This parameter is a string which specifies whether the options contract is of CALL or PUT type. If the option is a call options then please input the string "CALL", if the option is a put option then please input "PUT".
CurrentTime
The absolute time in years when the contract is evaluated. That is, if we wish to evaluate the contract on the 1st Jan 2010, then the currentTime should be set to 2010. If however we wish to evaluate the contract on the 1st July 2010, then the currentTime should be set to 2010.5.
Maturity
The absolute time in years when the option contract expires. For example, if the contract expires on 1st Jan 2010, then the maturity should be set to 2010. If however the contract expires on the 1st July 2010, then the maturity should be set to 2010.5.
InitialPrice
The price of the underlying asset at the currentTime. Please note that we evaluate the option for the currentTime, which may not be not present time until the maturity of the option contract.
Strike
The strike (or exercise) price of the option. This is the price at which the right to buy (in the case of a Call option) or the right to sell (in the case of a Put option) provide by the option can be acted upon.
InOut
If you are evaluating an `in Parisian option' then you should input IN, if you are evaluating an `out Parisian option' then you should input OUT. Recall the an `in Parisian option' at expiry pays out if the option was triggered, and an `out Parisian option' becomes worthless if the option is triggered.
UpDown
If you are evaluating an `up Parisian option' then you should input UP, if you are evaluating an `down Parisian option' then you should input DOWN. Recall, that a Parisian option is an `up option' if the trigger barrier is higher than the initial underlying asset price, or is a `down option' if the trigger barrier is lower than the initial underlying asset price.
BarrierLevel
The price level of the underlying asset at which the Parisian option is triggered.
Rebate
The compensation paid at maturity to the holder of the Parisian option if the option is not trigger and hence the (normal) payoff is not paid.
MonitorInterval
The periods in years between consecutive readings of the market variable which triggers the Parisian option. Note that since no market variable can be continuously monitored it is usual that the contract will explicitly state at what intervals the market variable on which the contracts depends is read. The monitoring interval will imply a sequence of moments in time at which the market variables values are recorded and used to determine whether the trigger has been met.
Note that the length of the monitoring periods should be smaller than the time step periods used within the Monte Carlo procedure. If this is not the case then the time steps intervals will be taken to be equal to the monitoring period.
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TimeToTrigger
This is the minimum continuous amount of time in years for which the barrier condition must to satisfied in order for the contract to be triggered.
RiskFreeRate
The risk free interest rate at the point currentTime expressed in decimal format (i.e. 1 percent = 0.01).
Volatility
An estimate of the volatility of the underlying asset (or market variable) which the option depends on at the time currentTime, expressed in decimal format (i.e. 1 percent = 0.01). See the Volatility class within the Options XL Service for procedures which assist in the estimation of the volatility.
TimeSteps
The total number of time divisions used in the construction of a Monte Carlo simulation. Please note that as this parameter is increased the synthetic Random walks will converge to `real' continuous Random walks. Therefore, as the number of time steps increases the expectation of a higher level of accuracy will also increase. Also note that the computational time required will also increase in proportion to the number of time steps used.
RandomWalks
The total number of Random walks used within the Monte Carlo simulation. As the number of Random walks increases so the corresponding accuracy (in the sense given below) increase along with a proportional increase in the computation time. Note that since Monte Carlo is a probabilistic procedure the `accuracy' can only be interpreted in a probabilistic sense. That is, as the number of Random walks increases the corresponding accuracy will increase in the sense that for a given confidence level, the corresponding confidence intervals width will decrease like: two times, one over the root of N, where N is the number of Random walks. Please see the PDF documentation for a precise formulation of the confidence interval of the Monte Carlo procedure and further discussion.
Remarks
Classification of Parisian Options
Parisian options are a variant of Barrier options where the underlying assets
price is required to be above or below a given level for a given period of time in
order to trigger the barrier. The effect of reaching this barrier will depend on the
exact type of option considered. The type of Barrier Option are classified in
accordance with the following criteria:
Put or Call: Determines whether the option when triggered gives the holder the
right to buy or sell the underlying asset.
Knock In or Knock Out: If the option is of In type then the payoff is triggered
if the barrier is reached, if the option is of Out type then the option payoff
is triggered if the barrier is NOT reached. In the case of the knock Out option if the
barrier is reached then the option will expire worthless.
Up or Down: An Up Parisian option is an option where the trigger barrier is higher
than the initial price, where a Down Parisian option is an option where the trigger
barrier is lower than the initial price.
Excel Remarks
The full name of this function inside Excel is Exotic_BlackScholes_ParisianMC.