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/******************************************************************************
Author: Joaquín Béjar García
Email: jb@taunais.com
Date: 30/11/24
******************************************************************************/
//! # Probability Analysis Module
//!
//! This module provides comprehensive probability and risk analysis tools for
//! option strategies, including profit probability calculations, risk metrics,
//! and price movement analysis.
//!
//! ## Core Components
//!
//! ### Strategy Probability Analysis
//!
//! ```rust
//! use positive::Positive;
//!
//! pub struct StrategyProbabilityAnalysis {
//! pub probability_of_profit: Positive,
//! pub probability_of_max_profit: Positive,
//! pub probability_of_max_loss: Positive,
//! pub expected_value: Positive,
//! pub break_even_points: Vec<Positive>,
//! pub risk_reward_ratio: Positive,
//! }
//! ```
//!
//! ### Probability Analysis Trait
//!
//! ```rust
//! use positive::Positive;
//! use optionstratlib::pricing::Profit;
//! use optionstratlib::strategies::Strategies;
//! use optionstratlib::error::ProbabilityError;
//!
//! use optionstratlib::strategies::probabilities::{PriceTrend, StrategyProbabilityAnalysis, VolatilityAdjustment};
//!
//! pub trait ProbabilityAnalysis: Strategies + Profit {
//! fn analyze_probabilities(
//! &self,
//! volatility_adj: Option<VolatilityAdjustment>,
//! trend: Option<PriceTrend>
//! ) -> Result<StrategyProbabilityAnalysis, ProbabilityError>;
//!
//! fn expected_value(
//! &self,
//! volatility_adj: Option<VolatilityAdjustment>,
//! trend: Option<PriceTrend>
//! ) -> Result<Positive, ProbabilityError>;
//! }
//! ```
//!
//! ## Usage Examples
//!
//! ### Basic Strategy Analysis
//!
//! ```rust
//! # fn run() -> Result<(), optionstratlib::error::Error> {
//! use rust_decimal_macros::dec;
//! use tracing::info;
//! use optionstratlib::model::types::{ OptionStyle, OptionType, Side};
//! use optionstratlib::strategies::probabilities::{ProbabilityAnalysis, VolatilityAdjustment, PriceTrend, StrategyProbabilityAnalysis};
//! use optionstratlib::ExpirationDate;use positive::Positive;
//! use positive::pos_or_panic;
//! use optionstratlib::strategies::bear_call_spread::BearCallSpread;
//!
//! let strategy = BearCallSpread::new(
//! "SP500".to_string(),
//! pos_or_panic!(5781.88), // underlying_price
//! pos_or_panic!(5750.0), // long_strike_itm
//! pos_or_panic!(5820.0), // short_strike
//! ExpirationDate::Days(Positive::TWO),
//! pos_or_panic!(0.18), // implied_volatility
//! dec!(0.05), // risk_free_rate
//! Positive::ZERO, // dividend_yield
//! Positive::TWO, // long quantity
//! pos_or_panic!(85.04), // premium_long
//! pos_or_panic!(29.85), // premium_short
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.73), // close_fee_long
//! pos_or_panic!(0.73), // close_fee_short
//! )?;
//! let analysis = strategy.analyze_probabilities(None, None)?;
//!
//! info!("Analysis: {:?}", analysis);
//! # Ok(())
//! # }
//! ```
//!
//! ### Analysis with Volatility Adjustment
//!
//! ```rust
//! # fn run() -> Result<(), optionstratlib::error::Error> {
//! use rust_decimal_macros::dec;
//! use optionstratlib::ExpirationDate;
//! use optionstratlib::strategies::probabilities::{ProbabilityAnalysis, VolatilityAdjustment};
//! use positive::Positive;
//! use positive::pos_or_panic;
//! use optionstratlib::strategies::bear_call_spread::BearCallSpread;
//!
//! let strategy = BearCallSpread::new(
//! "SP500".to_string(),
//! pos_or_panic!(5781.88), // underlying_price
//! pos_or_panic!(5750.0), // long_strike_itm
//! pos_or_panic!(5820.0), // short_strike
//! ExpirationDate::Days(Positive::TWO),
//! pos_or_panic!(0.18), // implied_volatility
//! dec!(0.05), // risk_free_rate
//! Positive::ZERO, // dividend_yield
//! Positive::TWO, // long quantity
//! pos_or_panic!(85.04), // premium_long
//! pos_or_panic!(29.85), // premium_short
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.73), // close_fee_long
//! pos_or_panic!(0.73), // close_fee_short
//! )?;
//!
