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

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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. Check FAQs

C = P c \cdot P normal \cdot (D 1) - (K \cdot \exp (- R f \cdot t s)) \cdot P normal \cdot (D 2)

C - Theoretical Price of Call Option?P_c - Current Stock Price?P_normal - Normal Distribution?D₁ - Cumulative Distribution 1?K - Option Strike Price?R_f - Risk Free Rate?t_s - Time to Expiration of Stock?D₂ - Cumulative Distribution 2?

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

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Here is how the Black-Scholes-Merton Option Pricing Model for Call Option equation looks like with Values.

Here is how the Black-Scholes-Merton Option Pricing Model for Call Option equation looks like with Units.

Here is how the Black-Scholes-Merton Option Pricing Model for Call Option equation looks like.

7568.2558 = 440 \cdot 0.05 \cdot (350) - (90 \cdot \exp (- 0.3 \cdot 2.25)) \cdot 0.05 \cdot (57.5)

7568.2558 = 440 \cdot 0.05 \cdot (350) - (90 \cdot \exp (- 0.3 \cdot 2.25)) \cdot 0.05 \cdot (57.5)

7568.2558 = 440 \cdot 0.05 \cdot (350) - (90 \cdot \exp (- 0.3 \cdot 2.25)) \cdot 0.05 \cdot (57.5)

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

Follow our step by step solution on how to calculate Black-Scholes-Merton Option Pricing Model for Call Option?

FIRST Step Consider the formula

C = P c \cdot P normal \cdot (D 1) - (K \cdot \exp (- R f \cdot t s)) \cdot P normal \cdot (D 2)

Next Step Substitute values of Variables

∴

C = 440 \cdot 0.05 \cdot (350) - (90 \cdot \exp (- 0.3 \cdot 2.25)) \cdot 0.05 \cdot (57.5)

Next Step Prepare to Evaluate

∴

C = 440 \cdot 0.05 \cdot (350) - (90 \cdot \exp (- 0.3 \cdot 2.25)) \cdot 0.05 \cdot (57.5)

Next Step Evaluate

∴

C = 7568.2557761678

LAST Step Rounding Answer

∴

C = 7568.2558

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

Variables

Functions

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.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Theoretical Price of Call Option

Current Stock Price

Current Stock Price is the present purchase price of security.

Symbol: P_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Current Stock Price

Normal Distribution

The normal distribution is a type of continuous probability distribution for a real-valued random variable.

Symbol: P_normal

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Normal Distribution

Cumulative Distribution 1

Cumulative Distribution 1 here represents the standard normal distribution function of stock price.

Symbol: D₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cumulative Distribution 1

Option Strike Price

Option Strike Price indicates the predetermined price at which an option can be bought or sold when it's exercised.

Symbol: K

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Option Strike Price

Risk Free Rate

The Risk Free Rate is the theoretical rate of return of an investment with zero risks.

Symbol: R_f

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Risk Free Rate

Time to Expiration of Stock

Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value.

Symbol: t_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time to Expiration of Stock

Cumulative Distribution 2

Cumulative Distribution 2 refers to the standard normal distribution function of a stock price.

Symbol: D₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cumulative Distribution 2

exp

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

Syntax: exp(Number)

Other formulas in Forex Management category

Go Cumulative Distribution One

D 1 = \frac{\ln (\frac{P c}{K}) + (R f + \frac{{v us}^{2}}{2}) \cdot t s}{v us \cdot \sqrt{t s}}

Go Cumulative Distribution Two

D 2 = D 1 - v us \cdot \sqrt{t s}

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

Black-Scholes-Merton Option Pricing Model for Call Option evaluator 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 evaluate 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 evaluate Black-Scholes-Merton Option Pricing Model for Call Option using this online evaluator? To use this online evaluator 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.

FAQs on Black-Scholes-Merton Option Pricing Model for Call Option

What is the formula to find Black-Scholes-Merton Option Pricing Model for Call Option?

The formula of Black-Scholes-Merton Option Pricing Model for Call Option is expressed as 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). Here is an example- 7568.256 = 440*0.05*(350)-(90*exp(-0.3*2.25))*0.05*(57.5).

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

With 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) we can find Black-Scholes-Merton Option Pricing Model for Call Option using the formula - 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). This formula also uses Exponential Growth (exp) function(s).

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

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

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

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

Other formulas in Forex Management category

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

FAQs on Black-Scholes-Merton Option Pricing Model for Call Option

Variable Name