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Mathematical Formulas Reference

This appendix provides a comprehensive reference of all mathematical formulas used throughout the use.com whitepaper. Formulas are organized by category for easy reference.


Trading & Order Book

Order Matching


Price-Time Priority: Priority=(Price_Level,Timestamp)Priority = (Price_Level, Timestamp)Priority=(Price_Level,Timestamp)


Orders at better prices execute first; at same price, earlier orders execute first.


Order Book Depth: Depth=∑i=1nVolumei at price level PiDepth = \sum_{i=1}^{n} Volume_i \text{ at price level } P_iDepth=∑i=1n​Volumei​ at price level Pi​


Mid Price: Mid_Price=Best_Bid+Best_Ask2Mid_Price = \frac{Best_Bid + Best_Ask}{2}Mid_Price=2Best_Bid+Best_Ask​


Spread: Spread=Best_Ask−Best_BidSpread = Best_Ask - Best_BidSpread=Best_Ask−Best_Bid


Spread Percentage: Spread_%=Best_Ask−Best_BidMid_Price×100%Spread_\% = \frac{Best_Ask - Best_Bid}{Mid_Price} \times 100\%Spread_%=Mid_PriceBest_Ask−Best_Bid​×100%


Order Execution


Market Order Fill Price (with slippage): Fill_Price=∑i=1nVolumei×Pricei∑VolumeiFill_Price = \sum_{i=1}^{n} \frac{Volume_i \times Price_i}{\sum Volume_i}Fill_Price=∑i=1n​∑Volumei​Volumei​×Pricei​​


Limit Order Execution:


Execute=1(Pricemarket≤Pricelimit, buy)Execute=1(Pricemarket≥Pricelimit, sell)Execute=0otherwise\begin{aligned} Execute &= 1 && (Price_{market} \le Price_{limit},\ \text{buy}) \ Execute &= 1 && (Price_{market} \ge Price_{limit},\ \text{sell}) \ Execute &= 0 && \text{otherwise} \end{aligned}ExecuteExecuteExecute​=1=1=0​​(Pricemarket​≤Pricelimit​, buy)(Pricemarket​≥Pricelimit​, sell)otherwise​


Time-Weighted Average Price (TWAP): TWAP=∑i=1nPriceinTWAP = \frac{\sum_{i=1}^{n} Price_i}{n}TWAP=n∑i=1n​Pricei​​


Volume-Weighted Average Price (VWAP): VWAP=∑i=1n(Pricei×Volumei)∑i=1nVolumeiVWAP = \frac{\sum_{i=1}^{n} (Price_i \times Volume_i)}{\sum_{i=1}^{n} Volume_i}VWAP=∑i=1n​Volumei​∑i=1n​(Pricei​×Volumei​)​


Risk Management

Margin & Leverage


Initial Margin: Initial_Margin=Position_ValueLeverageInitial_Margin = \frac{Position_Value}{Leverage}Initial_Margin=LeveragePosition_Value​


Maintenance Margin: Maintenance_Margin=Position_Value×Maintenance_RateMaintenance_Margin = Position_Value \times Maintenance_RateMaintenance_Margin=Position_Value×Maintenance_Rate


Available Margin: Available_Margin=Equity−Used_MarginAvailable_Margin = Equity - Used_MarginAvailable_Margin=Equity−Used_Margin


Margin Level: Margin_Level=EquityUsed_Margin×100%Margin_Level = \frac{Equity}{Used_Margin} \times 100\%Margin_Level=Used_MarginEquity​×100%


Maximum Position Size: Max_Position=Available_Balance×LeverageMax_Position = Available_Balance \times LeverageMax_Position=Available_Balance×Leverage


Liquidation


Liquidation Price (Long): Liquidation_Price=Entry_Price×Leverage−Maintenance_Rate×LeverageLeverageLiquidation_Price = Entry_Price \times \frac{Leverage - Maintenance_Rate \times Leverage}{Leverage}Liquidation_Price=Entry_Price×LeverageLeverage−Maintenance_Rate×Leverage​


