## Market Class Asset

java.lang.Object Market.Asset

Direct Known Subclasses:
ConstantVolatilityAsset, DeterministicVolAsset

public abstract class Asset
extends java.lang.Object

Interface and default methods for all assets (deterministic or stochastic volatility, deterministic or stochastic rates).

Generally works with discounted prices S^B(t)=S(t)/B(t), where S is the asset and B the riskfree bond. This eliminates interest rates from direct consideration.

PATH COMPUTATION: the basic procedure is to continue a path which has already been realized until time t from this time t to the horizon (branching at time t).

Here we are simulating future scenarios conditioned on all information available at time t (the realized path on [0,t]). This is what is needed for the computation of conditional expectations conditioning on information available at time t. The computation of entire paths is then merely a continuation from time t=0.

Path simulation is driven by an array Z[ ] of standard normal Z-increments. These increments should be stored so that they can be reused through simple random sign change (eg. antithetic paths). The integer nSignChange is the number of sign changes applied to an existing array of Z-increments before a new array is computed.

Time is measured in discrete units (the time step dt). Thus integer time t corresponds to continuous time t*dt.

 Constructor Summary Asset(int T, double dt, double S_0, double q, int nSignChange)           Constructor, call from concrete subclass.

 Method Summary  double dividendReductionFactor(int t)           Reduces price by future dividends.  double forwardPrice(int t)           Forward price at horizon T.  double[] get_B()           Reference to the array B[ ] containing the riskfree bond.  double get_dt()           Size of time step.  int get_nSignChange()           Number of times the Z-increments are reused through random sign changes before new increments are generated.  double get_q()           Constant dividend yield.  double get_S_0()           Asset price S(0) at time t=0.  double[] get_S()           Reference to the array S[ ] containing the discounted asset price path.  double get_sigmaSqrtdt(int t)           sigma(t)*sqrt(dt), where sigma(t) is the volatility of the asset.  int get_T()           Number of time steps to horizon.  boolean get_volatilityIsDeterministic()           True if the volatility of the asset is deterministic, false otherwise.  double[] get_Z()           Reference to the array Z[ ] of standard normal increments driving the current asset price path.  void newPath(int whichProbability)           New independent path of riskfree bond and discounted asset (driven by new independent Z-increments).  void newPathBranch(int whichProbability, int t)           Continues a path of the riskfree bond and discounted asset from time t to the horizon (branching at time t).  int pathSegment(int whichProbability, int t, Trigger trg)           Continues a path of the riskfree bond and the discounted asset which exists up to time t from this time t to the next time s>t at which the Trigger trg is triggered or s=T, whichever comes first, and returns this time s.  double Sigma(int t)           sqrt(\int_t^T sigma^2(u)du), where sigma(u) is the volatility of the asset.  void simulationInit(int t)           Sets up a path simulation (t=0) or a simulation of branches of an existing path (t>0, conditional expectations). abstract  void timeStep(int whichProbability, int t)           Time step of riskfree bond and discounted asset price from discrete time t to time t+1.  void timeStep(int whichProbability, int t, int s)           Single time step of riskfree bond and discounted asset price from discrete time t to time s, skipping intermediate times if possible, driven by new Brownian increments.

 Methods inherited from class java.lang.Object clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

 Constructor Detail

### Asset

public Asset(int T,
double dt,
double S_0,
double q,
int nSignChange)

Constructor, call from concrete subclass.

Parameters:
T - Number of time steps to horizon.
dt - Size of time step.
S_0 - Asset price S(0).
q - Dividend yield.
nSignChange - Number of times the Z-increments are reused through random sign changes.
 Method Detail

### get_T

public int get_T()

Number of time steps to horizon.

### get_dt

public double get_dt()

Size of time step.

### get_S_0

public double get_S_0()

Asset price S(0) at time t=0.

### get_q

public double get_q()

Constant dividend yield.

### get_nSignChange

public int get_nSignChange()

### get_volatilityIsDeterministic

public boolean get_volatilityIsDeterministic()

True if the volatility of the asset is deterministic, false otherwise.

