The TimeSwitch function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European style discrete time switch option using Pechtl’s model. See Multiple Exercise Options for a further explanation.
TimeSwitch 
(OptionType, ModelStatistic, Asset, Strike, TimeExpire, NumTimeUnits, AccruedAmt, TimeInterval, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, InterestType, YieldType) 
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculation.
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 •StrikeSensitivity = 11 •ImpliedStrike = 13 
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. 
TimeExpire 
Time, expressed in either Days or Years (depending on the TimeFormat value), until the options expiration. Must be > 0. 
NumTimeUnits 
The number of time units where the option has already fulfilled it condition to add a fixed amount. 
AccruedAmt 
The accrued amount that accumulates for each time interval that the asset price has been below the strike price. 
TimeInterval 
The time interval that the accrued amount accumulates at. 
Volatility 
Annualized volatility of the underlying security. Must be > 0. 
InterestRate 
Riskfree 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. 
Example
Calculate all of functions for a discrete timeswitch call option with 225 days until maturity, where the investor accumulates $4 each day (TimeInterval = 1) the stock price exceeds the $30 strike price. The current asset price is $36, five time units have passed, the riskfree interest rate is 8% per annum, the yield rate is 5% 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: 
2.283219 
Asset 
36 

2 
Delta: 
0.048337 
Strike 
30 

3 
Gamma: 
0.018943 
TimeExpire 
225 

4 
Theta: 
2.282746 
NumTimeUnits 
5 

5 
Implied Vol.: 
0.356644 
AccruedAmt 
4 

6 
Vega: 
0.017654 
TimeInterval 
1 

7 
Rho: 
0.006911 
Volatility 
20% 

8 
Psi: 
0.007163 
InterestRate 
8% 

9 
Lambda: 
0.762145 
YieldRate 
5% 

11 
Strike Sensitivity: 
0.058005 
MarketPrice 
2 

13 
Implied Strike: 
32.817601 
TimeFormat 
Days 



