Libor.LiborDerivatives.LiborDerivative
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java.lang.Object
A derivative whose payoff is a functional of the path of a Libor
process. Since our implementation of the Libor process computes forward
Libors L_i only at the reset times T_j the
payoff H must be a deterministic function
H=H(L_j(T_k); k<=j). This case covers caps, swaps, swaptions
trigger swaps, Bermudian swaptions and others but does not cover more
exotic derivatives which must evaluate Libors more frequently.
| Constructor Summary | |
LiborDerivative(LiborProcess LP)
Payoff computed from full Libor paths, no control variate or lognormal Libor vector. |
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LiborDerivative(LiborProcess LP,
int k,
int Tmax)
Optimized, only the Libors which are needed computed only as far as needed (speed). |
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LiborDerivative(LiborProcess LP,
int k,
int Tmax,
LiborVector LV)
Optimized, only the Libors which are needed computed only as far as needed (speed), allocates log-normal Libor vector for fast valuation. |
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| Method Summary | |
double |
analyticForwardPrice(int t)
The value of the time T_n-forward price at
discrete time t (continuous time T_t). |
ControlledRandomVariable |
controlledForwardPayoff()
The controlled forward transported payoff as a random variable. |
double |
controlledMonteCarloForwardPrice(int t,
int nPath)
The value of the time T_n-forward price at time
discrete t (continuous time T_t). |
double |
controlVariateMean(int t)
Mean of the control variate conditioned on the state of the Libor path at time t. |
double[] |
currentControlledForwardPayoff()
Payoff-Controlvariate pair computed from current Libor path. |
abstract double |
currentForwardPayoff()
Forward transported payoff computed from the current Libor path using the array LP.X of true Libors only. |
RandomVariable |
forwardPayoff()
The forward transported payoff as a random variable. |
RandomVariable |
lognormalForwardPayoff()
The lognormalForwardPayoff() as a random variable based
on the log-normal Libor vector this.LV as a proxy for
the vector of true Libors. |
double |
lognormalForwardPayoffSample()
The forward transported payoff seen from time t=0 and
computed from a new sample of the Libor vector this.LV
instead of true Libors derived from paths of the underlying
LiborProcess. |
double |
lognormalMonteCarloForwardPrice(int nPath)
The value of the time T_n-forward price at time
discrete t=0 (continuous time T_t)
computed by direct simulation of the approximating log-normal
Libor vector this.LV instead of true Libor paths
(speed). |
double |
monteCarloForwardPrice(int t,
int nPath)
The value of the time T_n-forward price at
discrete time t (continuous time T_t). |
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Constructor Detail |
public LiborDerivative(LiborProcess LP,
int k,
int Tmax,
LiborVector LV)
Optimized, only the Libors which are needed computed only as far as needed (speed), allocates log-normal Libor vector for fast valuation.
"Payoff" means payoff transported forward to the horizon
T=T_n. The parameters k,Tmax allow us to
avoid the costly computation of full Libor paths.
LP - underlying Libor process.k - Libors needed to compute payoff: L_j; j>=k.Tmax - computation of payoff needs Libors until time
Tmax.LV - log-normal approximate Libor vector for fast valuation
public LiborDerivative(LiborProcess LP,
int k,
int Tmax)
T=T_n. The parameters k,Tmax allow us to
avoid the costly computation of full Libor paths.
LP - underlying Libor process.k - Libors needed to compute payoff: L_j; j>=k.Tmax - computation of payoff needs Libors until time
Tmax.public LiborDerivative(LiborProcess LP)
Payoff computed from full Libor paths, no control variate or lognormal Libor vector.
LP - underlying Libor process.| Method Detail |
public abstract double currentForwardPayoff()
Forward transported payoff computed from the current Libor path
using the array LP.X of true Libors only.
Here LP is the underlying Libor process.
If the option has payoffs at several points along the path these
must all be transported forward and aggregated at the horizon
T_n.
Why the forward transporting? Recall that we are simulating the
Libor dynamics under the forward martingale measure P_n.
Consequently a Monte Carlo simulation computes expectations
E^{P_n} in this probability and we compute the forward
price c_t(H) of an option H at time
t as the conditional expectation E^{P_n}_t(h).
This formula is correct only if h is the value of the
option payoff(s) at time T_n.
public RandomVariable forwardPayoff()
public double controlVariateMean(int t)
t.
This is a default implementation (error message and program abort)
intended to be overidden in concrete subclasses which do implement
a control variate.
public double[] currentControlledForwardPayoff()
Payoff-Controlvariate pair computed from current Libor path.
Can make use of the array LP.X of true Libors or
of one or both of the log-normal approximations
LP.X0, LP.X1. Make sure the boolean flags
controlVariateNeedsX0, controlVariateNeedsX1
are set from the implementing concrete subclass to ensure that
the underlying Libor process computes the corresponding paths
forward.
This is a default implementation (error message and program abort) intended to be overidden in concrete subclasses which do implement a control variate.
public ControlledRandomVariable controlledForwardPayoff()
public double lognormalForwardPayoffSample()
The forward transported payoff seen from time t=0 and
computed from a new sample of the Libor vector this.LV
instead of true Libors derived from paths of the underlying
LiborProcess.
This is a default implementation (error message and program abort) intended to be overidden in concrete subclasses.
The idea is to replace the simulation of Libor paths with the much
faster direct simulation of the log-normal Libor approximations. One
hopes that the distribution of the approximation is sufficiently close
to the distribution of true Libor. In our implementations we rely on
the X0 approximation. Run the program
Examples.LiborPaths.java to see how closely the
X0-paths track true Libor.
Note that this applies only to prices computed at time
t=0.
public RandomVariable lognormalForwardPayoff()
lognormalForwardPayoff() as a random variable based
on the log-normal Libor vector this.LV as a proxy for
the vector of true Libors.
public double analyticForwardPrice(int t)
T_n-forward price at
discrete time t (continuous time T_t).
This is a default implementation (error message and program abort)
intended to be overidden in concrete subclasses.
t - current disrete time.
public double monteCarloForwardPrice(int t,
int nPath)
T_n-forward price at
discrete time t (continuous time T_t).
t - current disrete time.nPath - number of Libor paths simulated.
public double controlledMonteCarloForwardPrice(int t,
int nPath)
T_n-forward price at time
discrete t (continuous time T_t).
t - current disrete time.nPath - number of Libor paths simulated.public double lognormalMonteCarloForwardPrice(int nPath)
The value of the time T_n-forward price at time
discrete t=0 (continuous time T_t)
computed by direct simulation of the approximating log-normal
Libor vector this.LV instead of true Libor paths
(speed).
nPath - number of Libor vector samples.
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