Simplified: Liquidation_Pricelong=Entry_Price×(1−1Leverage+Maintenance_Rate)Liquidation_Price_{long} = Entry_Price \times (1 - \frac{1}{Leverage} + Maintenance_Rate)Liquidation_Pricelong​=Entry_Price×(1−Leverage1​+Maintenance_Rate)


Liquidation Price (Short): Liquidation_Priceshort=Entry_Price×(1+1Leverage−Maintenance_Rate)Liquidation_Price_{short} = Entry_Price \times (1 + \frac{1}{Leverage} - Maintenance_Rate)Liquidation_Priceshort​=Entry_Price×(1+Leverage1​−Maintenance_Rate)


Example (Long position):


  • Entry: $50,000
  • Leverage: 10×
  • Maintenance: 0.5%
  • Liquidation: $50,000 × (1 - 0.1 + 0.005) = $45,250


Distance to Liquidation: Distance=∣Current_Price−Liquidation_Price∣Current_Price×100%Distance = \frac{|Current_Price - Liquidation_Price|}{Current_Price} \times 100\%Distance=Current_Price∣Current_Price−Liquidation_Price∣​×100%


Profit & Loss


Unrealized PnL (Long): PnLlong=(Current_Price−Entry_Price)×Position_SizePnL_{long} = (Current_Price - Entry_Price) \times Position_SizePnLlong​=(Current_Price−Entry_Price)×Position_Size


Unrealized PnL (Short): PnLshort=(Entry_Price−Current_Price)×Position_SizePnL_{short} = (Entry_Price - Current_Price) \times Position_SizePnLshort​=(Entry_Price−Current_Price)×Position_Size


PnL Percentage: PnL_%=PnLInitial_Margin×100%PnL_\% = \frac{PnL}{Initial_Margin} \times 100\%PnL_%=Initial_MarginPnL​×100%


Return on Equity (ROE): ROE=PnLEquity×100%ROE = \frac{PnL}{Equity} \times 100\%ROE=EquityPnL​×100%


Risk Metrics


Value at Risk (VaR): VaR=Position_Value×Volatility×ZscoreVaR = Position_Value \times Volatility \times Z_{score}VaR=Position_Value×Volatility×Zscore​


Where Z-score for 95% confidence = 1.645


Portfolio Risk: Portfolio_Risk=∑i=1n∑j=1nwiwjσiσjρijPortfolio_Risk = \sqrt{\sum_{i=1}^{n} \sum_{j=1}^{n} w_i w_j \sigma_i \sigma_j \rho_{ij}}Portfolio_Risk=∑i=1n​∑j=1n​wi​wj​σi​σj​ρij​​


Sharpe Ratio: Sharpe=Return−Risk_Free_RateVolatilitySharpe = \frac{Return - Risk_Free_Rate}{Volatility}Sharpe=VolatilityReturn−Risk_Free_Rate​


Maximum Drawdown: Max_Drawdown=Trough_Value−Peak_ValuePeak_Value×100%Max_Drawdown = \frac{Trough_Value - Peak_Value}{Peak_Value} \times 100\%Max_Drawdown=Peak_ValueTrough_Value−Peak_Value​×100%


Fee Calculations

Trading Fees


Base Trading Fee: Fee=Trade_Volume×Fee_RateFee = Trade_Volume \times Fee_RateFee=Trade_Volume×Fee_Rate


Fee with Volume Discount: Fee=Trade_Volume×Base_Rate×(1−Volume_Discount)Fee = Trade_Volume \times Base_Rate \times (1 - Volume_Discount)Fee=Trade_Volume×Base_Rate×(1−Volume_Discount)


