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java.lang.Object Hedging.VectorHedge
A hedge for an option on a basket (asset vector). Provides methods to compute the profit/loss from hedging an option using various deltas:
computed under the two following probabilities:
The hedge is rebalanced whenever the Trigger rebalance triggers a hedge trade. The hedge is checked against price paths of the underlying simulated under the market probability.
At each trade nonanalytic hedge weights are derived from conditional expectations which can be computed under the market or the risk neutral probability.
Monte Carlo deltas are computed under the risk
neutral probability while minimum variance deltas are computed under
the market proability. This is based on what works best in the one
dimensional case where we have kept all options open. The flag
whichDelta
indicate which type
of deltas are used in the hedge.
Constructor Summary  
VectorHedge(Basket underlying,
BasketOption option,
VectorStrategy hedgeStrategy)

Method Summary  
RandomVariable 
discountedHedgeGain()
The discounted hedge gain as a random variable. 
RandomVector 
discountedHedgeGainAndNumberOfTrades()
The discounted hedge gain (return_value[0]) and number of trades (return_value[1]) as a random vector. 
VectorStrategy 
get_hedgeStrategy()
The trading strategy in the asset used to hedge the option payoff (delta hedging with our various deltas). 
BasketOption 
get_option()
The option to be hedged. 
Basket 
get_underlying()
The asset underlying the option to be hedged. 
double[] 
hedgeMeanAndStandardDeviation(int nPaths)
Computes mean (return_value[0]) and standard deviation (return_value[1]) of the profit and loss from hedging a short position in the option (on one share of the underlying). 
double[] 
hedgeMeanAndStandardDeviation(int nPaths,
int m,
javax.swing.JProgressBar jPrgBar)
Same as hedgeMeanAndStandardDeviation(int) with progress
reported to progress bar. 
RandomVector 
hedgeStatistics()
The newHedgeStatistics() as a random vector. 
double 
newDiscountedHedgeGain()
Computes the discounted profit and loss of hedging a short position in one option along one path of the underlying. 
double[] 
newDiscountedHedgeGainAndNumberOfTrades()
Computes the discounted profit and loss (return_value[0]) and the number of trades (return_value[1]) when hedging a short position in one option on one share of the underlying along one path of the underlying. 
double[] 
newHedgeStatistics()
Computes the following vector x of statistics associated with hedging a short position in one option on one share of the underlying from a new independent path of the underlying: 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 
public VectorHedge(Basket underlying, BasketOption option, VectorStrategy hedgeStrategy)
underlying
 asset underlying the option.option
 option to be hedged.hedgeStrategy
 trading strategy hedging the option payoff..Method Detail 
public Basket get_underlying()
public BasketOption get_option()
public VectorStrategy get_hedgeStrategy()
public double newDiscountedHedgeGain()
Computes the discounted profit and loss of hedging a short position in one option along one path of the underlying.
Price paths of the underlying asset are simulated in the market probability and the hedge is rebalance whenever the Trigger rebalance triggers a hedge trade.
Assume that nonanalytic hedge deltas are used. Each time a hedge trade occurs the computation of the new hedge weights involves conditional expectations which are computed via branching price paths of the underlying asset, a very time consuming activity.
The option price path C[0] must be initialized with the option price at time zero before this routine is called. Note that this price is the martingale price of the option based on frictionless trading and perfect theoretical duplication of the option payoff. Sell at this price at your own risk.
public RandomVariable discountedHedgeGain()
The discounted hedge gain as a random variable.
The parameter t will be disregarded, ie. no conditional expectations. We don't need them and they are hard to implement.
public double[] hedgeMeanAndStandardDeviation(int nPaths)
Computes mean (return_value[0]) and standard deviation (return_value[1]) of the profit and loss from hedging a short position in the option (on one share of the underlying). The gain is computed for the combined strategy hedgeStrategy + option short position.
nPaths
 number of price paths of underlying against which hedge is
checked.public double[] hedgeMeanAndStandardDeviation(int nPaths, int m, javax.swing.JProgressBar jPrgBar)
Same as hedgeMeanAndStandardDeviation(int)
with progress
reported to progress bar.
nPaths
 number of paths.m
 progress report updated every m paths.jPrgBar
 target of progress report.public double[] newDiscountedHedgeGainAndNumberOfTrades()
Computes the discounted profit and loss (return_value[0]) and the number of trades (return_value[1]) when hedging a short position in one option on one share of the underlying along one path of the underlying.
See also newDiscountedHedgeGain()
.
The option price path C[0] must be initialized with the option price at time zero before this routine is called.
public RandomVector discountedHedgeGainAndNumberOfTrades()
The discounted hedge gain (return_value[0]) and number of trades (return_value[1]) as a random vector.
The parameter t will be disregarded, ie. no conditional expectations. We don't need them and they are hard to implement.
public double[] newHedgeStatistics()
Computes the following vector x of statistics associated with hedging a short position in one option on one share of the underlying from a new independent path of the underlying:
See also newDiscountedHedgeGain()
. The strategy is assumed to be
financed completely by borrowing at the risk free rate without using the
premium.
The option price path C[0] must be initialized with the option price at time zero before this routine is called.
public RandomVector hedgeStatistics()
The newHedgeStatistics()
as a random vector.
The parameter t will be disregarded, ie. no conditional expectations. We don't need them and they are hard to implement.


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