_aversion * self.sigma * self.sigma / self.eta);
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return self.eta * total_shares * total_shares * kappa / tanh(kappa * T);
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}
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};
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// -- Self-test ------------------------------------------------------------
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pub fn main() !void {
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const stdout = std.io.getStdOut().writer();
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try stdout.print("M3g Market Microstructure Sim -- Zig {s}\n\n", .{@tagName(std.Target.Os.Tag.linux)});
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// Order book test
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try stdout.print("Order book (spread, slippage):\n", .{});
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var book = OrderBook.init();
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book.addOrder(.{ .price = 1800.0, .quantity = 5.0, .side = .bid, .id = 1 });
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book.addOrder(.{ .price = 1799.0, .quantity = 10.0, .side = .bid, .id = 2 });
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book.addOrder(.{ .price = 1798.0, .quantity = 20.0, .side = .bid, .id = 3 });
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book.addOrder(.{ .price = 1801.0, .quantity = 5.0, .side = .ask, .id = 4 });
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book.addOrder(.{ .price = 1802.0, .quantity = 10.0, .side = .ask, .id = 5 });
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book.addOrder(.{ .price = 1805.0, .quantity = 20.0, .side = .ask, .id = 6 });
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try stdout.print(" best bid: {d:.2} best ask: {d:.2}\n", .{ book.bestBid(), book.bestAsk() });
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try stdout.print(" spread: {d:.2}\n", .{book.spread()});
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const slip_small = book.estimateSlippage(3.0, .bid);
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const slip_large = book.estimateSlippage(20.0, .bid);
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try stdout.print(" slippage (3 ETH buy): {d:.6}\n", .{slip_small});
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try stdout.print(" slippage (20 ETH buy): {d:.6}\n", .{slip_large});
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// L2: larger orders produce greater slippage
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if (slip_large > slip_small) {
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try stdout.print(" L2 non-linear slippage: PASS\n\n", .{});
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} else {
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try stdout.print(" L2 non-linear slippage: FAIL\n\n", .{});
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}
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// Almgren-Chriss test
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try stdout.print("Almgren-Chriss optimal execution:\n", .{});
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const ac = AlmgrenChriss{
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.lambda = 0.001,
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.eta = 0.01,
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.sigma = 0.02,
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.risk_aversion = 1.0e-6,
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};
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var schedule: [5]f64 = undefined;
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ac.optimalTrajectory(100.0, 30.0, 5, &schedule);
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try stdout.print(" schedule (5 buckets, 100 shares, 30 min):\n", .{});
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for (schedule, 0..) |s, i| {
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try stdout.print(" bucket {d}: {d:.4}\n", .{ i + 1, s });
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}
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const cost = ac.executionCost(100.0, 30.0);
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try stdout.print(" total cost: {d:.4}\n\n", .{cost});
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// BoundedPrediction test
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try stdout.print("BoundedPrediction:\n", .{});
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const bp = try BoundedPrediction.init(0.0034, 0.0018, 0.0052, 8.50, "next_trade");
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try stdout.print(" slippage: {d:.4} [{d:.4}, {d:.4}]\n", .{ bp.value, bp.lower_bound, bp.upper_bound });
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try stdout.print(" confidence: {d:.2}/10.00\n\n", .{bp.confidence});
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// Invariant checks
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try stdout.print("Invariant checks:\n", .{});
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if (BoundedPrediction.init(5.0, 6.0, 8.0, 7.0, "1h")) |_| {
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try stdout.print(" L2 bounds: FAIL\n", .{});
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} else |_| {
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try stdout.print(" L2 bounds: PASS (rejected lower > value)\n", .{});
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}
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if (BoundedPrediction.init(5.0, 4.0, 8.0, 11.0, "1h")) |_| {
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try stdout.print(" Confidence range: FAIL\n", .{});
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} else |_| {
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try stdout.print(" Confidence range: PASS (rejected 11.0 > 10.0)\n", .{});
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}
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try stdout.print("\nAll models operational.\n", .{});
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}
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