Fee with Token Discount: Fee=Trade_Volume×Base_Rate×(1−Volume_Discount)×(1−Token_Discount)Fee = Trade_Volume \times Base_Rate \times (1 - Volume_Discount) \times (1 - Token_Discount)Fee=Trade_Volume×Base_Rate×(1−Volume_Discount)×(1−Token_Discount)


Effective Fee Rate: Effective_Rate=Base_Rate×(1−Volume_Discount)×(1−Token_Discount)Effective_Rate = Base_Rate \times (1 - Volume_Discount) \times (1 - Token_Discount)Effective_Rate=Base_Rate×(1−Volume_Discount)×(1−Token_Discount)


Example:


  • Volume: $1M
  • Base rate: 0.10%
  • Volume discount: 20%
  • Token discount: 25%
  • Effective rate: 0.10% × 0.80 × 0.75 = 0.06%
  • Fee: $1M × 0.06% = $600


Maker-Taker Model


Maker Rebate: Rebate=Trade_Volume×Maker_Rebate_RateRebate = Trade_Volume \times Maker_Rebate_RateRebate=Trade_Volume×Maker_Rebate_Rate


Net Fee (Maker): Net_Fee=Trade_Volume×(Maker_Fee−Maker_Rebate)Net_Fee = Trade_Volume \times (Maker_Fee - Maker_Rebate)Net_Fee=Trade_Volume×(Maker_Fee−Maker_Rebate)


Net Fee (Taker): Net_Fee=Trade_Volume×Taker_FeeNet_Fee = Trade_Volume \times Taker_FeeNet_Fee=Trade_Volume×Taker_Fee


Fee Tiers


Volume Tier Calculation: Tier=f(30_Day_Volume)Tier = f(30_Day_Volume)Tier=f(30_Day_Volume)


Fee Savings: Savings=(Base_Fee−Discounted_Fee)×Annual_VolumeSavings = (Base_Fee - Discounted_Fee) \times Annual_VolumeSavings=(Base_Fee−Discounted_Fee)×Annual_Volume


Tokenomics

Token Supply


Circulating Supply: Circulating=Total_Supply−Locked_Tokens−Burned_TokensCirculating = Total_Supply - Locked_Tokens - Burned_TokensCirculating=Total_Supply−Locked_Tokens−Burned_Tokens


Inflation Rate: Inflation=New_TokensExisting_Supply×100%Inflation = \frac{New_Tokens}{Existing_Supply} \times 100\%Inflation=Existing_SupplyNew_Tokens​×100%


Deflation Rate (with burns): Deflation=Burned_TokensTotal_Supply×100%Deflation = \frac{Burned_Tokens}{Total_Supply} \times 100\%Deflation=Total_SupplyBurned_Tokens​×100%


Token Valuation


Market Capitalization: Market_Cap=Circulating_Supply×Token_PriceMarket_Cap = Circulating_Supply \times Token_PriceMarket_Cap=Circulating_Supply×Token_Price


Fully Diluted Valuation (FDV): FDV=Total_Supply×Token_PriceFDV = Total_Supply \times Token_PriceFDV=Total_Supply×Token_Price


Price-to-Sales Ratio: P/S=Market_CapAnnual_RevenueP/S = \frac{Market_Cap}{Annual_Revenue}P/S=Annual_RevenueMarket_Cap​


Token Velocity: Velocity=Transaction_VolumeAverage_Token_HoldingsVelocity = \frac{Transaction_Volume}{Average_Token_Holdings}Velocity=Average_Token_HoldingsTransaction_Volume​


Vesting


Linear Vesting: Unlocked=Total_Allocation×Time_ElapsedVesting_PeriodUnlocked = Total_Allocation \times \frac{Time_Elapsed}{Vesting_Period}Unlocked=Total_Allocation×Vesting_PeriodTime_Elapsed​


Cliff Vesting:


