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java.lang.Object Options.Option Options.PathIndependentOption
The payoff of the option depends only on S(T) but not on S(t), t < T.
Overrides methods of the class Option
with more
efficient algorithms taking advantage of the fact that only S(T) is
needed to compute the option payoff and hence long time steps can be taken
in the simulation of the underlying asset.
Information: the information available at time t for conditioning is the history of the price path of the underlying asset on the interval [0,t] (up to the present). Conditioning on this information means to limit simulations of the price of the underlying asset to paths which are branches of the current path where branching occurs at time t.
Default control variate: as default control variate for the discounted option payoff we use the discounted price S[T]=S^B(t) of the underlying at expiration simulated under the risk neutral probability.
Field Summary 
Fields inherited from class Options.Option 
ANALYTIC_DELTA, ANALYTIC_MINIMUM_VARIANCE_DELTA, ANALYTIC_QUOTIENT_DELTA, MARKET_PROBABILITY, MINIMUM_VARIANCE_DELTA, MONTE_CARLO_DELTA, QUOTIENT_DELTA, RISK_NEUTRAL_PROBABILITY 
Constructor Summary  
PathIndependentOption(Asset asset,
java.lang.String name)

Method Summary  
ControlledRandomVariable 
controlledDiscountedPayoff()
The discounted payoff as a controlled random variable using the default control variate. 
RandomVariable 
discountedPayoff()
The discounted option payoff as a random variable. 
double 
minimumVarianceDelta(int whichProbability,
int t,
int nPath)
The minimum variance delta at time t (see file "HedgeWeights.ps") minimizing the squared hedge error over the next time step. 
double 
minimumVarianceDelta(int whichProbability,
int t,
int nPath,
Trigger rebalance)
Same as minimumVarianceDelta(int,int,int) but the
hedge is rebalanced when the next hedge trade is triggered and the
squared error minimized over the stochastic time interval until
the next hedge trade. 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 
public PathIndependentOption(Asset asset, java.lang.String name)
asset
 underlying asset.name
 name of the option.Method Detail 
public RandomVariable discountedPayoff()
discountedPayoff
in class Option
public ControlledRandomVariable controlledDiscountedPayoff()
The discounted payoff as a controlled random variable using the default control variate. Underlying is modelled in the risk neutral probability.
controlledDiscountedPayoff
in class Option
public double minimumVarianceDelta(int whichProbability, int t, int nPath)
The minimum variance delta at time t (see file "HedgeWeights.ps") minimizing the squared hedge error over the next time step. If the underlying evolves in the risk neutral probability, the stepwise hedge error have zero mean and are uncorrelated. In this case these weights minimize the step wise and cumulative hedge error variance.
It is assumed that a path S of the underlying has been computed up to time t.
Use for hedges rebalancing at each time step. No standard deviation is computed so we do not need to pay attention to the fact that paths of the underlying may come in groups of dependent paths. It's not efficient here to introduce random variables to compute the conditional expectations, we do it directly.
WARNING: the computation is extremely slow (O(nPath^2)) if the underlying evolves in the market probability and no analytic option price is implemented. Otherwise it is O(nPath).
minimumVarianceDelta
in class Option
whichProbability
 probability for simulation (risk neutral/market).t
 current time (time of branching).nPath
 number of asset price path branches expended on each
conditional expectation.public double minimumVarianceDelta(int whichProbability, int t, int nPath, Trigger rebalance)
Same as minimumVarianceDelta(int,int,int)
but the
hedge is rebalanced when the next hedge trade is triggered and the
squared error minimized over the stochastic time interval until
the next hedge trade.
minimumVarianceDelta
in class Option
whichProbability
 probability for simulation (risk neutral/market).t
 current time (time of branching).nPath
 number of asset price path branches expended on each
conditional expectation.rebalance
 triggers the hedge trades.


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