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

STEP 0: Pre-Calculation Summary
Formula Used
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)
P = K*exp(-Rf*ts)*(-D2)-Pc*(-D1)
This formula uses 1 Functions, 7 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 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.
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.
Current Stock Price - Current Stock Price is the present purchase price of security.
Cumulative Distribution 1 - Cumulative Distribution 1 here represents the standard normal distribution function of stock price.
STEP 1: Convert Input(s) to Base Unit
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
Current Stock Price: 440 --> No Conversion Required
Cumulative Distribution 1: 350 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = K*exp(-Rf*ts)*(-D2)-Pc*(-D1) --> 90*exp(-0.3*2.25)*(-57.5)-440*(-350)
Evaluating ... ...
P = 151365.115523356
STEP 3: Convert Result to Output's Unit
151365.115523356 --> No Conversion Required
FINAL ANSWER
151365.115523356 151365.1 <-- Theoretical Price of Put Option
(Calculation completed in 00.004 seconds)

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Black-Scholes-Merton Option Pricing Model for Call Option
​ LaTeX ​ 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
​ LaTeX ​ 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))
Black-Scholes-Merton Option Pricing Model for Put Option
​ LaTeX ​ 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)
Cumulative Distribution Two
​ LaTeX ​ Go Cumulative Distribution 2 = Cumulative Distribution 1-Volatile Underlying Stock*sqrt(Time to Expiration of Stock)

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

​LaTeX ​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)
P = K*exp(-Rf*ts)*(-D2)-Pc*(-D1)

Black-Scholes-Merton Option Pricing Model for Put Option

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.
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 Put Option?

Black-Scholes-Merton Option Pricing Model for Put Option calculator 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 calculate 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 calculate Black-Scholes-Merton Option Pricing Model for Put Option using this online calculator? To use this online calculator for Black-Scholes-Merton Option Pricing Model for Put Option, enter Option Strike Price (K), Risk Free Rate (Rf), Time to Expiration of Stock (ts), Cumulative Distribution 2 (D2), Current Stock Price (Pc) & Cumulative Distribution 1 (D1) and hit the calculate button. Here is how the Black-Scholes-Merton Option Pricing Model for Put Option calculation can be explained with given input values -> 151365.1 = 90*exp(-0.3*2.25)*(-57.5)-440*(-350).

FAQ

What is Black-Scholes-Merton Option Pricing Model for 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 and is represented as P = K*exp(-Rf*ts)*(-D2)-Pc*(-D1) or 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). 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, Current Stock Price is the present purchase price of security & Cumulative Distribution 1 here represents the standard normal distribution function of stock price.
How to calculate Black-Scholes-Merton Option Pricing Model for 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 is calculated using 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 calculate Black-Scholes-Merton Option Pricing Model for Put Option, you need Option Strike Price (K), Risk Free Rate (Rf), Time to Expiration of Stock (ts), Cumulative Distribution 2 (D2), Current Stock Price (Pc) & Cumulative Distribution 1 (D1). With our tool, you need to enter the respective value for Option Strike Price, Risk Free Rate, Time to Expiration of Stock, Cumulative Distribution 2, Current Stock Price & Cumulative Distribution 1 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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