//! let vol_adj = Some(VolatilityAdjustment {
//! base_volatility: pos_or_panic!(0.20), // 20% base volatility
//! std_dev_adjustment: pos_or_panic!(0.10), // 10% adjustment
//! });
//!
//! let _analysis = strategy.analyze_probabilities(vol_adj, None)?;
//! # Ok(())
//! # }
//! ```
//!
//! ### Analysis with Price Trend
//!
//! ```rust
//! # fn run() -> Result<(), optionstratlib::error::Error> {
//! use rust_decimal_macros::dec;
//! use optionstratlib::ExpirationDate;
//! use positive::Positive;
//! use positive::pos_or_panic;
//! use optionstratlib::strategies::bear_call_spread::BearCallSpread;
//! use optionstratlib::strategies::probabilities::{PriceTrend, ProbabilityAnalysis};
//! let strategy = BearCallSpread::new(
//! "SP500".to_string(),
//! pos_or_panic!(5781.88), // underlying_price
//! pos_or_panic!(5750.0), // long_strike_itm
//! pos_or_panic!(5820.0), // short_strike
//! ExpirationDate::Days(Positive::TWO),
//! pos_or_panic!(0.18), // implied_volatility
//! dec!(0.05), // risk_free_rate
//! Positive::ZERO, // dividend_yield
//! Positive::TWO, // long quantity
//! pos_or_panic!(85.04), // premium_long
//! pos_or_panic!(29.85), // premium_short
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.78), // open_fee_long
//! pos_or_panic!(0.73), // close_fee_long
//! pos_or_panic!(0.73), // close_fee_short
//! )?;
//! let trend = Some(PriceTrend {
//! drift_rate: 0.05, // 5% annual drift
//! confidence: 0.95, // 95% confidence level
//! });
//!
//! let _analysis = strategy.analyze_probabilities(None, trend)?;
//! # Ok(())
//! # }
//! ```
//!
//! ### Price Range Probability Analysis
//!
//! ```rust
//! # fn run() -> Result<(), optionstratlib::error::Error> {
//! use tracing::info;
//! use optionstratlib::strategies::probabilities::calculate_price_probability;
//! use optionstratlib::ExpirationDate;
//! use positive::Positive;
//! use positive::pos_or_panic;
//!
//! let (prob_below, prob_in_range, prob_above) = calculate_price_probability(
//! &Positive::HUNDRED, // current price
//! &pos_or_panic!(95.0), // lower bound
//! &pos_or_panic!(105.0), // upper bound
//! None, // volatility adjustment
//! None, // trend
//! &ExpirationDate::Days(pos_or_panic!(30.0)),
//! None // risk-free rate
//! )?;
//! info!("Probabilities: {}, {}, {}", prob_below, prob_in_range, prob_above);
//! # Ok(())
//! # }
//! ```
//!
//! ## Mathematical Models
//!
//! ### Expected Value Calculation
//!
//! The expected value is calculated using:
//! ```text
//! E[V] = Σ P(Si) * V(Si)
//! ```
//! where:
//! - Si: Price scenario i
//! - P(Si): Probability of scenario i
//! - V(Si): Value at scenario i
//!
//! ### Price Movement Probability
//!
//! Uses log-normal distribution with drift:
//! ```text
//! ln(ST/S0) ~ N(μT, σ²T)
//! ```
//! where:
//! - ST: Price at time T
//! - S0: Current price
//! - μ: Drift rate
//! - σ: Volatility
//! - T: Time to expiration
//!
//! ## Performance Considerations
//!
//! - Probability calculations: O(n) where n is the number of price points
//! - Expected value calculation: O(n) for n scenarios
//! - Memory usage: O(1) for single point calculations
//! - Cache results when analyzing multiple scenarios
//!
//! ## Implementation Notes
//!
//! - All probabilities are strictly positive (Positive)
//! - Volatility adjustments affect both mean and standard deviation
//! - Price trends are incorporated through drift adjustment
//! - Break-even points are calculated numerically
//! - Risk metrics use absolute values for consistency
//!
//! ## Error Handling
//!
//! The module returns Result types for all main functions, with errors for:
//! - Invalid time parameters (negative or zero time to expiry)
//! - Invalid volatility (zero or negative)
//! - Invalid probability bounds (outside [\0,1\])
//! - Invalid price ranges (upper < lower bound)
pub
pub
pub use StrategyProbabilityAnalysis;
pub use ProbabilityAnalysis;
pub use ;