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    P&L Calculations (Options)
    bybit2024-10-25 10:38:25

    For traders, it’s important to know how to calculate profit and loss before placing an order. Here’s a guide to help you better understand the relationship between different variables and profit & loss calculations.



     





    Average Entry Price

    When traders place new orders for the existing Options contract, the entry price will change accordingly. 

     

    Formula

    Position Average Price = [(Last Position Quantity × Last Position Average Price) + (Traded Quantity × Traded Price)/(Last Position Quantity + Traded Quantity)]

     

    Example

    Ann holds a 0.1 BTC BTC-31DEC21-48000-C, with an entry price of $3,500. She believes that the price of BTC will continue to rise in the near future. Ann decides to increase her call options, and opens a new call option of 0.1 BTC at the entry price of $4,000.

     

    Average Entry Price = [(0.1 × 3,500) + (0.1 × 4,000)/(0.1 + 0.1)] = $3,750






     

     

     

    Unrealized P&L 

    Unrealized P&L (UPL) is the current profit or loss of open positions. Based on the direction of your position — long or short — the formula used to calculate the unrealized profit and loss will be different.

     

    Buy Option

    Sell Option

    Description

    For traders who believe that the underlying asset’s price will rise in the future, they can choose to buy call or sell put options.

    For traders who think that the underlying asset’s price will drop in the future, they can choose to buy put or sell call options.

    Formula

    UPL = (Mark Price − Average Entry Price) × Position Quantity

    UPL = (Average Entry Price − Mark Price) × Position Quantity

    Example

    Ann buys a 0.1 BTC BTC-31DEC21-48000-C, with an entry price of $3,500. The price of BTC rises, and when the Mark price reaches $4,500, the unrealized P&L of the option she holds is [(4,500 − 3,500) × 0.1] = 100 USDC.

    Bob sells a 0.3 BTC BTC-31DEC21-50000-C with an average entry price of $2,600. The price of BTC rises, and when the mark price reaches $2,800, the unrealized P&L of the option he holds is [(2,600 − 2,800) × 0.3] = −60 USDC.

     

    Note: All Options contracts are settled in USDC.






     

     

     

    ROI

    ROI shows the percentage return on investment for each position.

     

    Buy Option

    Sell Option

    Formula 

    (Cross Margin Mode)

    (Mark Price - Average Entry Price)/ Average Entry Price

    (Average Entry Price - Mark Price)/ Average Entry Price

    Examples 

    under Cross Margin Mode 

    Sally buys a 0.1 BTC BTC-23NOV23-36000-C, with an entry price of $4,700. 


    The price of BTC rises, and when the Mark price reaches $4,900, the unrealized P&L of the option she holds is [(4,900 − 4,700) × 0.1] = 20 USDC.


    ROI = 20 / 4700 = 0.43%

    Bob sells a 0.1 BTC BTC-23NOV23-36000-P, with an entry price of $4,700. 


    The price of BTC rises, and when the Mark price reaches $4,900, the unrealized P&L of the option she holds is [(4,700 - 4,900) × 0.1] = -20 USDC.


    ROI = -20 / 4700 = -0.43%

    Formula 

    (Portfolio Margin Mode)

    The calculation of options' ROI within the portfolio margin takes into account the underlying asset as a whole.


    ROI = Unrealized P&L of Derivatives on Underlying Assets/Initial Margin of Underlying Assets

    Delivery ROI

    (Delivery Cash Flow  - Average Entry Price * Quantity - Fee to Open - Delivery Fee) / (Average Entry Price * Quantity)

    (Delivery Cash Flow + Average Entry Price * Quantity - Fee to Open - Delivery Fee) / (Average Entry Price * Quantity)






     

     

     

    Closed P&L

    Closed P&L is the profit and loss that occurs when the trader closes the position.

     

    Formula

    Closed P&L for Buy Call/ Put = (Traded Price − Position Average Price) × Traded Quantity − Trading Fees (open and closed position)

     

    Closed P&L for Sell Call/ Put = (Position Average Price − Traded Price) × Traded Quantity − Trading Fees (open and closed position)



    Example 

    Sell Call: The BTC index price is $44,900. Bob sells a 0.3 BTC BTC-31DEC21-50000-C, with an average entry price of $2,600. When the price of BTC drops to $44,000, he closes the position early at a mark price of $2,400. 

