{
  "count": 30,
  "formulas": [
    {
      "id": "options.bsm.price",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Black-Scholes-Merton European option price",
      "summary": "Price of a European call or put on an asset paying a continuous dividend yield.",
      "inputs": [
        "S",
        "K",
        "r",
        "q",
        "sigma",
        "T",
        "type"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/models/#bsm-closed-form-with-yield"
        }
      ]
    },
    {
      "id": "options.bsm.greeks",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Black-Scholes-Merton Greeks",
      "summary": "Delta, gamma, vega, theta and rho in closed form, with dividend yield.",
      "inputs": [
        "S",
        "K",
        "r",
        "q",
        "sigma",
        "T",
        "type"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/greeks/#greeks-delta"
        }
      ]
    },
    {
      "id": "options.implied_vol",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Implied volatility from a European option price",
      "summary": "Inverts Black-Scholes-Merton for sigma by Newton on vega with a bisection safeguard.",
      "inputs": [
        "price",
        "S",
        "K",
        "r",
        "q",
        "T",
        "type"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/volatility/#iv-newton-on-vega"
        }
      ]
    },
    {
      "id": "options.put_call_parity",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Put-call parity",
      "summary": "European put price implied by a call price, or the reverse, with continuous yield.",
      "inputs": [
        "S",
        "K",
        "r",
        "q",
        "T",
        "call",
        "put"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/strategies/#put-call-parity"
        }
      ]
    },
    {
      "id": "options.vertical_spread",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Vertical spread payoff arithmetic",
      "summary": "Maximum profit, maximum loss and breakeven for the four two-leg verticals.",
      "inputs": [
        "type",
        "k_low",
        "k_high",
        "net_premium",
        "multiplier"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/strategies/#payoff-bull-call-spread"
        }
      ]
    },
    {
      "id": "options.kelly",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Kelly fraction for a binary bet",
      "summary": "Optimal fraction of bankroll to risk given win probability and payoff ratio.",
      "inputs": [
        "p",
        "b"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/probability/#kelly-sizing"
        },
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/portfolio/#fractional-kelly"
        }
      ]
    },
    {
      "id": "options.expected_move",
      "version": "1.0.0",
      "site": "options.wiki",
      "title": "Expected move from implied volatility",
      "summary": "One and two standard deviation moves over a horizon under a lognormal diffusion.",
      "inputs": [
        "S",
        "sigma",
        "T"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/probability/#expected-move-vs-breakeven"
        }
      ]
    },
    {
      "id": "bonds.price",
      "version": "1.0.0",
      "site": "fixed-income.wiki",
      "title": "Bond price from yield",
      "summary": "Present value of a level-coupon bond on a coupon date at a street-convention yield.",
      "inputs": [
        "coupon_rate",
        "face",
        "years",
        "frequency",
        "yield"
      ],
      "cite": [
        {
          "site": "fixed-income.wiki",
          "url": "https://fixed-income.wiki/price-yield/#pv-from-schedule"
        }
      ]
    },
    {
      "id": "bonds.ytm",
      "version": "1.0.0",
      "site": "fixed-income.wiki",
      "title": "Yield to maturity from price",
      "summary": "Solves the street-convention yield that discounts the coupon schedule to the observed price.",
      "inputs": [
        "price",
        "coupon_rate",
        "face",
        "years",
        "frequency"
      ],
      "cite": [
        {
          "site": "fixed-income.wiki",
          "url": "https://fixed-income.wiki/price-yield/#street-convention-ytm"
        }
      ]
    },
    {
      "id": "bonds.risk",
      "version": "1.0.0",
      "site": "fixed-income.wiki",
      "title": "Duration, convexity and DV01",
      "summary": "Macaulay and modified duration, convexity and money duration for a level-coupon bond.",
      "inputs": [
        "coupon_rate",
        "face",
        "years",
        "frequency",
        "yield"
      ],
      "cite": [
        {
          "site": "fixed-income.wiki",
          "url": "https://fixed-income.wiki/risk/#modified-duration"
        }
      ]
    },
    {
      "id": "hf.sharpe",
      "version": "1.0.0",
      "site": "hedgefund.wiki",
      "title": "Annualized Sharpe ratio from a return series",
      "summary": "Mean excess return over sample standard deviation, scaled by the square root of periods per year.",
      "inputs": [
        "returns",
        "rf_per_period",
        "periods_per_year"
      ],
      "cite": [
        {
          "site": "hedgefund.wiki",
          "url": "https://hedgefund.wiki/terms/sharpe-ratio/"
        },
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/performance/#sharpe-ratio"
