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java.lang.Object Market.Asset Market.ConstantVolatilityAsset Market.JumpAsset
A ConstantVolatilityAsset
with jumps. For each time step of size
dt
the returns make a single
jump with probability lambda*dt
.
The size of the jump is
jumpSize=max{ min{X^2,1.5}, 0.4}
X
is normal N(0,rho)
. Thus if
rho
is small the jumps are predominantly downward and if
rho
is large the jumps are predominantly upward. Moreover
we allow the asset price to jump up most 30%, down at most 40%.
This asset serves mainly as a test class to check the performance of hedge weights. How badly are hedges using analytic deltas computed under the assumption of asset price continuity affected by jumps and how much better do the model independent hedge weights perform?
Constructor Summary  
JumpAsset(int T,
double dt,
int nSignChange,
double S_0,
double r,
double q,
double mu,
double sigma,
double lambda,
double rho)

Method Summary  
void 
newPath(int whichProbability)
Computes a new discounted price path driven by new (as opposed to sign changed) Zincrements. 
void 
newPathBranch(int whichProbability,
int t)
Continues a discounted asset price path existing up to time t from this time t to the horizon (branching at time t). 
int 
pathSegment(int whichProbability,
int t,
Trigger trg)
Continues a discounted price path which exists up to time t from 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. 
void 
timeStep(int whichProbability,
int t)
Time step t > t+1 of discounted asset price path driven by a new (as opposed to sign changed) Zincrement. 
void 
timeStep(int whichProbability,
int t,
int s)
Single time step t > s of discounted price path driven by new Zincrement. 
Methods inherited from class Market.ConstantVolatilityAsset 
get_mu, get_r, get_sigma, get_sigmaSqrtdt, markovChain, newWienerIncrements, Sigma, simulationInit 
Methods inherited from class Market.Asset 
dividendReductionFactor, forwardPrice, get_B, get_dt, get_nSignChange, get_q, get_S_0, get_S, get_T, get_volatilityIsDeterministic, get_Z 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 
public JumpAsset(int T, double dt, int nSignChange, double S_0, double r, double q, double mu, double sigma, double lambda, double rho)
T
 Number of time steps to horizon.dt
 Size of time step.nSignChange
 Number of times the
Zincrements are reused through random sign
changes.S_0
 Asset price S(0).r
 Constant short rate.q
 Constant dividend yield.mu
 Constant asset price drift.sigma
 Constant asset price volatility.lambda
 jump intensityrho
 see thisMethod Detail 
public void newPathBranch(int whichProbability, int t)
Continues a discounted asset price path existing up to time t from this time t to the horizon (branching at time t).
The Zincrements driving the path branch are the next set of Zincrements in a group of nSignChange dependent sets of increments which differ only by sign. Only after nSignChange sign changes is a new set of Zincrements computed.
newPathBranch
in class ConstantVolatilityAsset
whichProbability
 Probability for simulation (market/risk neutral).t
 Current time (time at which the new path branch starts).public void timeStep(int whichProbability, int t)
Time step t > t+1 of discounted asset price path driven by a new (as opposed to sign changed) Zincrement.
Sets the value S[t+1] in the price path and registers the standard normal increment Z[t] generated to drive the time step. This increment is used in the computation of some hedge deltas.
timeStep
in class ConstantVolatilityAsset
whichProbability
 probability for simulation (market/risk neutral)t
 branching time (time at which new branch starts)public void timeStep(int whichProbability, int t, int s)
Single time step t > s of discounted price path driven by new Zincrement. Sets only the value S[s] in the price path S[ ].
timeStep
in class ConstantVolatilityAsset
whichProbability
 Probability for simulation (market/risk neutral).t
 Current time.s
 Future time to be reached.public int pathSegment(int whichProbability, int t, Trigger trg)
Continues a discounted price path which exists up to time t from 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. No sign changes are applied to the Zincrements and so a new independent path branch is computed.
pathSegment
in class ConstantVolatilityAsset
whichProbability
 Probability for simulation (market/risk neutral).t
 Current time (time at which new path branch starts).trg
 triggers stopping the path.public void newPath(int whichProbability)
Computes a new discounted price path driven by new (as opposed to sign changed) Zincrements. Thus the new path is indpendent of preceeding paths.
newPath
in class ConstantVolatilityAsset
whichProbability
 Probability for simulation (market/risk neutral).


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