🐋
Moby
  • Let’s Get Started
    • 🐋 About Moby
    • ⚡ Our Vision
    • 🤓 Your Guidebook
      • Get Setup
        • Connect Wallet
        • Trade Options
        • 0DTE Options
        • Provide Liquidity
      • Fees & Instruments
        • Fee Generation
        • Fee Distribution
        • Instruments
      • Testnet
  • How it’s Built
    • 🚀 Synchronized Liquidity Engine (SLE)
    • 🧮 Options Pricing Model
      • Mark Price
        • Futures Index
        • Implied Volatility
      • Risk Premium
        • Deriving Greeks
        • Risk Premium Calculation
        • Risk Managing Mechanism
    • 🤖 Architecture
      • Liquidity Provision Mechanism
      • Options Listing Standard
      • How to Open / Close / Settle Position
      • Synchronized Liquidity Engine (SLE)
      • Options Position Tokens
      • Tools to Maximize Capital Efficiency
    • ⚙️ Key Features
      • High Leverage & Limited Risk with No Liquidation
      • Narrow Spread with Dynamic Risk Premium
      • Guaranteed Settlement
      • Capital Efficiency Improvements with Combo Options
      • Even Higher Capital Efficiency with Clearing House
      • Abundant Liquidity for All Options
      • Composable Options for Structured Products
      • High Profitability for LPs
      • Real-Time Automatically Hedged OLP
      • Upcoming Features
    • ⛓ DeFi Options Vault
      • 🐻 Berachain DeFi Options Vault
        • 🔒 Architecture
        • 📈 Options Strategy
  • How it’s Driven
    • 🛡️ Building the Safest DeFi Protocol
      • Safety Features
      • Smart Contract Audit & Real-Time Security Monitoring
    • 🏛 Backed by Decentralized Governance
      • Governance
    • 🌐 Led by the Best Partners & Community
      • Arbitrum X Moby
      • Engagement Programs
  • Need More Info?
    • 📚 Resource Library
      • Developer Resources & Educational Contents
      • Terms & Conditions
      • Glossary
      • FAQ
  • Developers
    • Moby Traders API
      • REST API
        • General
        • Account
        • Market
    • Trade Scripts
      • Prerequisites
      • Open Positions
      • Close Positions
    • Interfaces & ABI
      • PositionManager.sol
      • SettleManager.sol
      • RewardRouterV2.sol
      • OptionsMarket.sol
    • Appendix 1: Parameters for Open/Close Options
    • Appendix 2: the Diff between optionId and optionTokenId
    • Appendix 3: Sample Moby Contract Module for Developers
Powered by GitBook
On this page
  • What is Mark Price?
  • Call Option Pricing Formula
  • Put Option Pricing Formula
  1. How it’s Built
  2. 🧮 Options Pricing Model

Mark Price

What is Mark Price?

Mark Price is used as the reference price of the position token and is added to Risk Premium to calculate Execution Price, which is the basis for trading options.

F : Futures price of the underlying asset adjusted for the expiration date

σ : Log-normal with constant volatility

r : Risk-free interest rate

K : Strike price

T : Time to expiry

Call Option Pricing Formula

c=e−rT[FN(d1)−KN(d2)]c = e^{-rT} [FN(d_1) - KN(d_2)] c=e−rT[FN(d1​)−KN(d2​)]

Put Option Pricing Formula

p=e−rT[KN(−d2)−FN(−d1)]p = e^{-rT} [KN(-d_2) - FN(-d_1)]p=e−rT[KN(−d2​)−FN(−d1​)]
Where,Where,Where,
d1=ln⁡(F/K)+(σ2/2)TσTd1 = \frac{\ln(F/K) + (\sigma^2/2)T}{\sigma\sqrt{T}} d1=σT​ln(F/K)+(σ2/2)T​
d2=ln⁡(F/K)−(σ2/2)TσT=d1−σTd2 = \frac{\ln(F/K) - (\sigma^2/2)T}{\sigma\sqrt{T}} = d1 - \sigma\sqrt{T} d2=σT​ln(F/K)−(σ2/2)T​=d1−σT​
N(x)=Cumulative Normal Distribution FunctionN(x) = \text{Cumulative Normal Distribution Function} N(x)=Cumulative Normal Distribution Function

This is why pricing must essentially use the futures price and implied volatility of the underlying asset. This data is currently sourced from the most reliable CEX in real-time, which is why Moby's options prices are the most real-time and accurate reflection of the market price, while other DeFi protocols' options prices are out of sync with the actual market price.

Previous🧮 Options Pricing ModelNextFutures Index

Last updated 1 year ago