The Lookback function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European floating strike lookback option using Goldman, Sosin, and Gatto’s model. See Lookback Options for a further explanation.
Lookback |
(OptionType, ModelStatistic, Asset, Strike, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, InterestType, 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 •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. |
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. |
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 Lookback call option whose asset price 0.5 years from expiration is $18.25, the exercise price is $18, the risk-free interest rate is 6% per annum, the yield rate is 2.5% per annum, and the annual volatility is 30%. All of the rates are considered continuous. So, |
Input |
|
Output |
|||
Variable |
Value |
|
Function |
Name |
Value |
OptionType |
Call |
|
1 |
Theoretical: |
2.994572 |
Asset |
18.25 |
|
2 |
Delta: |
0.212325 |
Strike |
18 |
|
3 |
Gamma: |
0.191744 |
TimeExpire |
0.5 |
|
4 |
Theta: |
-0.007750 |
Volatility |
30% |
|
5 |
Implied Vol.: |
0.300620 |
InterestRate |
6% |
|
6 |
Vega: |
0.087604 |
YieldRate |
2.5% |
|
7 |
Rho: |
0.039332 |
MarketPrice |
3 |
|
8 |
Psi: |
-0.054305 |
TimeFormat |
Years |
|
9 |
Lambda: |
1.293984 |
|
|
|
11 |
Strike Sens.: |
-0.048909 |
|
|
|
13 |
Implied Strike: |
17.906620 |