FxPaul

Math in finance or vice versa

Exponential Ornstein-Uhlenbeck process and USD/CHF

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In the previous post USD/CHF is considered to follow a mean-reverting process. Let’s look at the dynamics of the process during the days of year 2010.

Calibration procedure

Calibration is simple: get logs of prices and calibrate against classic Ornstein-Uhlenbeck process as it is described here.

Results

As we see, there is no big difference in the estimations between exponential and standard OUP. But months January and September are definitive outliers in the calibration.

Monthly results of the exponential OUP calibration for year 2010
Month Average price Classical sigma Exponential mu Sigma Theta
1 1.4278 1.8326% 0.5148 0.6456% 0.0015
2 1.3684 1.3585% 1.3643 0.6985% 0.2947
3 1.3573 1.2259% 1.3548 0.6298% 0.2416
4 1.3425 1.3054% 1.3386 0.6762% 0.2330
5 1.2564 2.9217% 1.2381 1.1792% 0.2779
6 1.2213 1.3893% 1.2202 0.8245% 0.2661
7 1.2773 1.9837% 1.2928 0.6876% 0.2394
8 1.2903 2.1478% 1.2667 0.6817% 0.0729
9 1.3069 3.0655% 3.5107 0.6522% 0.0033
10 1.3892 1.0219% 1.3916 0.7735% 0.7108
11 1.3662 3.0439% 1.6002 0.8443% -0.0211
12 1.3218 0.9633% 1.3247 0.7268% 0.5666
Monthly results of the logarithmic OUP calibration for year 2010
Month Average price Classical sigma Mu Sigma Theta
1 1.4278 1.8326% 1.4830 0.6456% 0.0019
2 1.3684 1.3585% 0.7329 0.6984% 0.4071
3 1.3573 1.2259% 0.7381 0.6297% 0.3277
4 1.3425 1.3054% 0.7470 0.6768% 0.3135
5 1.2564 2.9217% 0.8075 1.1797% 0.3534
6 1.2213 1.3893% 0.8195 0.8245% 0.3231
7 1.2773 1.9837% 0.7734 0.6875% 0.3054
8 1.2903 2.1478% 0.7889 0.6817% 0.0958
9 1.3069 3.0655% -0.1389 0.6522% 0.0036
10 1.3892 1.0219% 0.7186 0.7733% 0.9841
11 1.3662 3.0439% 0.6210 0.8444% -0.0297
12 1.3218 0.9633% 0.7549 0.7267% 0.7495
Monthly results of the standard OUP calibration for year 2010
Month Average price Classical sigma Mu Sigma Theta
1 1.4278 1.8326% 0.8954 0.9208% 0.0040
2 1.3684 1.3585% 1.3643 0.9541% 0.2924
3 1.3573 1.2259% 1.3549 0.8537% 0.2418
4 1.3425 1.3054% 1.3387 0.9075% 0.2329
5 1.2564 2.9217% 1.2382 1.4798% 0.2818
6 1.2213 1.3893% 1.2203 1.0054% 0.2676
7 1.2773 1.9837% 1.2931 0.8783% 0.2340
8 1.2903 2.1478% 1.2665 0.8782% 0.0721
9 1.3069 3.0655% 5.1571 0.8559% 0.0011
10 1.3892 1.0219% 1.3916 1.0752% 0.7108
11 1.3662 3.0439% 1.6441 1.1564% -0.0162
12 1.3218 0.9633% 1.3247 0.9615% 0.5642
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Written by fxpaul

July 25, 2011 at 14:19

Posted in trading math

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