Main Content

Convert time series arrays to functions of time and state

adds optional name-value pair arguments. `F`

= ts2func(___,`Name,Value`

)

When you specify

`Array`

as a scalar or a vector (row or column),`ts2func`

assumes that it represents a univariate time series.`F`

returns an array with one less dimension than the input time series array`Array`

with which`F`

is associated. Thus, when`Array`

is a vector, a 2-dimensional matrix, or a three-dimensional array,`F`

returns a scalar, vector, or 2-dimensional matrix, respectively.When the scalar time

*t*at which`ts2func`

evaluates the function`F`

does not coincide with an observation time in`Times`

,`F`

performs a zero-order-hold interpolation. The only exception is if*t*precedes the first element of`Times`

, in which case*F(t)*=*F(Times(1))*.To support Monte Carlo simulation methods, the output function

`F`

returns an`NVars`

-by-`1`

column vector or a two-dimensional matrix with`NVars`

rows.The output function

`F`

is always a deterministic function of time,*F(t)*, and may always be called with a single input regardless of the`Deterministic`

flag. The distinction is that when`Deterministic`

is false, the function`F`

may also be called with a second input, an`NVars`

-by-`1`

state vector*X(t)*, which is a placeholder and ignored. While*F(t)*and*F(t,X)*produce identical results, the former specifically indicates that the function is a deterministic function of time, and may offer significant performance benefits in some situations.

[1] 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.

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

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

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

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

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