Black-Scholes-Merton Option Pricing Model for Call Option Calculator

✖Current Stock Price is the present purchase price of security.ⓘ Current Stock Price [P_c]			+10% -10%
✖The normal distribution is a type of continuous probability distribution for a real-valued random variable.ⓘ Normal Distribution [P_normal]			+10% -10%
✖Cumulative Distribution 1 here represents the standard normal distribution function of stock price.ⓘ Cumulative Distribution 1 [D₁]			+10% -10%
✖Option Strike Price indicates the predetermined price at which an option can be bought or sold when it's exercised.ⓘ Option Strike Price [K]			+10% -10%
✖The Risk Free Rate is the theoretical rate of return of an investment with zero risks.ⓘ Risk Free Rate [R_f]			+10% -10%
✖Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value.ⓘ Time to Expiration of Stock [t_s]			+10% -10%
✖Cumulative Distribution 2 refers to the standard normal distribution function of a stock price.ⓘ Cumulative Distribution 2 [D₂]			+10% -10%

✖Theoretical Price of Call Option is based on the current implied volatility, the strike price of the option, and how much time is left until expiration.ⓘ Black-Scholes-Merton Option Pricing Model for Call Option [C]

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Black-Scholes-Merton Option Pricing Model for Call Option

Formula

`"C" = "P"_{"c"}*"P"_{"normal"}*("D"_{"1"})-("K"*exp(-"R"_{"f"}*"t"_{"s"}))*"P"_{"normal"}*("D"_{"2"})`

Example

`"7568.256"="440"*"0.05"*("350")-("90"*exp(-"0.30"*"2.25"))*"0.05"*("57.5")`

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Black-Scholes-Merton Option Pricing Model for Call Option Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2)
C = P_c*P_normal*(D₁)-(K*exp(-R_f*t_s))*P_normal*(D₂)
This formula uses 1 Functions, 8 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Theoretical Price of Call Option - Theoretical Price of Call Option is based on the current implied volatility, the strike price of the option, and how much time is left until expiration.
Current Stock Price - Current Stock Price is the present purchase price of security.
Normal Distribution - The normal distribution is a type of continuous probability distribution for a real-valued random variable.
Cumulative Distribution 1 - Cumulative Distribution 1 here represents the standard normal distribution function of stock price.
Option Strike Price - Option Strike Price indicates the predetermined price at which an option can be bought or sold when it's exercised.
Risk Free Rate - The Risk Free Rate is the theoretical rate of return of an investment with zero risks.
Time to Expiration of Stock - Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value.
Cumulative Distribution 2 - Cumulative Distribution 2 refers to the standard normal distribution function of a stock price.

STEP 1: Convert Input(s) to Base Unit

Current Stock Price: 440 --> No Conversion Required
Normal Distribution: 0.05 --> No Conversion Required
Cumulative Distribution 1: 350 --> No Conversion Required
Option Strike Price: 90 --> No Conversion Required
Risk Free Rate: 0.3 --> No Conversion Required
Time to Expiration of Stock: 2.25 --> No Conversion Required
Cumulative Distribution 2: 57.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = P_c*P_normal*(D₁)-(K*exp(-R_f*t_s))*P_normal*(D₂) --> 440*0.05*(350)-(90*exp(-0.3*2.25))*0.05*(57.5)

Evaluating ... ...

C = 7568.2557761678

STEP 3: Convert Result to Output's Unit

7568.2557761678 --> No Conversion Required

FINAL ANSWER

7568.2557761678 ≈ 7568.256 <-- Theoretical Price of Call Option

(Calculation completed in 00.004 seconds)

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Black-Scholes-Merton Option Pricing Model for Call Option

Go Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2)

Cumulative Distribution One

Go Cumulative Distribution 1 = (ln(Current Stock Price/Option Strike Price)+(Risk Free Rate+Volatile Underlying Stock^2/2)*Time to Expiration of Stock)/(Volatile Underlying Stock*sqrt(Time to Expiration of Stock))

Fama-French Three-Factor Model

Go Excess Return on Asset = Asset Specific Alpha+Beta in Forex*(Return on Market Portfolio-Risk Free Rate)+(Sensitivity of the Asset to SMB*Small Minus Big+Sensitivity of the Asset to HML+Error Term)

Vasicek Interest Rate

Go Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk

Black-Scholes-Merton Option Pricing Model for Put Option

Go Theoretical Price of Put Option = Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock)*(-Cumulative Distribution 2)-Current Stock Price*(-Cumulative Distribution 1)