Unlocked={0t<TcliffAtotal t−TcliffTvestt≥TcliffUnlocked= \begin{cases} 0 & t < T_{cliff} \ A_{total}\,\dfrac{t-T_{cliff}}{T_{vest}} & t \ge T_{cliff} \end{cases}Unlocked=⎩⎨⎧​0Atotal​Tvest​t−Tcliff​​​t<Tcliff​t≥Tcliff​​


Vesting Schedule: Monthly_Unlock=Total_AllocationVesting_MonthsMonthly_Unlock = \frac{Total_Allocation}{Vesting_Months}Monthly_Unlock=Vesting_MonthsTotal_Allocation​


Buyback & Burn


Quarterly Burn Amount: Burn_Amount=Quarterly_Profit×Burn_PercentageBurn_Amount = Quarterly_Profit \times Burn_PercentageBurn_Amount=Quarterly_Profit×Burn_Percentage


Tokens Burned: Tokens_Burned=Burn_BudgetToken_PriceTokens_Burned = \frac{Burn_Budget}{Token_Price}Tokens_Burned=Token_PriceBurn_Budget​


Annual Burn Rate: Burn_Rate=∑Quarterly_BurnsTotal_Supply×100%Burn_Rate = \frac{\sum Quarterly_Burns}{Total_Supply} \times 100\%Burn_Rate=Total_Supply∑Quarterly_Burns​×100%


Supply After Burns: Supplyt=Supply0×(1−Burn_Rate)tSupply_t = Supply_0 \times (1 - Burn_Rate)^tSupplyt​=Supply0​×(1−Burn_Rate)t


Price Impact (theoretical): Price_New=Price_Old×Supply_OldSupply_NewPrice_New = Price_Old \times \frac{Supply_Old}{Supply_New}Price_New=Price_Old×Supply_NewSupply_Old​


Staking Rewards


Annual Percentage Yield (APY): APY=(1+rn)n−1APY = \left(1 + \frac{r}{n}\right)^n - 1APY=(1+nr​)n−1


Where r = nominal rate, n = compounding periods


Staking Rewards: Rewards=Staked_Amount×APY×Time_Staked365Rewards = Staked_Amount \times APY \times \frac{Time_Staked}{365}Rewards=Staked_Amount×APY×365Time_Staked​


Effective Staking Rate: Effective_Rate=Base_APY×(1+Loyalty_Bonus)×(1+Volume_Bonus)Effective_Rate = Base_APY \times (1 + Loyalty_Bonus) \times (1 + Volume_Bonus)Effective_Rate=Base_APY×(1+Loyalty_Bonus)×(1+Volume_Bonus)


Market Making

Spread Management


Optimal Spread: Spread∗=γσ2λSpread^* = \gamma \sigma \sqrt{\frac{2}{\lambda}}Spread∗=γσλ2​​


Where:


  • γ = risk aversion
  • σ = volatility
  • λ = order arrival rate


Bid-Ask Quotes: Bid=Mid_Price−Spread2Bid = Mid_Price - \frac{Spread}{2}Bid=Mid_Price−2Spread​ Ask=Mid_Price+Spread2Ask = Mid_Price + \frac{Spread}{2}Ask=Mid_Price+2Spread​


Inventory Management


Inventory Risk: Risk=Position×Volatility×TimeRisk = Position \times Volatility \times \sqrt{Time}Risk=Position×Volatility×Time​


Optimal Inventory: q∗=−δγσ2q^* = -\frac{\delta}{\gamma \sigma^2}q∗=−γσ2δ​


Where:


  • δ = drift
  • γ = risk aversion
  • σ = volatility


Inventory Skew: Skew=Current_Inventory−Target_InventoryMax_InventorySkew = \frac{Current_Inventory - Target_Inventory}{Max_Inventory}Skew=Max_InventoryCurrent_Inventory−Target_Inventory​


Pricing


Mid-Price Adjustment: Midadjusted=Midmarket+α×Inventory_SkewMid_{adjusted} = Mid_{market} + \alpha \times Inventory_SkewMidadjusted​=Midmarket​+α×Inventory_Skew


