CVEX Docs
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  • Website
  • Trading Terminal
  • Introduction
    • CVEX Overview
    • Component Breakdown and Definitions
    • Use Cases and Applications for Futures and Options
  • Background
    • The State of Cryptocurrency Trading and Problems Faced
    • Perpetual Contracts and Their Limitations
    • Options Trading in Crypto Markets
    • Conclusion
  • Protocol
    • Overview
    • Protocol Owner
    • Platforms
    • Price & Risk Oracles
    • Contracts
    • Order Types
    • Positions
    • Range Orders
    • Matching Engine
    • Collateral Token (USDC)
    • Frontends
    • Clearance Bots
    • CVEX Token
    • Fees & Rewards
  • Margin & Liquidations
    • Overview
    • Futures Mark Price
    • Black Scholes Model
    • Implied Volatility Surface
    • Premium Mark Price
    • Options Hedge Ratio
    • Value-at-Risk Model
    • Risk Parameters
    • Initial & Required Margin
    • Liquidation Protocol
    • Default Fund
    • Deleverage Queue
    • Default Prevention
  • Crypto Valley Exchange Platform
    • Overview
      • Case Studies
    • Contracts
    • Margin Model
    • Fees & Rewards
    • Go To Market Strategy
    • Affiliate Marketing
    • Market Makers
    • Brokers & Structured Product Providers
    • Front End & Builder Incentives
    • Price & Risk Oracles
  • Building on CVEX
    • Development Resource
  • Strategy
    • Security measures & Risk Prevention
    • Future Work
    • Legal & Compliance
    • Team and Advisors
    • Conclusion
  • Disclaimer
  • Credits
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  1. Margin & Liquidations

Premium Mark Price

The final step in the CVEX Protocol involves calculating the Premium Mark Price for each strike of call or put options, CCC and PPP respectively, that plays the same role as Mark Price for futures or perpetual contracts. For each strike, the protocol selects an implied volatility value from the interpolated volatility surface, based on strike price to futures price ratio. It then calculates the Premium Mark Price using the Futures Mark Price, strike price, chosen implied volatility, time to maturity, and risk-free interest rate, based on solving of Black Scholes equation:

C=e−rt[FΦ(d1)−KΦ(d2)]C = e^{-rt} [F\Phi(d_1) - K\Phi(d_2)] C=e−rt[FΦ(d1​)−KΦ(d2​)]
P=e−rt[KΦ(−d2)−FΦ(−d1)]P = e^{-rt} [K\Phi(-d_2) - F\Phi(-d_1)]P=e−rt[KΦ(−d2​)−FΦ(−d1​)]

Where d1d_1d1​and d2d_2d2​ parameters calculated as:

d1=1σT[ln⁡(FK)+(r+σ22)T]d_1 = \frac{1}{\sigma\sqrt{T}} \left[ \ln \left(\frac{F}{K}\right) + \left(r + \frac{\sigma^2}{2}\right) T \right]d1​=σT​1​[ln(KF​)+(r+2σ2​)T]
d2=d1−σTd_2 = d_1 - \sigma\sqrt{T}d2​=d1​−σT​

Here, KKK is strike price of the option, and Φ\PhiΦ represents the cumulative distribution function (CDF) of the standard normal distribution:

Φ(x)=12π∫−∞xe−t22dt\Phi(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-\frac{t^2}{2}} dt Φ(x)=2π​1​∫−∞x​e−2t2​dt

This methodology ensures that the Premium Mark Price remains sensitive to actual market fluctuations, capturing real-time market dynamics and trends via connection to the current Futures Mark Price. Simultaneously, it is safeguarded against price manipulations, as the reliance on an interpolated volatility surface provides a buffer against sporadic price anomalies.

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Last updated 1 year ago

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