     

    The Closed P&L of the option is 52 USDC, based on the following calculation: 

     [(2,600 − 2,400) × 0.3] − 44,900 × 0.3 × 0.03% − 44,000 × 0.3 × 0.03%.






     

     

     

    Delivery P&L

    This is generated when the Option expires.

     

    Formula

    Delivered RPL for Call Option = Maximum (Delivery Price − Strike Price, 0) × Position Quantity + Premium (receive or pay) − Delivery Fee − Trading Fee (open position)

     

    Delivered RPL for Put Option = Maximum (Strike Price − Delivery Price, 0) × Position Quantity + Premium (receive or pay) − Delivery Fee − Trading Fee (open position)

     

    Example 

     

    Buy Call:

    The BTC index price is $44,900. Ann buys a 0.1 BTC BTC-31DEC21-48000-C, with an entry price of $3,500. When the contract expires, the BTC delivery price is $52,000. It’s traded at a strike price of $48,000. The delivery P&L of the option is 47.873 USDC, based on the following calculation:

    Maximum (52,000 − 48,000, 0) × 0.1 − 3,500 × 0.1 − 44,900 × 0.1 × 0.03% − 52,000 × 0.1 × 0.015% 

     

    Let’s revisit Ann’s case, in which the BTC index price is $44,900. Ann holds a 0.1 BTC BTC-31DEC21-48000-C, with an entry price of $3,500. The delivery P&L of the option is 400 USDC.

    • Trading Fee = Minimum (0.03% × 44,900, 12.5% × 3,500) × 0.1 = 1.347 USDC

     

    Note: Trading fee for a single contract can never be higher than 12.5% of the option price.

     

    Let’s suppose that the estimated delivery price is $49,000 when the contract is about to expire.

    • Delivery Fee = Minimum [(0.015% × 49,000, 12.5% × (49,000 − 48,000)] × 0.1= 0.735 USDC

     

    As an option buyer, Ann needs to pay a premium to the seller to obtain the right to the call option.

     

    Formula:

    Premium = Traded Quantity × Traded Price

    • 0.1 × 3,500 = 350 USDC

    Delivery P&L = 400 − 1.347 − 0.735 − 350 = 47.918 USDC



    Closed P&L and Delivery P&L are different from Unrealized P&L and Realized P&L. It’s worth noting that Delivery P&L also takes premium into account. Please refer to the following table for details:

     

     

    Unrealized P&L 

    Closed P&L

    Realized P&L

    Delivery P&L

    Position P&L

    YES

    YES

    YES

    Trading Fees

    NO

    YES

    YES

    Delivery Fee

    NO

    NO

    YES

    Premium

    NO

    NO

    YES






     

     

     

    Realized P&L 

    Realized P&L is the profit and loss that occurs when the trader closes the position early. Please note that the Realized P&L in the position zone represents the total profit and loss of the position since the position has been held.

     

     

    Formula

    Realized P&L = Sum (Profit and loss on closed positions) − Trading Fees (open and closed positions)



    Example 

    Let's see how the Realized P&L displayed in the position zone changes in different scenarios.



    Scenario 1: Bob buys 0.4 BTC BTC-31DEC21-50000-C when the Option mark price is $2,400 and the BTC index price is $44,000.

     

    Trading Fee (open position) = 44,000 × 0.4 × 0.03% = 5.28 USDC

     

    In this case, the Realized P&L of Bob's position is −5.28 USDC.



    Scenario 2: The BTC index price rises to $44,900. Bob sells a 0.3 BTC BTC-31DEC21-50000-C, with an average entry price of $2,400. He closes the position at a mark price of $2,600. 

     

    Realized P&L (before)  = - 5.28 USDC

    Trading Fee (closed position) = 44,900 × 0.3 × 0.03% = 4.041 USDC

    Realized P&L = [(2,600 − 2,400) × 0.3] − 44,900 × 0.3 × 0.03% - 5.28 = 50.68 USDC



    Scenario 3: Now Bob only holds 0.1 BTC BTC-31DEC21-50000-C. Then, when the BTC index price is $45,000, he buys 0.2 BTC BTC-31DEC21-50000-C at $2,500.

     

    Realized P&L (before) = 50.68 USDC

    Trading Fee (open position) = 45,000 × 0.2 × 0.03% = 2.7 USDC

    Realized P&L (before) = 50.68 − 2.7 = 47.98 USDC

     

     

    For more detailed information about option fees, please refer to Bybit Option Fees Explained.

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