local_vol_calibration/
local_vol_calibration.rs

1//! The local volatility workflow end to end: quoted option prices ->
2//! implied vols -> implied surface -> Dupire local vol -> reprice.
3//!
4//! Run with:  cargo run --release --example local_vol_calibration
5
6mod common;
7
8use chrono::NaiveDate;
9use rustyqlib::core::curves::{Compounding, Tenor, YieldCurve};
10use rustyqlib::core::daycount::DayCountConvention;
11use rustyqlib::core::quotes::Quote;
12use rustyqlib::core::trade::PutOrCall;
13use rustyqlib::core::traits::Instrument;
14use rustyqlib::core::vols::VolSurface;
15use rustyqlib::equity::blackscholes::bs_price;
16use rustyqlib::equity::builder::EquityOptionBuilder;
17use rustyqlib::equity::local_vol::LocalVol;
18use rustyqlib::equity::montecarlo::McModel;
19use rustyqlib::equity::utils::Engine;
20use rustyqlib::equity::vol_surface::build_implied_vol_surface;
21
22const SPOT: f64 = 100.0;
23const RATE: f64 = 0.05;
24
25fn asof() -> NaiveDate {
26    NaiveDate::from_ymd_opt(2026, 1, 1).unwrap()
27}
28
29/// The "true" market smile we will generate quotes from and recover.
30fn true_vol(strike: f64, base: f64) -> f64 {
31    base - 0.001 * (strike - 100.0)
32}
33
34fn main() {
35    common::title("LOCAL VOLATILITY — quotes -> implied surface -> Dupire -> reprice");
36
37    let maturities = [
38        (NaiveDate::from_ymd_opt(2026, 7, 2).unwrap(), 0.23),
39        (NaiveDate::from_ymd_opt(2027, 1, 1).unwrap(), 0.25),
40    ];
41
42    common::section("Step 1: generate market quotes from a known skew");
43    println!("  sigma(K, T) = base(T) - 0.001 * (K - 100)");
44    let mut quotes = Vec::new();
45    for (maturity, base_vol) in maturities {
46        let t = (maturity - asof()).num_days() as f64 / 365.0;
47        for i in 0..13 {
48            let strike = 70.0 + 5.0 * i as f64;
49            let vol = true_vol(strike, base_vol);
50            let price = bs_price(SPOT, strike, RATE, 0.0, vol, t, PutOrCall::Call);
51            let mut option = EquityOptionBuilder::new()
52                .spot(SPOT)
53                .strike(strike)
54                .flat_vol(0.2) // placeholder: the solve does not use it
55                .flat_rate(RATE)
56                .valuation_date(asof())
57                .maturity_date(maturity)
58                .vanilla(PutOrCall::Call)
59                .build();
60            option.base.current_price = Quote::new(price);
61            quotes.push(Box::new(option));
62        }
63    }
64    println!("  {} quotes across {} expiries", quotes.len(), maturities.len());
65
66    common::section("Step 2: back out implied vols and build the surface");
67    let surface = build_implied_vol_surface(&quotes).expect("calibration failed");
68    println!("{surface}");
69
70    common::section("Step 3: check the surface recovers the input smile");
71    for (t, base_vol) in [(182.0 / 365.0, 0.23), (1.0, 0.25)] {
72        for strike in [70.0, 85.0, 100.0, 115.0, 130.0] {
73            let recovered = surface.vol(strike, SPOT, t);
74            common::check(
75                &format!("T={t:.3} K={strike}"),
76                recovered,
77                true_vol(strike, base_vol),
78                1e-6,
79            );
80        }
81    }
82
83    common::section("Step 4: Dupire local volatility from that surface");
84    let curve =
85        YieldCurve::flat(RATE, asof(), DayCountConvention::Act365, Compounding::Continuous).unwrap();
86    let lv = LocalVol::new(&surface, &curve, SPOT, 0.0, 0.0);
87    println!("  {:>8} {:>12} {:>12} {:>12}", "level", "t=0.25", "t=0.50", "t=1.00");
88    for level in [70.0, 85.0, 100.0, 115.0, 130.0] {
89        println!(
90            "  {level:>8.1} {:>12.4} {:>12.4} {:>12.4}",
91            lv.vol(level, 0.25),
92            lv.vol(level, 0.50),
93            lv.vol(level, 1.00)
94        );
95    }
96    common::note("local vol is steeper in strike than implied vol (the 'twice the slope' rule)");
97    common::note("the far wings are noisy: Dupire takes numerical derivatives of a");
98    common::note("piecewise-linear surface with flat extrapolation — trust the interior.");
99
100    common::section("Step 5: reprice the calibrating vanillas through local vol MC");
101    common::table_header();
102    for strike in [90.0, 100.0, 110.0] {
103        let expected = bs_price(SPOT, strike, RATE, 0.0, true_vol(strike, 0.25), 1.0, PutOrCall::Call);
104        common::row(
105            &format!("local vol MC, K={strike}"),
106            &EquityOptionBuilder::new()
107                .spot(SPOT)
108                .strike(strike)
109                .vol_surface(surface.clone())
110                .flat_rate(RATE)
111                .valuation_date(asof())
112                .maturity_date(NaiveDate::from_ymd_opt(2027, 1, 1).unwrap())
113                .vanilla(PutOrCall::Call)
114                .engine(Engine::MonteCarlo)
115                .model(McModel::LocalVol)
116                .paths(50_000)
117                .build(),
118        );
119        println!("{:<34} {expected:>12.6}  <- Black-Scholes target at the quoted smile vol", "");
120    }
121
122    common::section("Local vol on the finite difference engine (no sampling noise)");
123    common::table_header();
124    for strike in [90.0, 100.0, 110.0] {
125        common::row(
126            &format!("local vol FD, K={strike}"),
127            &EquityOptionBuilder::new()
128                .spot(SPOT)
129                .strike(strike)
130                .vol_surface(surface.clone())
131                .flat_rate(RATE)
132                .valuation_date(asof())
133                .maturity_date(NaiveDate::from_ymd_opt(2027, 1, 1).unwrap())
134                .vanilla(PutOrCall::Call)
135                .engine(Engine::FiniteDifference)
136                .model(McModel::LocalVol)
137                .build(),
138        );
139    }
140
141    common::section("Sanity: a flat surface must give flat local vol");
142    let flat = VolSurface::flat(0.25, asof(), DayCountConvention::Act365).unwrap();
143    let flat_lv = LocalVol::new(&flat, &curve, SPOT, 0.0, 0.0);
144    for (level, t) in [(70.0, 0.25), (100.0, 1.0), (130.0, 2.0)] {
145        common::check(&format!("sigma_loc({level}, {t})"), flat_lv.vol(level, t), 0.25, 1e-6);
146    }
147
148    common::section("Term structure: local vol is the forward variance");
149    let term = VolSurface::from_strike_smiles(
150        &[Tenor::YearFraction(0.5), Tenor::YearFraction(1.0)],
151        &[vec![(100.0, 0.20)], vec![(100.0, 0.25)]],
152        asof(),
153        DayCountConvention::Act365,
154    )
155    .unwrap();
156    let term_lv = LocalVol::new(&term, &curve, SPOT, 0.0, 0.0);
157    // (0.25^2 * 1 - 0.20^2 * 0.5) / 0.5 = 0.085
158    common::check(
159        "sigma_loc between pillars = sqrt(fwd variance)",
160        term_lv.vol(100.0, 0.75),
161        0.085_f64.sqrt(),
162        1e-3,
163    );
164    println!();
165}
local_vol_calibration/local_vol_calibration.rs

local_vol_calibration/
local_vol_calibration.rs
