BjerksundStensland

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

BjerksundStenslandDivArr

(OptionType, ModelStatistic, AssetPrice, StrikePrice, 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

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

•Implied Strike = 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.

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 the values of an American call option whose asset price 75 days from expiration of an option is $93, the exercise price of the option is $90, the risk-free interest rate is 7.5% per annum, the yield rate is 8% per annum, and the annual volatility is 35%. This means that AssetPrice = $93, StrikePrice = $90, InterestRate = 7.5%, YieldRate = 8%, TimeExpire = 75 days and Volatility = 35%. There are no dividends and all interest rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

7.25944

OptionType

Call

2

Delta:

0.60344

Asset

93

3

Gamma:

0.02593

Strike

90

4

Theta:

-0.03532

TimeExpire

75

5

Implied Vol:

0.33370

Volatility

35%

6

Vega:

0.15931

InterestRate

7.50%

7

Rho:

0.08956

YieldRate

8.00%

8

Psi:

-0.10136

MarketPrice

7.00

9

Lambda:

7.73059

TimeFormat

Days

11

Strike Sensitivity:

-0.54289

13

Implied Strike:

90.48384

Calculate all of functions for the same option as the example above, but with dividends. The first dividend is expected to occur in 30 days and the second is expected to occur in 65 days or 35 days from the first dividend. The dividend amount is $1.5 for both dividends. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

5.58409

OptionType

Call

2

Delta:

0.52354

Asset

93

3

Gamma:

0.02768

Strike

90

4

Theta:

-0.03580

TimeExpire

75

5

Implied Vol:

0.43855

Volatility

35%

6

Vega:

0.16003

InterestRate

7.50%

7

Rho:

0.08089

YieldRate

8.00%

8

Psi:

-0.08843

MarketPrice

7.00

9

Lambda:

8.71933

TimeFormat

Days

11

Strike Sensitivity:

-0.46167

Div Amount

1.5

13

Implied Strike:

87.17574

Time Ex-Div

30

Div Frequency

35

Black-Scholes

Black-Scholes-French

Whaley

Eurodollar

Binomial

Jump Diffusion

Roll-Geske-Whaley

OptionsMC