ForwardStart

(OptionType, ModelStatistic, Asset, TimeStart, TimeExpire, Volatility, InterestRate, YieldRate, Alpha, MarketPrice, TimeFormat, InterestType, YieldType)

Argument

Description

OptionType

Alphanumeric value indicating the type of option:

•Call = 1 or "c" (case insensitive)

•Put = 2 or "p" (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

Asset

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

TimeStart

Time, expressed in either Days or Years (depending on the TimeFormat value), until the grant date (when the option forward starts).

Must be: 0 < TimeStart < TimeExpire.

TimeExpire

Time, expressed in either Days or Years (depending on the TimeFormat value), until the options expiration.

Must be: 0 < TimeStart < TimeExpire.

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. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldType argument.

Alpha

The strike price is set equal to Alpha times the asset price at TimeStart (Strike = Alpha*Asset). Must be > 0

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.

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 forward start call option with a forward start in 0.25 years and expires in 1 year. The option starts 5% out-of-the money, the asset price is $43, the risk-free interest rate is 6.5% per annum, the yield rate is 3% per annum, and the annual volatility is 20%. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

2.461591

Asset

43

2

Delta:

0.057246

TimeStart

0.25

3

Gamma:

0.000000

TimeExpire

1

4

Theta:

0.000202

Volatility

20%

5

Implied Vol.:

0.202666

InterestRate

6.5%

6

Vega:

0.144036

YieldRate

3%

7

Rho:

0.132591

Alpha

1.05

8

Psi:

-0.157207

MarketPrice

2.5

9

Lambda:

1.000000

TimeFormat

Years

Chooser

Complex Chooser

Compound

Compound Binomial

Executive

Time Switch

Writer Extendible