RustQuant_instruments 0.3.1

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// RustQuant: A Rust library for quantitative finance tools.
// Copyright (C) 2023 https://github.com/avhz
// Dual licensed under Apache 2.0 and MIT.
// See:
//      - LICENSE-APACHE.md
//      - LICENSE-MIT.md
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

use super::OptionContract;
use crate::{
    math::distributions::{gaussian::Gaussian, Distribution},
    time::{today, DayCountConvention},
};
use time::Date;

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// STRUCTS
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

/// Asian Option struct.
#[derive(derive_builder::Builder, Debug, Clone, Copy)]
pub struct AsianOptionAnalyticBackend {
    /// `S` - Initial price of the underlying.
    pub initial_price: f64,
    /// `K` - Strike price.
    pub strike_price: f64,
    /// `r` - Risk-free rate parameter.
    pub risk_free_rate: f64,
    /// `v` - Volatility parameter.
    pub volatility: f64,
    /// `q` - Dividend rate.
    pub dividend_rate: f64,

    /// `evaluation_date` - Valuation date.
    #[builder(default = "None")]
    pub evaluation_date: Option<Date>,

    /// `expiry_date` - Expiry date.
    pub expiration_date: Date,
}

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// IMPLEMENTATIONS
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

impl AsianOption {
    /// New Asian Option
    #[must_use]
    pub const fn new(
        initial_price: f64,
        strike_price: f64,
        risk_free_rate: f64,
        volatility: f64,
        dividend_rate: f64,
        evaluation_date: Option<Date>,
        expiration_date: Date,
    ) -> Self {
        Self {
            initial_price,
            strike_price,
            risk_free_rate,
            volatility,
            dividend_rate,
            evaluation_date,
            expiration_date,
        }
    }

    /// Geometric Continuous Average-Rate Price
    #[must_use]
    pub fn price_geometric_average(&self) -> (f64, f64) {
        let S = self.initial_price;
        let K = self.strike_price;
        // let T = self.time_to_maturity;
        let r = self.risk_free_rate;
        let v = self.volatility;
        let q = self.dividend_rate;

        // Compute time to maturity.
        let T = DayCountConvention::default().day_count_factor(
            self.evaluation_date.unwrap_or(today()),
            self.expiration_date,
        );

        let v_a = v / 3_f64.sqrt();
        let b = r - q;
        let b_a = 0.5 * (b - v * v / 6.0);

        let d1 = ((S / K).ln() + (b_a + 0.5 * v_a * v_a) * T) / (v_a * (T).sqrt());
        let d2 = d1 - v_a * (T).sqrt();

        let N = Gaussian::default();

        let c = S * ((b_a - r) * T).exp() * N.cdf(d1) - K * (-r * T).exp() * N.cdf(d2);
        let p = -S * ((b_a - r) * T).exp() * N.cdf(-d1) + K * (-r * T).exp() * N.cdf(-d2);

        (c, p)
    }
}

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// TESTS
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#[cfg(test)]
mod tests {
    use time::Duration;

    use super::*;
    use crate::assert_approx_equal;

    #[test]
    fn test_asian_geometric() {
        let expiry_date = today() + Duration::days(92);

        let AsianOption = AsianOption {
            initial_price: 80.0,
            strike_price: 85.0,
            risk_free_rate: 0.05,
            volatility: 0.2,
            evaluation_date: None,
            expiration_date: expiry_date,
            dividend_rate: -0.03,
        };

        let prices = AsianOption.price_geometric_average();

        // Value from Haug's book.
        assert_approx_equal!(prices.1, 4.6922, 0.0001);
    }
}