Quanto

(OptionType, ModelStatistic, Asset, Strike, ExchangeRate, TimeExpire, VolAsset, VolExch, IntRateDom, IntRateFor, YieldRate, Correlation, MarketPrice, TimeFormat, IntRateDomType, IntRateForType, 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

•Psi = 8

•Lambda = 9

•StrikeSensitivity = 11

•ImpliedStrike = 13

•Chi = 48

•ImpliedCorr = 50

•AssetImpliedVol = 51 (Implied Volatility of the underlying asset)

•ExchangeImpliedVol = 52 (Implied Volatility of the exchange rate)

•RhoDomestic = 53 (Rho of the Domestic interest rate)

•RhoForeign = 54 (Rho of the Foreign interest rate)

•ExchangeSensitivity = 55 (Sensitivity to a change in the exchange rate)

•AssetVega = 56 (Vega of the asset price's volatility)

•ExchangeVega = 57  (Vega of the exchange rate's volatility)

Asset

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

Strike

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.

ExchangeRate

The spot exchange rate. For options valued in domestic currency, it is specified in units of domestic currency per unit of foreign currency. For options valued in foreign currency, it is specified in units of foreign currency per unit of domestic currency.

TimeExpire

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

VolAsset

Annualized volatility of the underlying security. Must be > 0.

VolExch

Annualized volatility of the exchange rate. Must be > 0.

IntRateDom

Risk-free domestic interest rate expressed as a percentage. This rate is interpreted as a continuously compounded rate unless otherwise specified in the IntRateDomType argument. Must be > 0.

IntRateFor

Risk-free domestic interest rate expressed as a percentage. This rate is interpreted as a continuously compounded rate unless otherwise specified in the IntRateForType 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.

Correlation

The correlation between the underlying asset price and the exchange rate. Must be -1 < Correlation < 1.

MarketPrice

Optional. The selling price of the option in the marketplace. This input is required when any implied value is 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)

IntRateDomType

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

IntRateForType

Optional. Alphanumeric value indicating the type of IntRateFor 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 fixed exchange rate or Quanto call option whose asset price 220 days from expiration is $109.25, the exercise price is $109, the exchange rate is $1, the domestic risk-free interest rate is 7% per annum, the foreign risk-free interest rate is 6% per annum, the yield rate is 4% per annum, the annual volatility of the asset is 25%, the annual volatility of the exchange is 30%, and the correlation between the asset price and the currency rate is 0.5. All of the rates are considered continuous. So,

Input

Output

Variable

Value

Function

Name

Value

OptionType

Call

1

Theoretical:

7.623022

Asset

109.25

2

Delta:

0.494935

Strike

109

3

Gamma:

0.017814

ExchangeRate

1

4

Theta:

-0.014157

TimeExpire

220

8

Psi:

-0.325912

VolAsset

25%

9

Lambda:

7.093211

VolExch

30%

11

Strike Sens:

-0.426135

IntRateDom

7%

13

Implied Strike:

108.13127

IntRateFor

6%

48

Chi:

-2.444337

YieldRate

4%

50

Implied Corr.:

0.348348

Correlation

0.5

51

Implied Vol. A:

0.263889

MarketPrice

8

52

Implied Vol. E:

0.209009

TimeFormat

Days

53

Rho Domestic:

-0.045947

54

Rho Foreign:

0.325912

55

Exchange Sens:

7.623022

56

Vega Vol. A:

0.271627

57

Vega Vol. E:

-0.040739

Equity Linked FX

Foreign Equity

Takeover Foreign Exchange