        }
      ]
    },
    {
      "id": "hf.sortino",
      "version": "1.0.0",
      "site": "hedgefund.wiki",
      "title": "Annualized Sortino ratio from a return series",
      "summary": "Mean return above a minimum acceptable return over downside deviation.",
      "inputs": [
        "returns",
        "mar_per_period",
        "periods_per_year"
      ],
      "cite": [
        {
          "site": "hedgefund.wiki",
          "url": "https://hedgefund.wiki/terms/sortino-ratio/"
        },
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/performance/#sortino-ratio"
        }
      ]
    },
    {
      "id": "hf.max_drawdown",
      "version": "1.0.0",
      "site": "hedgefund.wiki",
      "title": "Maximum drawdown from a return series",
      "summary": "Largest peak-to-trough decline in cumulative wealth, with its location and recovery.",
      "inputs": [
        "returns"
      ],
      "cite": [
        {
          "site": "hedgefund.wiki",
          "url": "https://hedgefund.wiki/terms/drawdown/"
        },
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/drawdown/#maximum-drawdown"
        }
      ]
    },
    {
      "id": "hf.fee_net",
      "version": "1.0.0",
      "site": "hedgefund.wiki",
      "title": "Net return after management and incentive fees",
      "summary": "Single-period net-of-fee return under a management fee and an incentive fee above a hurdle.",
      "inputs": [
        "gross_return",
        "management_fee",
        "incentive_fee",
        "hurdle"
      ],
      "cite": [
        {
          "site": "hedgefund.wiki",
          "url": "https://hedgefund.wiki/terms/two-and-twenty/"
        },
        {
          "site": "pe-finance.wiki",
          "url": "https://pe-finance.wiki/economics/#preferred-return"
        }
      ]
    },
    {
      "id": "quant.annualize",
      "version": "1.0.0",
      "site": "quants.wiki",
      "title": "Annualization of periodic return and volatility",
      "summary": "Arithmetic and geometric annual return and annual volatility from periodic statistics.",
      "inputs": [
        "mean_per_period",
        "vol_per_period",
        "periods_per_year"
      ],
      "cite": [
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/performance/#annualisation-rules"
        }
      ]
    },
    {
      "id": "quant.var_parametric",
      "version": "1.0.0",
      "site": "quants.wiki",
      "title": "Parametric value at risk",
      "summary": "Normal-distribution VaR for a position over a horizon at a stated confidence.",
      "inputs": [
        "value",
        "sigma_per_period",
        "mu_per_period",
        "horizon_periods",
        "confidence"
      ],
      "cite": [
        {
          "site": "quants.wiki",
          "url": "https://quants.wiki/estimation/#close-to-close-volatility"
        },
        {
          "site": "hedgefund.wiki",
          "url": "https://hedgefund.wiki/terms/value-at-risk/"
        }
      ]
    },
    {
      "id": "pe.irr",
      "version": "1.0.0",
      "site": "pe-finance.wiki",
      "title": "Internal rate of return from periodic cash flows",
      "summary": "Solves the periodic rate that sets net present value to zero, and annualizes it.",
      "inputs": [
        "cash_flows",
        "periods_per_year"
      ],
      "cite": [
        {
          "site": "pe-finance.wiki",
          "url": "https://pe-finance.wiki/performance/#irr-vs-multiple"
        },
        {
          "site": "m-a.wiki",
          "url": "https://m-a.wiki/lbo/#irr-from-moic"
        }
      ]
    },
    {
      "id": "pe.multiples",
      "version": "1.0.0",
      "site": "pe-finance.wiki",
      "title": "DPI, RVPI, TVPI and MOIC",
      "summary": "Fund multiples from paid-in capital, distributions and residual value.",
      "inputs": [
        "paid_in",
        "distributions",
        "residual_nav"
      ],
      "cite": [
        {
          "site": "pe-finance.wiki",
          "url": "https://pe-finance.wiki/performance/#tvpi-dpi-rvpi"
        },
        {
          "site": "privatecredit.wiki",
          "url": "https://privatecredit.wiki/returns/#dpi-rvpi-tvpi"
        }
      ]
    },
    {
      "id": "vc.round",
      "version": "1.0.0",
      "site": "venture-capital.wiki",
      "title": "Priced round ownership with an option pool",
      "summary": "Post-money, investor and pool ownership, and price per share when the pool is created pre-money.",
      "inputs": [
        "pre_money",
        "new_money",
        "pool_pct_post",
        "existing_shares"
      ],
      "cite": [
        {
          "site": "venture-capital.wiki",
          "url": "https://venture-capital.wiki/dilution/#option-pool-shuffle"
        },
        {
          "site": "venture-capital.wiki",
          "url": "https://venture-capital.wiki/valuation/#post-money-identity"
        }
      ]
    },
    {
      "id": "ma.accretion_dilution",
      "version": "1.0.0",
      "site": "m-a.wiki",
      "title": "EPS accretion and dilution",
      "summary": "Pro forma EPS for an acquirer after issuing shares and financing cash consideration.",
      "inputs": [
        "acquirer_net_income",
        "acquirer_shares",
        "target_net_income",
        "new_shares_issued",
        "cash_paid",
        "financing_rate",