Quote Adjustment: Bidadjusted=Bid−β×InventorylongBid_{adjusted} = Bid - \beta \times Inventory_{long}Bidadjusted​=Bid−β×Inventorylong​ Askadjusted=Ask+β×InventoryshortAsk_{adjusted} = Ask + \beta \times Inventory_{short}Askadjusted​=Ask+β×Inventoryshort​


Performance Metrics

Latency


Average Latency: Latencyavg=∑i=1nLatencyinLatency_{avg} = \frac{\sum_{i=1}^{n} Latency_i}{n}Latencyavg​=n∑i=1n​Latencyi​​


Percentile Latency (e.g., P99): P99=99th percentile of latency distributionP99 = \text{99th percentile of latency distribution}P99=99th percentile of latency distribution


Throughput: Throughput=Total_TransactionsTime_PeriodThroughput = \frac{Total_Transactions}{Time_Period}Throughput=Time_PeriodTotal_Transactions​


Transactions Per Second (TPS): TPS=TransactionsSecondsTPS = \frac{Transactions}{Seconds}TPS=SecondsTransactions​


System Performance


Uptime Percentage: Uptime=Available_TimeTotal_Time×100%Uptime = \frac{Available_Time}{Total_Time} \times 100\%Uptime=Total_TimeAvailable_Time​×100%


Error Rate: Error_Rate=Failed_RequestsTotal_Requests×100%Error_Rate = \frac{Failed_Requests}{Total_Requests} \times 100\%Error_Rate=Total_RequestsFailed_Requests​×100%


Success Rate: Success_Rate=100%−Error_RateSuccess_Rate = 100\% - Error_RateSuccess_Rate=100%−Error_Rate


Financial Metrics

Revenue Metrics


Average Revenue Per User (ARPU): ARPU=Total_RevenueActive_UsersARPU = \frac{Total_Revenue}{Active_Users}ARPU=Active_UsersTotal_Revenue​


Customer Lifetime Value (LTV): LTV=ARPU×Average_Lifetime×Gross_MarginLTV = ARPU \times Average_Lifetime \times Gross_MarginLTV=ARPU×Average_Lifetime×Gross_Margin


Customer Acquisition Cost (CAC): CAC=Marketing_SpendNew_CustomersCAC = \frac{Marketing_Spend}{New_Customers}CAC=New_CustomersMarketing_Spend​


LTV/CAC Ratio: LTV/CAC=LTVCACLTV/CAC = \frac{LTV}{CAC}LTV/CAC=CACLTV​


Target: >3:1


Payback Period: Payback=CACMonthly_ARPUPayback = \frac{CAC}{Monthly_ARPU}Payback=Monthly_ARPUCAC​


Profitability Metrics


Gross Margin: Gross_Margin=Revenue−COGSRevenue×100%Gross_Margin = \frac{Revenue - COGS}{Revenue} \times 100\%Gross_Margin=RevenueRevenue−COGS​×100%


EBITDA: EBITDA=Revenue−Operating_ExpensesEBITDA = Revenue - Operating_ExpensesEBITDA=Revenue−Operating_Expenses


EBITDA Margin: EBITDA_Margin=EBITDARevenue×100%EBITDA_Margin = \frac{EBITDA}{Revenue} \times 100\%EBITDA_Margin=RevenueEBITDA​×100%


Net Profit Margin: Net_Margin=Net_IncomeRevenue×100%Net_Margin = \frac{Net_Income}{Revenue} \times 100\%Net_Margin=RevenueNet_Income​×100%


Return on Equity (ROE): ROE=Net_IncomeShareholders_Equity×100%ROE = \frac{Net_Income}{Shareholders_Equity} \times 100\%ROE=Shareholders_EquityNet_Income​×100%


Return on Assets (ROA): ROA=Net_IncomeTotal_Assets×100%ROA = \frac{Net_Income}{Total_Assets} \times 100\%ROA=Total_AssetsNet_Income​×100%