Forward Rate

Go Forward Rate = Spot Exchange Rate*ln((Domestic Interest Rate-Foreign Interest Rate)*Time to Maturity)

Cumulative Distribution Two

Go Cumulative Distribution 2 = Cumulative Distribution 1-Volatile Underlying Stock*sqrt(Time to Expiration of Stock)

Position Size in Forex

Go Position Size in Forex = (Account Equity*Risk Percentage in Forex)/(Stop Loss in Pips*Pip Value in Forex)

Profit for Call Buyer

Go Profit for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)-Call Premium

Interest Rate Parity

Go Forward Rate Constant = Spot Exchange Rate*((1+Interest Rate of Quote Currency)/(1+Interest Rate of Base Currency))

Gordon Growth Model

Go Current Stock Price = (Dividend Per Share)/(Required Rate of Return-Constant Growth Rate of Dividend)

Payoff for Call Buyer

Go Payoff for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)

Purchasing Power Parity Theory using Inflation

Go Exchange Rate Factor = ((1+Inflation in Home Country)/(1+Inflation in Foreign Country))-1

Intrinsic Value

Go Intrinsic Value = Share Price-Base Value

Black-Scholes-Merton Option Pricing Model for Call Option Formula

Black-Scholes-Merton Option Pricing Model for Call Option

The model is widely used in finance and has played a significant role in the development of the options market. The formula for the Black-Scholes-Merton model is used to calculate the theoretical price of both call and put options.
The Black-Scholes-Merton model makes several assumptions, including constant volatility, no dividends paid during the option's life, and that the option can only be exercised at expiration (European option). It provides a theoretical framework for pricing options, and the calculated option prices are often used as a benchmark for comparing with market prices. Keep in mind that the model has limitations and may not perfectly reflect real-world market conditions.

How to Calculate Black-Scholes-Merton Option Pricing Model for Call Option?

Black-Scholes-Merton Option Pricing Model for Call Option calculator uses Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2) to calculate the Theoretical Price of Call Option, The Black-Scholes-Merton Option Pricing Model for Call Option formula is defined as a mathematical model used to calculate the theoretical price of European-style options. It was developed by economists Fischer Black and Myron Scholes, with contributions from Robert Merton. Theoretical Price of Call Option is denoted by C symbol.

How to calculate Black-Scholes-Merton Option Pricing Model for Call Option using this online calculator? To use this online calculator for Black-Scholes-Merton Option Pricing Model for Call Option, enter Current Stock Price (P_c), Normal Distribution (P_normal), Cumulative Distribution 1 (D₁), Option Strike Price (K), Risk Free Rate (R_f), Time to Expiration of Stock (t_s) & Cumulative Distribution 2 (D₂) and hit the calculate button. Here is how the Black-Scholes-Merton Option Pricing Model for Call Option calculation can be explained with given input values -> 7568.256 = 440*0.05*(350)-(90*exp(-0.3*2.25))*0.05*(57.5).

FAQ

What is Black-Scholes-Merton Option Pricing Model for Call Option?

The Black-Scholes-Merton Option Pricing Model for Call Option formula is defined as a mathematical model used to calculate the theoretical price of European-style options. It was developed by economists Fischer Black and Myron Scholes, with contributions from Robert Merton and is represented as C = P_c*P_normal*(D₁)-(K*exp(-R_f*t_s))*P_normal*(D₂) or Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2). Current Stock Price is the present purchase price of security, The normal distribution is a type of continuous probability distribution for a real-valued random variable, Cumulative Distribution 1 here represents the standard normal distribution function of stock price, Option Strike Price indicates the predetermined price at which an option can be bought or sold when it's exercised, The Risk Free Rate is the theoretical rate of return of an investment with zero risks, Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value & Cumulative Distribution 2 refers to the standard normal distribution function of a stock price.

How to calculate Black-Scholes-Merton Option Pricing Model for Call Option?

The Black-Scholes-Merton Option Pricing Model for Call Option formula is defined as a mathematical model used to calculate the theoretical price of European-style options. It was developed by economists Fischer Black and Myron Scholes, with contributions from Robert Merton is calculated using Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2). To calculate Black-Scholes-Merton Option Pricing Model for Call Option, you need Current Stock Price (P_c), Normal Distribution (P_normal), Cumulative Distribution 1 (D₁), Option Strike Price (K), Risk Free Rate (R_f), Time to Expiration of Stock (t_s) & Cumulative Distribution 2 (D₂). With our tool, you need to enter the respective value for Current Stock Price, Normal Distribution, Cumulative Distribution 1, Option Strike Price, Risk Free Rate, Time to Expiration of Stock & Cumulative Distribution 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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