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

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Theoretical Price of Put Option is the fair value is equal to the difference between the option's strike price and the underlying asset. Check FAQs

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

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

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

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

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

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

151365.1155 = 90 \cdot \exp (- 0.3 \cdot 2.25) \cdot (- 57.5) - 440 \cdot (- 350)

151365.1155 = 90 \cdot \exp (- 0.3 \cdot 2.25) \cdot (- 57.5) - 440 \cdot (- 350)

151365.1155 = 90 \cdot \exp (- 0.3 \cdot 2.25) \cdot (- 57.5) - 440 \cdot (- 350)

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

P = 151365.115523356

LAST Step Rounding Answer

∴

P = 151365.1155

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

Variables

Functions

Theoretical Price of Put Option

Theoretical Price of Put Option is the fair value is equal to the difference between the option's strike price and the underlying asset.

Symbol: P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Theoretical Price of Put Option

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

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

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

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 Put Option?

Black-Scholes-Merton Option Pricing Model for Put Option evaluator uses 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) to evaluate the Theoretical Price of Put Option, The Black-Scholes-Merton Option Pricing Model for Put Option formula is defined as a mathematical model used to calculate the theoretical price of European-style options. Theoretical Price of Put Option is denoted by P symbol.

How to evaluate Black-Scholes-Merton Option Pricing Model for Put Option using this online evaluator? To use this online evaluator for Black-Scholes-Merton Option Pricing Model for Put Option, enter Option Strike Price (K), Risk Free Rate (R_f), Time to Expiration of Stock (t_s), Cumulative Distribution 2 (D₂), Current Stock Price (P_c) & Cumulative Distribution 1 (D₁) and hit the calculate button.

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

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

The formula of Black-Scholes-Merton Option Pricing Model for Put Option is expressed as 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). Here is an example- 151365.1 = 90*exp(-0.3*2.25)*(-57.5)-440*(-350).

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

With Option Strike Price (K), Risk Free Rate (R_f), Time to Expiration of Stock (t_s), Cumulative Distribution 2 (D₂), Current Stock Price (P_c) & Cumulative Distribution 1 (D₁) we can find Black-Scholes-Merton Option Pricing Model for Put Option using the formula - 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). This formula also uses Exponential Growth (exp) function(s).

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

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

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

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

Other formulas in Forex Management category

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

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

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