Construct a Markov Partition

Question: Construct a markov partition and describe the corresponding topological markov chain for automorphism? Answer: Simulation For estimating the price of Asian call option with given strike rate and standard deviations underlying instrument, we use the Monte Carlo simulation method by using the random functions for normal distribution in excel. We take a 200 random numbers with given specifications for simulation purpose. Then by using these simulated numbers, we estimate the price of the Asian call option with given strike rate. instrument 1 instrument 2 instrument 3 219.6759823 220.3476323 220.0348725 219.7255789 219.7624927 220.7143208 219.4773936 219.4980823 220.4666459 219.8581157 219.5165657 219.2242257 220.1962253 219.708898 219.9518975 220.2868262 219.9234449 219.9508279 220.2766364 219.9458286 219.8267615 219.9708214 219.4508302 220.1464849 219.9306978 220.5013692 220.159755 220.1590732 219.9114758 220.1643714 220.0420828 220.2206935 219.6581097 220.2608781 219.7039949 219.1097496 219.9926363 219.4540716 220.6610211 219.8290087 219.4183069 219.7421016 220.0819981 220.4578343 219.9886655 219.9609818 219.2870695 219.7988025 219.9515186 220.1718751 219.966784 219.540321 220.251472 219.78257 220.4601873 220.4800228 219.9289866 219.9037041 219.8332365 219.62744 219.6491746 219.4413059 220.7097334 220.0333014 219.8941446 219.6555612 220.2073069 219.5378577 220.0389047 219.828482 220.4214118 220.1605514 219.7448684 219.4548931 220.6715438 219.9962186 220.410458 219.5631826 219.8223384 219.4141171 220.0306114 220.3813229 219.7503908 220.1717472 220.1342914 219.2974446 219.8868208 219.7925281 220.1325973 219.4488496 220.132983 220.4837909 220.058267 219.7525645 220.3380862 219.9341147 220.3707966 219.6398843 220.0947497 220.3609236 219.9401959 219.8653875 219.8255952 219.3846444 219.8529731 220.3322742 219.7462076 219.8438515 220.3502631 220.0889165 219.7006359 220.0362713 219.8952899 220.8644589 219.7496242 220.1525187 220.2298881 220.199915 220.0676812 220.0206072 220.0802356 220.0650125 219.8055444 219.9732807 220.0154734 220.1724796 219.8486792 219.2759603 219.7805928 219.8551537 220.3439212 220.0667336 220.2566473 220.3407275 220.6064973 220.1513768 220.0113649 219.4236115 220.3063259 220.0255056 219.5471213 220.356405 219.6662283 219.2540364 220.0437007 219.6918098 220.1148673 220.2579561 220.6695475 220.6153238 220.1261044 220.3220561 219.6955169 219.7875004 219.6775519 219.8262311 220.064504 220.210529 220.1707127 220.2515457 220.4433503 220.0745211 220.0986823 219.7215484 220.4460815 220.0308126 219.2283592 220.3547046 219.716683 219.782445 220.8719973 220.2092903 219.0339869 220.1870459 220.4281469 220.3126537 220.2275039 219.9053724 219.5213329 220.1250215 219.9693307 220.2083724 219.8168196 219.5111802 219.8184427 219.6840484 219.8459518 219.3002537 219.1131503 219.5239016 220.3255319 219.7490945 220.5209132 219.950522 219.9306914 219.9046608 219.8288484 219.985071 220.5345462 220.2924032 220.2354162 220.0346335 220.0021282 219.5683791 220.036092 220.5139235 219.8286575 220.1999547 220.3889749 219.7374238 219.7882324 219.9798193 220.4802807 219.727214 220.1744327 219.5974634 219.8383489 219.169994 219.5041335 219.7387181 219.6708979 220.3115551 220.1252086 220.1138931 219.912044 220.4526116 220.4496695 219.9776338 220.0741817 219.9892431 220.4916401 219.6769948 221.0225494 219.5005126 219.8402762 219.3763284 219.2982516 219.9372351 219.9743381 220.2006257 219.7185811 220.1237016 220.1287836 219.935223 219.7749557 220.133222 219.9596727 220.2292327 220.3116498 219.986285 219.6295471 219.6364816 219.8929681 219.4438116 220.2617748 219.7208348 219.3962335 220.8055977 219.6677682 220.1575332 219.5140583 219.3156756 221.0394616 219.8017246 219.8286505 219.876375 220.0799558 220.2474295 220.4632982 219.2983037 219.7090406 219.9547908 219.9817256 219.7977278 