Growth Metrics


Year-over-Year Growth: YoY_Growth=Valuecurrent−ValuepreviousValueprevious×100%YoY_Growth = \frac{Value_{current} - Value_{previous}}{Value_{previous}} \times 100\%YoY_Growth=Valueprevious​Valuecurrent​−Valueprevious​​×100%


Compound Annual Growth Rate (CAGR): CAGR=(Ending_ValueBeginning_Value)1Years−1CAGR = \left(\frac{Ending_Value}{Beginning_Value}\right)^{\frac{1}{Years}} - 1CAGR=(Beginning_ValueEnding_Value​)Years1​−1


Month-over-Month Growth: MoM_Growth=Valuecurrent−ValuepreviousValueprevious×100%MoM_Growth = \frac{Value_{current} - Value_{previous}}{Value_{previous}} \times 100\%MoM_Growth=Valueprevious​Valuecurrent​−Valueprevious​​×100%


Derivatives

Perpetual Futures


Funding Rate: Funding_Rate=Mark_Price−Index_PriceIndex_PriceFunding_Rate = \frac{Mark_Price - Index_Price}{Index_Price}Funding_Rate=Index_PriceMark_Price−Index_Price​


Funding Payment: Payment=Position_Size×Funding_RatePayment = Position_Size \times Funding_RatePayment=Position_Size×Funding_Rate


Mark Price: Mark_Price=Index_Price×(1+Funding_Basis)Mark_Price = Index_Price \times (1 + Funding_Basis)Mark_Price=Index_Price×(1+Funding_Basis)


Liquidation Price (Perpetual Long): Liq_Price=Entry_Price×Leverage−Maintenance_Margin×Leverage−FundingLeverageLiq_Price = Entry_Price \times \frac{Leverage - Maintenance_Margin \times Leverage - Funding}{Leverage}Liq_Price=Entry_Price×LeverageLeverage−Maintenance_Margin×Leverage−Funding​


Options


Black-Scholes Call Option: C=S0N(d1)−Ke−rTN(d2)C = S_0 N(d_1) - K e^{-rT} N(d_2)C=S0​N(d1​)−Ke−rTN(d2​)


Where: d1=ln⁡(S0/K)+(r+σ2/2)TσTd_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}d1​=σT​ln(S0​/K)+(r+σ2/2)T​ d2=d1−σTd_2 = d_1 - \sigma\sqrt{T}d2​=d1​−σT​


Black-Scholes Put Option: P=Ke−rTN(−d2)−S0N(−d1)P = K e^{-rT} N(-d_2) - S_0 N(-d_1)P=Ke−rTN(−d2​)−S0​N(−d1​)


Option Greeks:


Delta: Δ=∂V∂S\Delta = \frac{\partial V}{\partial S}Δ=∂S∂V​


Gamma: Γ=∂2V∂S2\Gamma = \frac{\partial^2 V}{\partial S^2}Γ=∂S2∂2V​


Theta: Θ=∂V∂t\Theta = \frac{\partial V}{\partial t}Θ=∂t∂V​


Vega: V=∂V∂σ\mathcal{V} = \frac{\partial V}{\partial \sigma}V=∂σ∂V​


Rho: ρ=∂V∂r\rho = \frac{\partial V}{\partial r}ρ=∂r∂V​


Implied Volatility


Implied Volatility (from option price): σimplied=f−1(Option_Price,S,K,r,T)\sigma_{implied} = f^{-1}(Option_Price, S, K, r, T)σimplied​=f−1(Option_Price,S,K,r,T)


Solved numerically using Newton-Raphson method.


