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 |
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. |
Example
Calculate all of functions for a discrete time-switch 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 risk-free 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 |
|
|
|
|