﻿ Available Functions > Exotic Option Functions > Multiple Exercise Option Functions > Time Switch

# Time Switch Function   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