Eurodollar

(EuroModel, ExerciseType, OptionType, ModelStatistic, AssetPrice, StrikePrice, TimeExpire, Volatility, InterestRate, Iterations, MarketPrice, TimeFormat, InterestType)

Black Model

InterestRate = YieldRate

Black-Scholes Model

YieldRate = 0

Garman-Kohlhagen Model

YieldRate = Foreign Interest Rate

Argument

Description

EuroModel

Alphanumeric value indicating the model used to evaluate the Eurodollar option:

•Black-Scholes = 0 or "B" (case insensitive)

•Whaley = 1 or "W" (case insensitive)

•Binomial = 2 or "N" (case insensitive)

•Bjerksund-Stensland = 3 or "S" (case insensitive)

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

•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.

Iterations

Optional. The number of iterations used for the binomial model. Required for the binomial model. Must be > 5 when used.

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). If omitted, Days are used as the default. Specified as either:

•Days = 0 or "D" (case insensitive)

•Years = 1 or "Y" (case insensitive)

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 the functions for an American put option whose asset price 88 days from expiration of an option is $89.29, the exercise price of the option is $89.25, the risk-free interest rate is 7% per annum, and the annual volatility is 30% using the Binomial Model with 75 iterations. This means that EuroModel = BinomialEuro, Iterations = 75, AssetPrice = $89.29, StrikePrice = $89.25, InterestRate = 7%, TimeExpire = 88 days 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:

0.60373

OptionType

Put

2

Delta:

-0.51400

Asset

89.29

3

Gamma:

0.24841

Strike

89.25

4

Theta:

-0.00342

TimeExpire

88

5

Implied Vol:

0.49143

Volatility

30%

6

Vega:

0.02074

InterestRate

7.00%

7

Rho:

-0.00115

MarketPrice

1.00

8

Psi:

-0.00115

TimeFormat

Days

9

Lambda:

-9.11819

Iterations

75

11

Strike Sensitivity:

-0.46450

13

Implied Strike:

89.97444

Black-Scholes

Black-Scholes-French

Whaley

Binomial

Jump Diffusion

Bjerksund-Stensland

Roll-Geske-Whaley

OptionsMC