RollGeskeWhaleyCall

(ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, MarketPrice, TimeFormat, DivAmount, TimeExDiv, DivFrequency, InterestType)

RollGeskeWhaleyCallDivArr

(ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, Dividends, MarketPrice, TimeFormat, InterestType)

Argument

Description

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 Note: Rho and Psi are the same

•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.

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.

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.

Calculate all of functions for an American call option whose asset price two years from expiration of an option is $75, the exercise price of the option is $80, the risk-free interest rate is 7% per annum, and the annual volatility is 30%. This means that AssetPrice = $75, StrikePrice = $80, InterestRate = 7%, TimeExpire = 2 years and Volatility = 30%. There are no dividends and all interest rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

15.05605

OptionType

Call

2

Delta:

0.65173

Asset

75

3

Gamma:

0.01162

Strike

80

4

Theta:

-0.01454

TimeExpire

2

5

Implied Vol:

0.08947

Volatility

30%

6

Vega:

0.39216

InterestRate

7.00%

7

Rho:

0.67647

MarketPrice

7.00

8

Psi:

0.67647

TimeFormat

Years

9

Lambda:

3.24651

11

Strike Sensitivity:

-0.42280

13

Implied Strike:

106.26534

Calculate all of functions for the same option as the example above, but with dividends. The first dividend is expected to occur in .5 years and with additional dividends to follow every .5 years. The dividend amount is $1 for both dividends. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

13.13370

OptionType

Call

2

Delta:

0.61865

Asset

75

3

Gamma:

0.01260

Strike

80

4

Theta:

-0.01395

TimeExpire

2

5

Implied Vol:

0.14135

Volatility

30%

6

Vega:

0.38457

InterestRate

7.00%

7

Rho:

0.64779

MarketPrice

7.00

8

Psi:

0.64779

TimeFormat

Years

9

Lambda:

3.53279

Div Amount

1

11

Strike Sensitivity:

-0.39235

Time Ex-Div

0.5

13

Implied Strike:

100.46013

Div Frequency

0.5

Black-Scholes

Black-Scholes-French

Whaley

Eurodollar

Binomial

Jump Diffusion

Bjerksund-Stensland

OptionsMC