The Quanto function calculates the theoretical price, sensitivities, the implied volatility, the implied strike, and the implied correlation value of a European Fixed ExchangeRate ForeignEquity option (Quanto) using a riskneutral model developed by Dravid, Richardson, and Sun (1993). See Currency Translated Options for a further explanation.
Quanto 
(OptionType, ModelStatistic, Asset, Strike, ExchangeRate, TimeExpire, VolAsset, VolExch, IntRateDom, IntRateFor, YieldRate, Correlation, MarketPrice, TimeFormat, IntRateDomType, IntRateForType, YieldType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculations.
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 
Riskfree 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 
Riskfree 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. 
Example
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 riskfree interest rate is 7% per annum, the foreign riskfree 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 