Statistical Formulas

Volatility


Historical Volatility: σ=∑i=1n(Ri−Rˉ)2n−1\sigma = \sqrt{\frac{\sum_{i=1}^{n}(R_i - \bar{R})^2}{n-1}}σ=n−1∑i=1n​(Ri​−Rˉ)2​​


Annualized Volatility: σannual=σdaily×252\sigma_{annual} = \sigma_{daily} \times \sqrt{252}σannual​=σdaily​×252​


Exponentially Weighted Moving Average (EWMA): σt2=λσt−12+(1−λ)rt−12\sigma_t^2 = \lambda \sigma_{t-1}^2 + (1-\lambda) r_{t-1}^2σt2​=λσt−12​+(1−λ)rt−12​


Correlation


Correlation Coefficient: ρxy=∑(xi−xˉ)(yi−yˉ)∑(xi−xˉ)2∑(yi−yˉ)2\rho_{xy} = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i - \bar{x})^2 \sum(y_i - \bar{y})^2}}ρxy​=∑(xi​−xˉ)2∑(yi​−yˉ​)2​∑(xi​−xˉ)(yi​−yˉ​)​


Covariance: Cov(X,Y)=∑(xi−xˉ)(yi−yˉ)n−1Cov(X,Y) = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}Cov(X,Y)=n−1∑(xi​−xˉ)(yi​−yˉ​)​


Moving Averages


Simple Moving Average (SMA): SMAn=∑i=1nPriceinSMA_n = \frac{\sum_{i=1}^{n} Price_i}{n}SMAn​=n∑i=1n​Pricei​​


Exponential Moving Average (EMA): EMAt=Pricet×k+EMAt−1×(1−k)EMA_t = Price_t \times k + EMA_{t-1} \times (1-k)EMAt​=Pricet​×k+EMAt−1​×(1−k)


Where $k = \frac{2}{n+1}$


Liquidity Metrics

Order Book Liquidity


Bid-Ask Spread: Spread=Ask−BidMid_Price×100%Spread = \frac{Ask - Bid}{Mid_Price} \times 100\%Spread=Mid_PriceAsk−Bid​×100%


Market Depth: Depth±x%=∑Volume within ±x% of mid priceDepth_{\pm x\%} = \sum Volume \text{ within } \pm x\% \text{ of mid price}Depth±x%​=∑Volume within ±x% of mid price


Liquidity Score: Liquidity=VolumeSpread×VolatilityLiquidity = \frac{Volume}{Spread \times Volatility}Liquidity=Spread×VolatilityVolume​


Slippage


Expected Slippage: Slippage=Execution_Price−Expected_PriceExpected_Price×100%Slippage = \frac{Execution_Price - Expected_Price}{Expected_Price} \times 100\%Slippage=Expected_PriceExecution_Price−Expected_Price​×100%


Slippage Cost: Cost=Order_Size×Slippage_%Cost = Order_Size \times Slippage_\%Cost=Order_Size×Slippage_%


Conversion Formulas

Interest Rate Conversions


Daily to Annual: Annual_Rate=(1+Daily_Rate)365−1Annual_Rate = (1 + Daily_Rate)^{365} - 1Annual_Rate=(1+Daily_Rate)365−1


Annual to Daily: Daily_Rate=(1+Annual_Rate)1/365−1Daily_Rate = (1 + Annual_Rate)^{1/365} - 1Daily_Rate=(1+Annual_Rate)1/365−1


APR to APY: APY=(1+APRn)n−1APY = \left(1 + \frac{APR}{n}\right)^n - 1APY=(1+nAPR​)n−1


Where n = compounding periods per year


Price Conversions


Basis Points to Percentage: Percentage=Basis_Points10,000Percentage = \frac{Basis_Points}{10,000}Percentage=10,000Basis_Points​


Percentage to Basis Points: Basis_Points=Percentage×10,000Basis_Points = Percentage \times 10,000Basis_Points=Percentage×10,000


Conclusion


This comprehensive formula reference provides the mathematical foundation for all calculations used throughout the use.com platform. These formulas ensure consistent, accurate, and transparent operations across trading, risk management, tokenomics, and financial reporting.



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Updated on: 10/03/2026

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