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java.lang.Object Options.BasketOption
Interface and default methods to price and hedge a possibly path path dependent European option on a basket of underlying assets.
Pricing: analytic option prices (if analytic formulas exist) and Monte Carlo prices with and without control variates are computed.
Hedging: The profit and loss of hedging the option using three different hedge deltas:
is analyzed by computing mean and standard deviation from a sample of price paths 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.
Warning: the abstract class Option
does not initialize
the option price path. This is left to the concrete subclasses which can
decide wether analytic price formulas are available or not.
Field Summary  
protected java.lang.String 
name
name of option 
Constructor Summary  
BasketOption(Basket assets,
java.lang.String name)
Constructor, does not initialize the option price path. 
Method Summary  
ColtVector 
analyticDeltas(int t)
Default: undefined, abort. 
abstract double 
currentDiscountedPayoff()
Option payoff discounted to time t=0 and computed from the current discounted price path of the underlying basket. 
double 
discountedAnalyticPrice(int t)
Default: undefined, abort. 
double 
discountedMonteCarloPrice(double precision,
double confidence)
Monte Carlo price at time t=0 with price paths of the underlying simulated until desired precision is reached with desired confidence. 
double 
discountedMonteCarloPrice(int nPath)
Monte Carlo option price at time t=0. 
double 
discountedMonteCarloPrice(int t,
double precision,
double confidence)
Monte Carlo price at time t computed as a conditional expectation conditioned on information available at time t with price paths of the underlying simulated until desired precision is reached with desired confidence. 
double 
discountedMonteCarloPrice(int t,
int nPath)
Monte Carlo price at time t computed as a conditional expectation conditioned on information available at time t and computed from a sample of nPath (branches of) the price path of the underlying. 
RandomVariable 
discountedPayoff()
The discounted option payoff as a random variable based on the risk neutral probability. 
double[] 
get_C()
Reference to the array C[ ] containing the discounted option price path. 
int 
get_dim()
Dimension of underlying asset price vector (excluding the riskfree bond. 
double 
get_dt()
Size of time step. 
boolean 
get_hasAnalyticPrice()
True if and analytic formula for the option price
is implemented, false otherwise. 
int 
get_T()
Number of time steps to horizon. 
Basket 
get_underlying()
Reference to the underlying basket of asset. 
java.lang.String 
getName()
The name of the option (a string). 
ColtVector 
minimumVarianceDeltas(int t,
int nPath,
Trigger rebalance)
Warning: not implemented yet. 
ColtVector 
monteCarloDeltas(int t,
int nPath)
The vector of Monte Carlo deltas of the underlying assets at time t computed in the risk neutral probability. 
void 
newDiscountedPricePath(int whichProbability,
int nPath)
Computes one path of the underlying S and a corresponding path C of the option (discounted prices). 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Field Detail 
protected java.lang.String name
Constructor Detail 
public BasketOption(Basket assets, java.lang.String name)
Constructor, does not initialize the option price path. This is left to the concrete subclasses which can decide wether analytic price formulas are available or not.
assets
 the underlying basket of assets.name
 name of the option.Method Detail 
public int get_T()
public double get_dt()
public double[] get_C()
public java.lang.String getName()
public Basket get_underlying()
public int get_dim()
public boolean get_hasAnalyticPrice()
True
if and analytic formula for the option price
is implemented, false
otherwise.
public abstract double currentDiscountedPayoff()
public RandomVariable discountedPayoff()
public double discountedAnalyticPrice(int t)
public ColtVector analyticDeltas(int t)
public double discountedMonteCarloPrice(int t, int nPath)
Monte Carlo price at time t computed as a conditional expectation conditioned on information available at time t and computed from a sample of nPath (branches of) the price path of the underlying.
t
 current time (determines information to condition on).nPath
 number of path branches used to compute the option price.public double discountedMonteCarloPrice(int nPath)
Monte Carlo option price at time t=0.
nPath
 number of asset price paths used to compute the option price.public double discountedMonteCarloPrice(int t, double precision, double confidence)
Monte Carlo price at time t computed as a conditional expectation conditioned on information available at time t with price paths of the underlying simulated until desired precision is reached with desired confidence.
t
 current time (determines information to condition on).precision
 absolute error bound.confidence
 probability with which the precision is reached.public double discountedMonteCarloPrice(double precision, double confidence)
Monte Carlo price at time t=0 with price paths of the underlying simulated until desired precision is reached with desired confidence.
See discountedMonteCarloPrice(int,double,double)
.
precision
 absolute error bound.confidence
 probability with which the precision is reached.public void newDiscountedPricePath(int whichProbability, int nPath)
Computes one path of the underlying S and a corresponding path C of the option (discounted prices).
whichProbability
 probability for simulation (risk neutral/market).nPath
 number of asset price path branches used in the Monte Carlo
computation of the option price at each time step.public ColtVector monteCarloDeltas(int t, int nPath)
The vector of Monte Carlo deltas of the underlying assets at time t computed in the risk neutral probability. It is assumed that a price path of the underlying asset has been computed up to time t.
t
 current time (time of branching).nPath
 number of asset price path branches expended on each
conditional expectation.public ColtVector minimumVarianceDeltas(int t, int nPath, Trigger rebalance)
Warning: not implemented yet.
The vector of minimum variance deltas of the underlying assets computed in the risk neutral probability. The variance of the tracking is minimized over the interval to the next trade (trigger). It is assumed that a price path of the underlying asset has been computed up to time t.
t
 current time (time of branching).nPath
 number of asset price path branches expended on each
conditional expectation.rebalance
 trigger triggering the hedge trades.


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