JumpDiffusion

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

JumpDiffusionDivArr

(OptionType, ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, JumpsPerYear, PercentTotalVol, 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.

JumpsPerYear

The expected number of jumps per year.

PercentTotalVol

The annual price volatility of the underlying security.

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 functions for a European call option whose asset price 60 days from expiration of an option is $35.75, the exercise price of the option is $30, the risk-free interest rate is 6% per annum, the yield rate is 07% per annum, the annual volatility is 30%, the annual price volatility of the underlying security is 40%, and the expected number of jumps per year is 3. This means that the AssetPrice = $35.75, StrikePrice = $30, InterestRate = 6%, YieldRate = 0%, TimeExpire = 60 days, Volatility = 30%, PercentTotalVol = 40%, and JumpsPerYear = 3. There are no dividends and all interest rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

American

1

Theoretical:

6.17432

OptionType

Call

2

Delta:

0.94789

Asset

35.75

3

Gamma:

0.02175

Strike

3

4

Theta:

-0.00838

TimeExpire

60

5

Implied Vol:

0.44214

Volatility

30%

6

Vega:

0.01622

Jumps/Year

3

7

Rho:

0.04555

% Total Vol

40%

8

Psi:

-0.05570

InterestRate

6.00%

9

Lambda:

5.48836

MarketPrice

6.50

Black-Scholes

Black-Scholes-French

Whaley

Eurodollar

Binomial

Bjerksund-Stensland

Roll-Geske-Whaley

OptionsMC