        "tax_rate",
        "synergies"
      ],
      "cite": [
        {
          "site": "m-a.wiki",
          "url": "https://m-a.wiki/accretion-dilution/#pro-forma-eps"
        },
        {
          "site": "m-a.wiki",
          "url": "https://m-a.wiki/accretion-dilution/#accretion-percent"
        }
      ]
    },
    {
      "id": "ma.lbo_returns",
      "version": "1.0.0",
      "site": "m-a.wiki",
      "title": "LBO equity MOIC and IRR",
      "summary": "Equity multiple and annualized return from entry and exit enterprise values and net debt.",
      "inputs": [
        "entry_ev",
        "entry_net_debt",
        "exit_ev",
        "exit_net_debt",
        "years"
      ],
      "cite": [
        {
          "site": "m-a.wiki",
          "url": "https://m-a.wiki/lbo/#moic"
        },
        {
          "site": "m-a.wiki",
          "url": "https://m-a.wiki/lbo/#irr-from-moic"
        }
      ]
    },
    {
      "id": "credit.all_in_yield",
      "version": "1.0.0",
      "site": "privatecredit.wiki",
      "title": "All-in yield on a floating-rate loan",
      "summary": "Cash coupon plus straight-line accretion of original issue discount and upfront fees.",
      "inputs": [
        "base_rate",
        "spread",
        "oid_pct",
        "upfront_fee_pct",
        "years"
      ],
      "cite": [
        {
          "site": "privatecredit.wiki",
          "url": "https://privatecredit.wiki/pricing-mechanics/#all-in-yield"
        }
      ]
    },
    {
      "id": "credit.coverage",
      "version": "1.0.0",
      "site": "privatecredit.wiki",
      "title": "Leverage, coverage and loan-to-value",
      "summary": "The three ratios every credit agreement tests.",
      "inputs": [
        "ebitda",
        "cash_interest",
        "total_debt",
        "enterprise_value"
      ],
      "cite": [
        {
          "site": "privatecredit.wiki",
          "url": "https://privatecredit.wiki/covenants/#total-leverage-covenant"
        },
        {
          "site": "privatecredit.wiki",
          "url": "https://privatecredit.wiki/covenants/#interest-coverage"
        }
      ]
    },
    {
      "id": "cal.is_trading_day",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Is the US equity market open on a date",
      "summary": "Whether NYSE and Nasdaq hold a regular session on a date, with the reason and the session close time.",
      "inputs": [
        "date"
      ],
      "cite": [
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.holidays",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "US equity market holidays and early closes for a year",
      "summary": "Every full-day closure and 13:00 ET early close in a calendar year, NYSE rule set.",
      "inputs": [
        "year"
      ],
      "cite": [
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.trading_days_between",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Trading days between two dates",
      "summary": "Count of regular sessions between two dates, with the calendar-day count alongside.",
      "inputs": [
        "start",
        "end",
        "inclusive"
      ],
      "cite": [
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.add_trading_days",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Add or subtract trading days",
      "summary": "The session that lies n trading days after (or before) a date.",
      "inputs": [
        "date",
        "n"
      ],
      "cite": [
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.settlement",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Settlement date for a US securities trade",
      "summary": "Settlement date from a trade date under the US cycle: T+1 for equities and corporate bonds from 2024-05-28, T+2 before that; listed options settle T+1 throughout.",
      "inputs": [
        "trade_date",
        "cycle"
      ],
      "cite": [
        {
          "site": "sec.gov",
          "url": "https://www.sec.gov/newsroom/press-releases/2023-29"
        },
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.next_expiration",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Next listed-option expiration",
      "summary": "The next monthly (third Friday), weekly (Friday) or quarterly (last session of the quarter) expiration on or after a date, with time to expiry in trading days and year fractions.",
      "inputs": [
        "date",
        "kind",
        "count"
      ],
      "cite": [
        {
          "site": "options.wiki",
          "url": "https://options.wiki/"
        },
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    },
    {
      "id": "cal.year_fraction",
      "version": "1.0.0",
      "site": "wallstreet.wiki",
      "title": "Year fraction between two dates under a day-count basis",
      "summary": "ACT/365, ACT/360, 30/360 US, or trading-day/252 year fraction, the T that pricing formulas take.",
      "inputs": [
        "start",
        "end",
        "basis"
      ],
      "cite": [
        {
          "site": "fixed-income.wiki",
          "url": "https://fixed-income.wiki/"
        },
        {
          "site": "nyse.com",
          "url": "https://www.nyse.com/markets/hours-calendars"
        },
        {
          "site": "wallstreet.wiki",
          "url": "https://wallstreet.wiki/"
        }
      ]
    }
  ]
}