ferro_ta_core 1.1.2

Pure Rust core indicator library — no PyO3, no numpy dependency
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187

//! Option pricing models.

use super::normal::cdf;
use super::{OptionContract, OptionEvaluation, OptionKind, PricingModel};

fn invalid_inputs(underlying: f64, strike: f64, time_to_expiry: f64, volatility: f64) -> bool {
    !underlying.is_finite()
        || !strike.is_finite()
        || !time_to_expiry.is_finite()
        || !volatility.is_finite()
        || underlying <= 0.0
        || strike <= 0.0
        || time_to_expiry < 0.0
        || volatility < 0.0
}

/// Black-Scholes-Merton price with continuous carry/dividend yield.
pub fn black_scholes_price(
    spot: f64,
    strike: f64,
    rate: f64,
    dividend_yield: f64,
    time_to_expiry: f64,
    volatility: f64,
    kind: OptionKind,
) -> f64 {
    if invalid_inputs(spot, strike, time_to_expiry, volatility) || !rate.is_finite() {
        return f64::NAN;
    }
    if time_to_expiry == 0.0 {
        return match kind {
            OptionKind::Call => (spot - strike).max(0.0),
            OptionKind::Put => (strike - spot).max(0.0),
        };
    }

    let discount = (-rate * time_to_expiry).exp();
    let carry_discount = (-dividend_yield * time_to_expiry).exp();
    if volatility == 0.0 {
        return match kind {
            OptionKind::Call => (spot * carry_discount - strike * discount).max(0.0),
            OptionKind::Put => (strike * discount - spot * carry_discount).max(0.0),
        };
    }

    let sqrt_t = time_to_expiry.sqrt();
    let sigma_sqrt_t = volatility * sqrt_t;
    let d1 = ((spot / strike).ln()
        + (rate - dividend_yield + 0.5 * volatility * volatility) * time_to_expiry)
        / sigma_sqrt_t;
    let d2 = d1 - sigma_sqrt_t;

    match kind {
        OptionKind::Call => spot * carry_discount * cdf(d1) - strike * discount * cdf(d2),
        OptionKind::Put => strike * discount * cdf(-d2) - spot * carry_discount * cdf(-d1),
    }
}

/// Black-76 price using the forward price as the underlying input.
pub fn black_76_price(
    forward: f64,
    strike: f64,
    rate: f64,
    time_to_expiry: f64,
    volatility: f64,
    kind: OptionKind,
) -> f64 {
    if invalid_inputs(forward, strike, time_to_expiry, volatility) || !rate.is_finite() {
        return f64::NAN;
    }
    let discount = (-rate * time_to_expiry).exp();
    if time_to_expiry == 0.0 {
        return discount
            * match kind {
                OptionKind::Call => (forward - strike).max(0.0),
                OptionKind::Put => (strike - forward).max(0.0),
            };
    }
    if volatility == 0.0 {
        return discount
            * match kind {
                OptionKind::Call => (forward - strike).max(0.0),
                OptionKind::Put => (strike - forward).max(0.0),
            };
    }

    let sqrt_t = time_to_expiry.sqrt();
    let sigma_sqrt_t = volatility * sqrt_t;
    let d1 =
        ((forward / strike).ln() + 0.5 * volatility * volatility * time_to_expiry) / sigma_sqrt_t;
    let d2 = d1 - sigma_sqrt_t;

    let signed = kind.sign();
    discount * signed * (forward * cdf(signed * d1) - strike * cdf(signed * d2))
}

/// Model-dispatched option price.
pub fn model_price(input: OptionEvaluation) -> f64 {
    let contract = input.contract;
    match contract.model {
        PricingModel::BlackScholes => black_scholes_price(
            contract.underlying,
            contract.strike,
            contract.rate,
            contract.carry,
            contract.time_to_expiry,
            input.volatility,
            contract.kind,
        ),
        PricingModel::Black76 => black_76_price(
            contract.underlying,
            contract.strike,
            contract.rate,
            contract.time_to_expiry,
            input.volatility,
            contract.kind,
        ),
    }
}

/// Lower no-arbitrage bound for the option price.
pub fn price_lower_bound(contract: OptionContract) -> f64 {
    match contract.model {
        PricingModel::BlackScholes => {
            let discount = (-contract.rate * contract.time_to_expiry).exp();
            let carry_discount = (-contract.carry * contract.time_to_expiry).exp();
            match contract.kind {
                OptionKind::Call => {
                    (contract.underlying * carry_discount - contract.strike * discount).max(0.0)
                }
                OptionKind::Put => {
                    (contract.strike * discount - contract.underlying * carry_discount).max(0.0)
                }
            }
        }
        PricingModel::Black76 => {
            let discount = (-contract.rate * contract.time_to_expiry).exp();
            discount
                * match contract.kind {
                    OptionKind::Call => (contract.underlying - contract.strike).max(0.0),
                    OptionKind::Put => (contract.strike - contract.underlying).max(0.0),
                }
        }
    }
}

/// Upper no-arbitrage bound for the option price.
pub fn price_upper_bound(contract: OptionContract) -> f64 {
    match contract.model {
        PricingModel::BlackScholes => match contract.kind {
            OptionKind::Call => {
                contract.underlying * (-contract.carry * contract.time_to_expiry).exp()
            }
            OptionKind::Put => contract.strike * (-contract.rate * contract.time_to_expiry).exp(),
        },
        PricingModel::Black76 => {
            let discount = (-contract.rate * contract.time_to_expiry).exp();
            discount
                * match contract.kind {
                    OptionKind::Call => contract.underlying,
                    OptionKind::Put => contract.strike,
                }
        }
    }
}

#[cfg(test)]
mod tests {
    use super::{black_76_price, black_scholes_price};
    use crate::options::OptionKind;

    #[test]
    fn black_scholes_prices_are_reasonable() {
        let call = black_scholes_price(100.0, 100.0, 0.05, 0.0, 1.0, 0.2, OptionKind::Call);
        let put = black_scholes_price(100.0, 100.0, 0.05, 0.0, 1.0, 0.2, OptionKind::Put);
        assert!((call - 10.4506).abs() < 1e-3);
        assert!((put - 5.5735).abs() < 1e-3);
    }

    #[test]
    fn black_76_prices_are_reasonable() {
        let call = black_76_price(100.0, 100.0, 0.03, 1.0, 0.2, OptionKind::Call);
        let put = black_76_price(100.0, 100.0, 0.03, 1.0, 0.2, OptionKind::Put);
        assert!((call - 7.730_148).abs() < 1e-3);
        assert!((put - 7.730_148).abs() < 1e-3);
    }
}