### get_Z

public double[] get_Z()

Reference to the array Z[ ] of standard normal increments driving the current asset price path.

### get_B

public double[] get_B()

Reference to the array B[ ] containing the riskfree bond.

### get_S

public double[] get_S()

Reference to the array S[ ] containing the discounted asset price path.

### dividendReductionFactor

public double dividendReductionFactor(int t)

Reduces price by future dividends.

Parameters:
t - Current time.

### forwardPrice

public double forwardPrice(int t)

Forward price at horizon T.

Parameters:
t - Current time.

### get_sigmaSqrtdt

public double get_sigmaSqrtdt(int t)

sigma(t)*sqrt(dt), where sigma(t) is the volatility of the asset.

Polymorphic link to subclasses implementing this method. Default implementation is an error message.

Parameters:
t - Current time.

### Sigma

public double Sigma(int t)

sqrt(\int_t^T sigma^2(u)du), where sigma(u) is the volatility of the asset. For a constant volatility asset this is simply sigma*sqrt(tau), where tau is time to the horizon.

Polymorphic link to subclasses implementing this method. Default implementation is an error message.

Parameters:
t - Current time.

### simulationInit

public void simulationInit(int t)

Sets up a path simulation (t=0) or a simulation of branches of an existing path (t>0, conditional expectations). Default: nothing to do.

Parameters:
t - Time of branching.

### timeStep

public abstract void timeStep(int whichProbability,
int t)

Time step of riskfree bond and discounted asset price from discrete time t to time t+1. In case of nonstochastic interest rates the path of the riskfree bond is handled by the constuctor.

Routine to be implemented so as not to reuse previously generated Z-increments through sign changes. Thus a new independent path is generated from calls to timeStep.

Parameters:
whichProbability - Probability for simulation (market/risk neutral).
t - Current time.

### timeStep

public void timeStep(int whichProbability,
int t,
int s)

Single time step of riskfree bond and discounted asset price from discrete time t to time s, skipping intermediate times if possible, driven by new Brownian increments.

In some models large time steps t->s can be simulated without loss of accuracy in others predictor corrector simulation is reasonably accurate. In each case large time steps imply significant speedup as the asset price path has to be sampled only at the needed times.

Default implementation: steps through all intermediate times by calling timeStep(int). This should be overidden in concrete subclasses by more efficient methods if possible.

Parameters:
whichProbability - Probability for simulation (market/risk neutral).
t - Current time.
s - Time to be reached.

### newPathBranch

public void newPathBranch(int whichProbability,
int t)

Continues a path of the riskfree bond and discounted asset from time t to the horizon (branching at time t).

Default implementation: repeated calls to timeStep. Obviously that has function call overhead but it generates new independent path branches since Z-increments are not reused through sign changes. Override this with more efficient implementation if desired.

Parameters:
whichProbability - Probability for simulation (market/risk neutral).
t - time of branching.

### newPath

public void newPath(int whichProbability)

New independent path of riskfree bond and discounted asset (driven by new independent Z-increments).

Not implemented as newPathBranch(whichProbability,0) since this method may be overridden in subclasses so as to generate groups of dependent paths.

Parameters:
whichProbability - Probability for simulation (market/risk neutral).

### pathSegment

public int pathSegment(int whichProbability,
int t,
Trigger trg)

Continues a path of the riskfree bond and the discounted asset which exists up to time t from this time t to the next time s>t at which the Trigger trg is triggered or s=T, whichever comes first, and returns this time s.

The Trigger could be a signal triggering a hedge trade or option exercise for example.

Default implementation: repeated calls to timeStep. Obviously that has function call overhead but it generates new independent path branches since Z-increments are not reused through sign changes. Override this with more efficient implementation if desired.

Parameters:
whichProbability - Probability for simulation (market/risk neutral).
t - branching time (time at which new branch starts).
trg - Stopping time >= t until which the path is computed.