Cumulative Distribution One Calculator

✖Current Stock Price is the present purchase price of security.ⓘ Current Stock Price [P_c]			+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%
✖Volatile Underlying Stock is a stock with a price that fluctuates wildly hits new highs and lows or moves erratically.ⓘ Volatile Underlying Stock [v_us]			+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 1 here represents the standard normal distribution function of stock price.ⓘ Cumulative Distribution One [D₁]

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Formula

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Cumulative Distribution One

Formula

`"D"_{"1"} = (ln("P"_{"c"}/"K")+("R"_{"f"}+"v"_{"us"}^2/2)*"t"_{"s"})/("v"_{"us"}*sqrt("t"_{"s"}))`

Example

`"146.2577"=(ln("440"/"90")+("0.30"+("195")^2/2)*"2.25")/("195"*sqrt("2.25"))`

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Cumulative Distribution One Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
D₁ = (ln(P_c/K)+(R_f+v_us^2/2)*t_s)/(v_us*sqrt(t_s))
This formula uses 2 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Cumulative Distribution 1 - Cumulative Distribution 1 here represents the standard normal distribution function of stock price.
Current Stock Price - Current Stock Price is the present purchase price of security.
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.
Volatile Underlying Stock - Volatile Underlying Stock is a stock with a price that fluctuates wildly hits new highs and lows or moves erratically.
Time to Expiration of Stock - Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value.

STEP 1: Convert Input(s) to Base Unit

Current Stock Price: 440 --> No Conversion Required
Option Strike Price: 90 --> No Conversion Required
Risk Free Rate: 0.3 --> No Conversion Required
Volatile Underlying Stock: 195 --> No Conversion Required
Time to Expiration of Stock: 2.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D₁ = (ln(P_c/K)+(R_f+v_us^2/2)*t_s)/(v_us*sqrt(t_s)) --> (ln(440/90)+(0.3+195^2/2)*2.25)/(195*sqrt(2.25))

Evaluating ... ...

D₁ = 146.257733213869

STEP 3: Convert Result to Output's Unit

146.257733213869 --> No Conversion Required

FINAL ANSWER

146.257733213869 ≈ 146.2577 <-- Cumulative Distribution 1

(Calculation completed in 00.004 seconds)

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Created by Vishnu K

BMS College of Engineering (BMSCE), Bangalore

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< 14 Forex Management Calculators

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

Cumulative Distribution One Formula

Cumulative Distribution One

The formula for cumulative distribution calculates a standardized measure of how many standard deviations the current stock price is from the strike price, taking into account the risk-free interest rate, volatility, and time to expiration. A higher value of this generally indicates a higher probability that the option will be exercised.

How to Calculate Cumulative Distribution One?

Cumulative Distribution One calculator uses 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)) to calculate the Cumulative Distribution 1, The Cumulative Distribution one formula is defined as a formula used in various financial models and theories to analyze and evaluate different aspects of financial markets, investments, and corporate finance. Cumulative Distribution 1 is denoted by D₁ symbol.

How to calculate Cumulative Distribution One using this online calculator? To use this online calculator for Cumulative Distribution One, enter Current Stock Price (P_c), Option Strike Price (K), Risk Free Rate (R_f), Volatile Underlying Stock (v_us) & Time to Expiration of Stock (t_s) and hit the calculate button. Here is how the Cumulative Distribution One calculation can be explained with given input values -> 146.2533 = (ln(440/90)+(0.3+195^2/2)*2.25)/(195*sqrt(2.25)).

FAQ

What is Cumulative Distribution One?

The Cumulative Distribution one formula is defined as a formula used in various financial models and theories to analyze and evaluate different aspects of financial markets, investments, and corporate finance and is represented as D₁ = (ln(P_c/K)+(R_f+v_us^2/2)*t_s)/(v_us*sqrt(t_s)) or 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)). Current Stock Price is the present purchase price of security, 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, Volatile Underlying Stock is a stock with a price that fluctuates wildly hits new highs and lows or moves erratically & Time to Expiration of Stock occurs when the options contract becomes void and no longer carries any value.

How to calculate Cumulative Distribution One?

The Cumulative Distribution one formula is defined as a formula used in various financial models and theories to analyze and evaluate different aspects of financial markets, investments, and corporate finance is calculated using 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)). To calculate Cumulative Distribution One, you need Current Stock Price (P_c), Option Strike Price (K), Risk Free Rate (R_f), Volatile Underlying Stock (v_us) & Time to Expiration of Stock (t_s). With our tool, you need to enter the respective value for Current Stock Price, Option Strike Price, Risk Free Rate, Volatile Underlying Stock & Time to Expiration of Stock 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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