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**Superclasses: **

Cox-Ingersoll-Ross mean-reverting square root diffusion models

`cir`

objects derive from the `sdemrd`

(SDE with drift rate expressed
in mean-reverting form) class. Use the `cir`

constructor to create `cir`

objects
to simulate sample paths of `NVARS`

state variables
expressed in mean-reverting drift-rate form. These state variables
are driven by `NBROWNS`

Brownian motion sources of
risk over `NPERIODS`

consecutive observation periods,
approximating continuous-time CIR stochastic processes with square
root diffusions.

This method allows you to simulate any vector-valued SDE of the form:

$$d{X}_{t}=S(t)[L(t)-{X}_{t}]dt+D(t,{X}_{t}^{\frac{1}{2}})V(t)d{W}_{t}$$

*X*is an_{t}`NVARS`

-by-`1`

state vector of process variables.*S*is an`NVARS`

-by-`NVARS`

matrix of mean reversion speeds (the rate of mean reversion).*L*is an`NVARS`

-by-`1`

vector of mean reversion levels (long-run mean or level).*D*is an`NVARS`

-by-`NVARS`

diagonal matrix, where each element along the main diagonal is the square root of the corresponding element of the state vector.*V*is an`NVARS`

-by-`NBROWNS`

instantaneous volatility rate matrix.*dW*is an_{t}`NBROWNS`

-by-`1`

Brownian motion vector.

`CIR = cir(Speed,Level,Sigma)`

constructs
a default `cir`

object.

`CIR = cir(Speed,Level,Sigma,`

constructs
a `Name,Value`

)`cir`

object with additional options specified
by one or more `Name,Value`

pair arguments.

`Name`

is a property name and `Value`

is
its corresponding value. `Name`

must appear inside
single quotes (`''`

). You can specify several name-value
pair arguments in any order as `Name1,Value1,…,NameN,ValueN`

.

For more information on constructing a `cir`

object,
see `cir`

.

simBySolution | Simulate approximate solution of diagonal-drift HWV processes |

The following figure illustrates the inheritance relationships among SDE classes.

For more information, see SDE Class Hierarchy.

Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).

When you specify the required input parameters as arrays, they are associated with a specific parametric form. By contrast, when you specify either required input parameter as a function, you can customize virtually any specification.

Accessing the output parameters with no inputs simply returns the original input specification. Thus, when you invoke these parameters with no inputs, they behave like simple properties and allow you to test the data type (double vs. function, or equivalently, static vs. dynamic) of the original input specification. This is useful for validating and designing methods.

When you invoke these parameters with inputs, they behave like
functions, giving the impression of dynamic behavior. The parameters
accept the observation time *t* and a state vector *X _{t}*,
and return an array of appropriate dimension. Even if you originally
specified an input as an array,

`cir`

treats it as
a static function of time and state, by that means guaranteeing that
all parameters are accessible by the same interface.Ait-Sahalia, Y. “Testing Continuous-Time Models of the
Spot Interest Rate.” *The Review of Financial Studies*,
Spring 1996, Vol. 9, No. 2, pp. 385–426.

Ait-Sahalia, Y. “Transition Densities for Interest Rate
and Other Nonlinear Diffusions.” *The Journal of
Finance*, Vol. 54, No. 4, August 1999.

Glasserman, P. *Monte Carlo Methods in Financial Engineering.* New
York, Springer-Verlag, 2004.

Hull, J. C. *Options, Futures, and Other Derivatives*,
5th ed. Englewood Cliffs, NJ: Prentice Hall, 2002.

Johnson, N. L., S. Kotz, and N. Balakrishnan. *Continuous
Univariate Distributions.* Vol. 2, 2nd ed. New York, John
Wiley & Sons, 1995.

Shreve, S. E. *Stochastic Calculus for Finance II:
Continuous-Time Models.* New York: Springer-Verlag, 2004.

`diffusion`

| `drift`

| `interpolate`

| `sdeddo`

| `simByEuler`

| `simulate`

- Simulating Equity Prices
- Simulating Interest Rates
- Stratified Sampling
- Pricing American Basket Options by Monte Carlo Simulation
- Base SDE Models
- Drift and Diffusion Models
- Linear Drift Models
- Parametric Models
- Class Attributes (MATLAB)
- Property Attributes (MATLAB)
- SDEs
- SDE Models
- SDE Class Hierarchy
- Performance Considerations

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