219.9382466 219.9281086 219.6758443 220.3681428 220.3276993 220.2228261 219.5766722 219.9593118 220.1414341 219.9965541 219.7774483 219.7166309 219.9731245 219.9823645 219.7694112 219.5014914 220.0077505 219.9605445 219.532974 219.8069067 220.1838623 220.8909463 219.7691663 220.1952824 219.5092011 219.8992066 219.8592071 219.1884156 220.4345214 219.944232 220.373977 220.0872288 220.2841343 220.0263149 220.1019688 219.9869165 219.0532492 220.1707932 219.8189205 220.64922 219.4404165 219.7919844 219.6670013 220.1344606 220.1237922 221.1360877 220.2706761 219.9819161 219.7515156 219.730967 219.9075277 220.6166012 220.2907204 219.6129569 219.9738904 219.3386466 220.2038409 220.4066947 219.7554912 220.1769617 220.186065 221.078883 219.4497774 219.8335289 220.191939 220.2238865 219.8751315 219.9903659 219.7439641 220.440786 220.5898368 219.9444885 219.6456994 219.4660102 220.229026 219.9620206 219.5433481 220.4495972 220.9126558 219.9637287 220.3414451 219.8272647 220.3355427 219.8286601 219.361957 219.8511305 219.5539638 219.5354062 220.0679669 219.7727714 220.1038705 220.2303306 219.6071678 219.3829337 220.4928661 220.2375566 220.0487324 219.8721794 219.939299 220.7737609 220.1668807 219.9008935 219.9562147 219.8019351 219.8073143 219.9326782 220.4641441 219.942942 219.7575201 219.9487601 219.9549847 219.7680197 220.7358732 220.4239228 220.402389 220.1567141 219.6648885 220.0591567 219.8782293 219.9716924 219.954955 220.0051958 220.3301997 219.3734576 219.433781 220.0408386 220.853698 220.2965764 220.3105906 219.8005166 219.4901768 219.6584436 220.2871526 220.3574407 219.7338247 220.0575209 220.2014239 219.89514 219.8792162 220.0573184 220.0178085 220.4667456 220.1377866 219.3715132 218.9782529 220.4253703 219.6958135 219.2795435 220.0786742 220.4066426 219.4738147 219.4851421 220.3568374 220.7804155 219.7979907 219.7953747 220.8827599 220.4813848 219.6922429 219.6756811 220.3224511 219.4385623 220.1414971 220.6978939 219.8637055 219.1070822 219.5899297 220.5275532 219.605556 219.9686236 220.0701396 220.8020142 219.9368261 220.0361077 220.2396975 220.5133526 219.7111722 220.0571003 219.5154993 220.0408412 221.0678195 220.2067349 219.7824925 220.2337419 219.5051906 220.1794207 220.1934546 219.7305986 220.3444864 219.4099728 220.5264553 220.2783369 220.2843821 220.3161119 220.3500132 219.7941849 220.293295 220.5088353 219.9206156 220.9304619 219.9336171 220.1212744 219.538694 220.4234496 219.9858994 220.4206608 219.9446966 219.5243146 220.4049411 219.7706244 220.6008121 220.2334007 220.0369687 219.3086969 220.1993059 219.6772484 219.4304837 220.2249294 219.7844896 219.7347655 219.3967025 220.0790198 219.8529926 220.2428666 219.8494491 219.4586982 219.6723133 219.858517 219.8918824 219.6670754 220.122231 219.4074382 219.6801805 219.7851938 220.3789868 219.9530757 220.37798 219.5799584 219.7179697 220.1662784 220.6114598 219.952456 220.6423368 220.3429799 219.83696 219.9228754 219.7786691 219.6294396 219.8571675 220.215004 220.2129776 219.9807262 219.9481035 220.0790002 220.0096913 220.2468746 220.2241346 219.9400602 219.353437 219.970067 219.6195795 219.4129248 220.8182978 220.3304116 219.9750328 219.5768611 220.1461334 219.7945317 220.1952682 220.2734598 220.3394934 219.9135204 219.8260698 219.9394369 220.3463924 220.395148 219.4088175 219.9303964 219.7698845 219.378215 219.8339588 220.0419733 220.0786018 219.593613 219.6564521 219.639398 219.5551214 219.884718 219.5747772 219.5026826 219.7720738 218.5308975 220.6183647 219.552332 220.2686192 219.7453633 219.8801149 219.8628771 220.0044759 219.9527655 220.3189091 219.7258036 219.8243177 220.2562392 220.3010169 220.2549908 220.2460441 220.1371717 219.7149642 219.8408353 219.9901618 220.5304945 219.9366251 219.5468179 220.0856559 219.3090742 220.0738911 219.9488241 219.376169 220.0728481 219.7806877 220.0460774 220.0475743 219.9623219 219.9283733 220.1809847