Numerical method for pricing american options under regime
Interest Rate Modeling With Cox Ingersoll Ross
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11. The Discounting Factor B Ti-1 -1 The factor which discounts the option price to time 0 is determined from the following equation: Which can be approximated using the trapezoid method as
12. Generating Short Term Rates Simulation from CIR Model In its discretized form, the Cox Ingersoll Ross model looks the following way: Where σ , θ , and κ are deterministic parameters, and W is a normally distributed random number. Given the parameters σ , θ , κ , and r(t= 0) one can easily construct an iteration procedure to obtain short term rates in a given interval starting from zero.
![What Is That – Monte Carlo? ,[object Object],where g(y) is an arbitrary function, f(y) is a probability density function, and A is the range of integration. To obtain an estimate of E(g) , we pick a number N of sample values (y t ) at random from the probability density function f(y) .](https://image.slidesharecdn.com/interestratemodelingwithcoxingersollross-12613705628596-phpapp02/85/Interest-Rate-Modeling-With-Cox-Ingersoll-Ross-1-320.jpg)
![[object Object],This simple equation is the quintessence of Monte Carlo method: An integral is interpreted as the average value of a function over an interval that contains a fixed number of points chosen in random.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)