Exchange

(ExerciseType, ModelStatistic, Asset1, Asset2, TimeExpire, Volatility1, Volatility2, YieldRate1, YieldRate2, Correlation, QtyAsset1, QtyAsset2, MarketPrice, TimeFormat, Yield1Type, Yield2Type)

Argument

Description

ExerciseType

Alphanumeric value indicating the exercise type:

•American = 0 or "a" (case insensitive)

•European = 1 or "e" (case insensitive)

ModelStatistic

Numeric value indicating the type of function required for the return value:

•Theoretical = 1

•Theta = 4

•Delta1 = 30

•Delta2 = 31

•Gamma1 = 32

•Gamma2 = 33

•ImpliedVol1 = 34

•ImpliedVol2 = 35

•Vega1 = 36

•Vega2 = 37

•Psi1 = 38

•Psi2 = 39

•Lambda1 = 42

•Lambda2 = 43

•Chi = 48

•ImpliedCorrelation = 50

Asset1

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

Asset2

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

TimeExpire

Time, expressed in either Days or Years (depending on the TimeFormat value), until the options expiration. Must be > 0.

Volatility1

Annualized volatility of the asset one. Must be > 0.

Volatility2

Annualized volatility of the asset two. Must be > 0.

YieldRate1

Yield, expressed as a percentage (dividends or interest yield), of the first underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the Yield1Type argument.

YieldRate2

Yield, expressed as a percentage (dividends or interest yield), of the second underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the Yield2Type argument.

Correlation

The correlation between the first underlying asset price and the second underlying asset price.

Must be -1 < Correlation < 1.

QtyAsset1

Optional. The quantity of asset one. If omitted, QtyAsset1=1.

QtyAsset1 must be > 0.

QtyAsset2

Optional. The quantity of asset two. If omitted, QtyAsset2=1.

QtyAsset2 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)

Yield1Type

Optional. Alphanumeric value indicating the type of YieldRate1 to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used.

Yield2Type

Optional. Alphanumeric value indicating the type of YieldRate2 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 of a European style exchange option which is 150 days from expiration, the first asset price is $23, the second asset price is $20, the yield rate of the first asset is 9% per annum, the yield rate of the second asset is 6% per annum, the correlation is 0.6, the annual volatility of the first asset is 25%, and the annual volatility of the second asset is 15%. All rates are considered continuous and the quantities are set to 1. So,

Input

Output

Variable

Value

Function

Name

Value

ExerciseType

European

1

Theoretical:

2.876415

Asset1:

23

4

Theta:

-0.000129

Asset2:

20

30

Delta Asset 1:

0.823934

TimeExpire

150

31

Delta Asset 2:

-0.803704

Volatility1:

25%

32

Gamma 1:

0.074495

Volatility2:

15%

33

Gamma 2:

0.098520

YieldRate1:

9%

34

Implied Vol. 1:

0.292530

YieldRate2:

6%

35

Implied Vol. 2:

0.025829

Correlation:

0.6

36

Vega Vol. 1:

0.025911

QtyAsset1

1

37

Vega Vol. 2:

0.000000

QtyAsset2

1

38

Psi Yield 1:

-0.077879

MarketPrice:

3

39

Psi Yield 2:

0.066058

TimeFormat

Days

42

Lambda 1:

6.588233

43

Lambda 2:

-5.588233

48

Chi:

-0.607287

50

Implied Corr:

0.394422

Dual Strike

Exchange Binomial

Exchange on Exchange

Portfolio

Rainbow

Rainbow Binomial

Spread

Spread Binomial

Two Asset Correlation