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https://github.com/Mihirkansara/nexus-quant-terminal.git
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Claude
78cd5c2ef7
Reiner-Rubinstein/Haug single barriers with rebates and Broadie-Glasserman-Kou discrete-monitoring correction, touch ladder, smile-consistent digitals on the vanna-volga smile, Dual Currency Investment fair-APR ladder with offer audit (platform margin, implied vol paid), and a KO accumulator Monte Carlo with zero-cost strike and optional Merton jumps. Validated against Haug Table 4-13 and discrete Monte Carlo. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FpiqUMAyo4RL5DdQHMWbwE
97 lines
5.0 KiB
Python
97 lines
5.0 KiB
Python
"""Exotics desk: Haug reference values, parity, BGK vs Monte Carlo, touches, DCI, accumulator."""
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import numpy as np
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import pytest
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from fastapi.testclient import TestClient
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from app.core.exotics import (accumulator_report, barrier_mc, barrier_price, dci_quote,
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digital_prices, gk_vanilla, simulate_paths, touch_prices)
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from app.main import app
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S, T, R, Q, V = 100.0, 0.5, 0.08, 0.04, 0.25
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client = TestClient(app)
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@pytest.mark.parametrize("cp,d,k,K,H,ref", [
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# Haug (2007) Table 4-13, rebate 3.
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("call", "down", "out", 90, 95, 9.0246), ("call", "down", "in", 90, 95, 7.7627),
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("call", "up", "out", 90, 105, 2.6789), ("call", "up", "in", 90, 105, 14.1112),
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("put", "down", "out", 90, 95, 2.2798), ("put", "down", "in", 90, 95, 2.9586),
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("put", "up", "out", 90, 105, 3.7760), ("put", "up", "in", 90, 105, 1.4653),
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])
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def test_haug_table(cp, d, k, K, H, ref):
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assert barrier_price(S, K, H, T, R, Q, V, cp == "call", d, k, 3.0) == pytest.approx(ref, abs=1e-4)
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def test_in_out_parity_and_breached():
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for cp in (True, False):
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for d, H in (("down", 95), ("up", 105)):
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for K in (90, 100, 110):
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tot = barrier_price(S, K, H, T, R, Q, V, cp, d, "in") + barrier_price(S, K, H, T, R, Q, V, cp, d, "out")
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assert tot == pytest.approx(gk_vanilla(S, K, T, R, Q, V, cp), abs=1e-9)
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assert barrier_price(S, 100, 101, T, R, Q, V, True, "down", "out", 2.0) == 2.0
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assert barrier_price(S, 100, 99, T, R, Q, V, True, "up", "in") == pytest.approx(gk_vanilla(S, 100, T, R, Q, V))
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@pytest.mark.parametrize("K,H,c,d,k", [(100, 95, True, "down", "out"), (100, 105, False, "up", "in")])
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def test_bgk_matches_discrete_mc(K, H, c, d, k):
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mc, se = barrier_mc(S, K, H, T, R, Q, V, c, d, k, n_steps=126, n_paths=100_000)
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bgk = barrier_price(S, K, H, T, R, Q, V, c, d, k, monitoring_per_year=252)
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cont = barrier_price(S, K, H, T, R, Q, V, c, d, k)
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assert abs(bgk - mc) < 4 * se + 0.01
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assert abs(cont - mc) > abs(bgk - mc)
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def test_touches_vs_mc():
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t = touch_prices(S, 110, T, R, Q, V, monitoring_per_year=252)
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p = simulate_paths(S, T, R, Q, V, 126, 100_000, np.random.default_rng(1))
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nt = np.exp(-R * T) * (~(p >= 110).any(axis=1)).mean()
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assert t["no_touch"] == pytest.approx(nt, abs=0.006)
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assert t["no_touch"] + t["one_touch_at_expiry"] == pytest.approx(np.exp(-R * T))
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assert t["one_touch_at_hit"] > t["one_touch_at_expiry"] # paid earlier when r > 0
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def test_smile_digital_is_minus_dC_dK():
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"""With a skewed σ(K) the digital equals the finite-difference −∂C/∂K."""
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sig = lambda K: 0.25 - 0.002 * (K - 100)
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K, h = 102.0, 1e-3
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fd = -(gk_vanilla(S, K + h, T, R, Q, sig(K + h)) - gk_vanilla(S, K - h, T, R, Q, sig(K - h))) / (2 * h)
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d = digital_prices(S, K, T, R, Q, 0.25, smile_vol=sig(K), smile_slope=-0.002)
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assert d["call_smile"] == pytest.approx(fd, abs=1e-6)
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assert d["call_smile"] > d["call_flat"] # negative skew richens call digitals
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def test_dci_fair_apr_and_implied_vol():
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q = dci_quote(60000, 65000, 7 / 365, 0.04, 0.0, 0.5, "sell_high")
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assert 0 < q["prob_conversion"] < 0.5 and q["fair_apr"] > 0
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audit = dci_quote(60000, 65000, 7 / 365, 0.04, 0.0, 0.5, "sell_high", offered_apr=q["fair_apr"] * 0.8)
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assert audit["margin_apr"] > 0 and audit["implied_vol_paid"] < 0.5
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hi = dci_quote(60000, 65000, 7 / 365, 0.04, 0.0, 0.8, "sell_high")
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assert hi["fair_apr"] > q["fair_apr"]
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def test_accumulator_zero_cost():
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rep = accumulator_report(S, 0.5, 0.04, 0.0, 0.3, ko_pct=105, n_paths=5000)
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assert abs(rep["pv_to_client"]) < 1e-6
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assert rep["zero_cost_strike"] < S and 0 < rep["prob_knock_out"] < 1
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j = accumulator_report(S, 0.5, 0.04, 0.0, 0.3, ko_pct=105, n_paths=5000,
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jump={"lambda": 4, "mean": -0.05, "sd": 0.05})
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assert j["pnl"]["p01"] < rep["pnl"]["p01"] # crash jumps fatten the loss tail
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def test_endpoints():
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base = {"pair": "XAUUSD", "S": 2650, "T": 0.25, "r_d": 0.0525, "r_f": 0.0, "sigma": 0.18}
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r = client.post("/api/exotics/barrier", json={**base, "K": 2650, "H_down": 2450, "H_up": 2850,
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"rr25": 0.02, "bf25": 0.005})
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assert r.status_code == 200, r.text
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js = r.json()
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assert len(js["rows"]) == 8 and len(js["touch_ladder"]) == 24
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assert js["digital"]["smile_adjustment"] != 0
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assert client.post("/api/exotics/barrier", json={**base, "K": 2650, "H_down": 2700, "H_up": 2850}).status_code == 422
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r = client.post("/api/exotics/dci", json={**base, "pair": "BTCUSD", "S": 60000, "T": 7 / 365, "sigma": 0.5,
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"offered_apr": 0.3, "strike_pct_offer": 105})
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assert r.status_code == 200 and all(x["strike_pct"] > 100 for x in r.json()["ladder"])
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r = client.post("/api/exotics/accumulator", json={**base, "n_paths": 2000})
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assert r.status_code == 200 and r.json()["zero_cost_strike"] < 2650
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assert client.post("/api/exotics/dci", json={**base, "pair": "NOPE"}).status_code == 404
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