BlackScholesFrench

(ExerciseType, OptionType, ModelStatistic, AssetPrice, StrikePrice, TradingDays, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, DivAmount, TimeExDiv, DivFrequency, DividendStyle, InterestType, YieldType)

BlackScholesFrenchDivArr

(ExerciseType, OptionType, ModelStatistic, AssetPrice, StrikePrice, TradingDays, TimeExpire, Volatility, InterestRate, YieldRate, Dividends, MarketPrice, TimeFormat, InterestType, YieldType)

Black Model

InterestRate = YieldRate

Black-Scholes Model

YieldRate = 0

Garman-Kohlhagen Model

YieldRate = Foreign Interest Rate

Argument

Description

ExerciseType

Alphanumeric value indicating the exercise type:

•American = 0 or "a" (case insensitive)

•European = 1 or "e" (case insensitive)

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (case insensitive)

•Straddle = 3 or "s" (case insensitive)

ModelStatistic

Numeric value indicating the type of function required for the return value:

•Theoretical = 1

•Delta = 2

•Gamma = 3

•Theta = 4

•ImpliedVol = 5

•Vega = 6

•Rho = 7

•Psi = 8

•Lambda = 9

•IntrinsicValue = 10

•StrikeSensitivity = 11

•TimeValue = 12

•ImpliedStrike = 13

AssetPrice

The price of the underlying asset. Must be > 0.

StrikePrice

The price at which the asset can be purchased if the option is a call or sold if the option is a put. Must be > 0

TimeTrading

Calendar Days expressed in either Days or Years (depending on the TimeFormat value) until the options expiration. Must be > 0.

TimeExpire

Time expressed in either Days or Years (depending on the TimeFormat value) until the options expiration. Must be > 0.

Volatility

Annualized volatility of the underlying security. Must be > 0.

InterestRate

Risk-free interest rate expressed as a percentage. This rate is interpreted as a continuously compounded rate unless otherwise specified in the InterestType argument. Must be > 0.

YieldRate

Yield expressed as a percentage (dividends or interest yield) of the underlying asset price. For futures contracts, the Yield Rate is the same as the Interest Rate. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldType argument.

Dividends*

A two-dimensional array or range of Dividend Dates and Amount pairs where the first column is the date and the second is the amount. The Dividend Dates are a range (array) of ascending unique values. All dividend dates and amounts must both be > 0.

As an example:

       Dividends      

Date         Amount

0.0             0.20

0.5             0.15

1.0             0.30

1.5             0.25

2.0             0.15

2.5             0.40

*Used for the DivArr (Dividend Array) based model only

MarketPrice

Optional. The selling price of the option in the marketplace. This input is required when implied volatility and strike are calculated. Price must be > 0.

TimeFormat

Optional. Alphanumeric value indicating the format of the time arguments (i.e. TimeExpire, TimeExDiv, DivFrequency). If omitted, Days are used as the default. Specified as either:

•Days = 0 or "D" (case insensitive)

•Years = 1 or "Y" (case insensitive)

DivAmount

Optional. The amount of the dividend(s). If omitted, an amount of 0 is used. Amount must be > 0.

TimeExDiv

Optional. The time in Days or Years until the first dividend is received. If omitted, a value of 0 is used and therefore no dividends are assessed. Value must be > 0 for dividends to be considered.

DivFrequency

Optional. The time in Days or Years between dividend payments. If omitted, a value of 0 is used and therefore the only dividend assessed occurs at the TimeExDiv time. The value must be > 0 for multiple dividends to be considered.

DividendStyle

Optional. Numeric value indicating the Style or method that dividends are handled. If omitted, the discrete cash method is used (i.e. DividendStyle = 0).

•Discrete cash flow method = 0

•Continuous yield method = 1

InterestType

Optional. Alphanumeric value indicating the type of InterestRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used.

YieldType

Optional. Alphanumeric value indicating the type of YieldRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a continuously compounded rate is used.

Calculate all of functions for a European put option whose asset price 72 Days from expiration of an option is $45, there are 63 calendar days (i.e. Trading Days) until expiration, the exercise price of the option is $50, the risk-free interest rate is 8% per annum, the yield rate is 9% per annum and the annual volatility is 25%. This means that AssetPrice = $45, StrikePrice = $50, InterestRate = 8%, YieldRate = 9% (i.e. the Garman-Kohlhagen Model), TimeTrading = 63 days, TimeExpire = 72 days, and Volatility = 25%. There are no dividends and all interest rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

5.63955

OptionType

Put

2

Delta:

-0.80818

Asset

45

3

Gamma:

0.05288

Strike

50

4

Theta:

-0.00906

TimeTrading

63

5

Implied Vol:

0.48269

TimeExpire

72

6

Vega:

0.05204

Volatility

25%

7

Rho:

-0.06774

InterestRate

8.00%

8

Psi:

0.06037

YieldRate

9.00%

9

Lambda:

-6.63424

MarketPrice

7.00

11

Strike Sensitivity:

0.83700

TimeFormat

Days

13

Implied Strike:

51.74439

Calculate all of functions for the same option as the example above, but with dividends. The first dividend is expected to occur in 25 days and the second is expected to occur in 55 days or 30 days from the first dividend. The dividend amount is $1 for both dividends. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

7.26375

OptionType

Put

2

Delta:

-0.86087

Asset

45

3

Gamma:

0.03734

Strike

50

4

Theta:

-0.00799

TimeTrading

63

5

Implied Vol:

0.16232

TimeExpire

72

6

Vega:

0.04318

Volatility

25%

7

Rho:

-0.08738

InterestRate

8.00%

8

Psi:

0.07305

YieldRate

9.00%

9

Lambda:

-5.33319

MarketPrice

7.00

11

Strike Sensitivity:

0.88592

TimeFormat

Days

13

Implied Strike:

49.70086

Div Amount

1

Time Ex-Div

25

Div Frequency

30

Black-Scholes

Whaley

Eurodollar

Binomial

Jump Diffusion

Bjerksund-Stensland

Roll-Geske-Whaley

OptionsMC