Drift (annual) Volatility(annual) Drift (daily) Volatility(daily) Drift (mean)8% 37% 0.0317% 2.3308% -0.05891%

1 2 3 4N(0,1) 0.0359193434162853 0.9777027616583 0.800664702025 -0.200706704Log return 0.024811% 2.219902% 1.807265% -0.526712%Price(t) £100.02 £102.24 £101.82 £99.47

Antonis Iaponas:After the conversation we had today I have build this simulation in order for you to see what I meant, this is a very simple Monte Carlo simulation based on geometric Brownian motion where we generate random shocks in order to drive our graph, (by pressing F9 you can watch different trends of the graph and paths you can have in a market), you can simulate also with different ways and with different distributions and using levy process where you can mimic more realistically the effect of the market. The volatility, eg. The implied, can be extracted from Black-Scholes models and then incorporated into the model. Also other ways to estimate volatility , you can build other models like Garch (1,1) where it incorporates mean reversion or EWMA which it does not have mean reversion, where you can estimate your volatility using the historic data. Now by using levy process you can incorporate jumps in the market. This is one way you can build a model. Developing further a Monte Carlo simulation can give very good approximations how the FOREX market develops. I am very attracted in working on a new model as it is very interesting for me and have alot of experiences from my masters in Cass Business School.

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49£88.00£90.00£92.00£94.00£96.00£98.00

£100.00£102.00£104.00£106.00£108.00

Initial stock£100

5 6 7 8 9 10 11-1.07486915 -1.3729154862 0.361065495 -0.52786034382 1.152782006 -0.22065112 0.28290321-2.564193% -3.258874% 0.782656% -1.289236% 2.627974% -0.573198% 0.600477%

£97.47 £96.79 £100.79 £98.72 £102.66 £99.43 £100.60

Antonis Iaponas:After the conversation we had today I have build this simulation in order for you to see what I meant, this is a very simple Monte Carlo simulation based on geometric Brownian motion where we generate random shocks in order to drive our graph, (by pressing F9 you can watch different trends of the graph and paths you can have in a market), you can simulate also with different ways and with different distributions and using levy process where you can mimic more realistically the effect of the market. The volatility, eg. The implied, can be extracted from Black-Scholes models and then incorporated into the model. Also other ways to estimate volatility , you can build other models like Garch (1,1) where it incorporates mean reversion or EWMA which it does not have mean reversion, where you can estimate your volatility using the historic data. Now by using levy process you can incorporate jumps in the market. This is one way you can build a model. Developing further a Monte Carlo simulation can give very good approximations how the FOREX market develops. I am very attracted in working on a new model as it is very interesting for me and have alot of experiences from my masters in Cass Business School.

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49£88.00£90.00£92.00£94.00£96.00£98.00

£100.00£102.00£104.00£106.00£108.00

12 13 14 15 16 17 18-0.96679854 -1.39467458 -0.18480757 0.84777877 -0.326139466 0.038748477 -1.631607976-2.312304% -3.309590% -0.489655% 1.917078% -0.819068% 0.031405% -3.861829%

£97.71 £96.74 £99.51 £101.94 £99.18 £100.03 £96.21

19 20 21 22 23 24 25-0.542510081 1.0150860416 -0.0647831 0.01709735 -1.970597642 -1.36110515 0.43420014

-1.323381% 2.307034% -0.209904% -0.019059% -4.651940% -3.231347% 0.953117%£98.69 £102.33 £99.79 £99.98 £95.45 £96.82 £100.96

26 27 28 29 30 310.35069851621 -0.077480529 1.0975585554 0.834801562885 0.71935935516 1.2431875143

0.758493% -0.239499% 2.499260% 1.886831% 1.617760% 2.838689%£100.76 £99.76 £102.53 £101.90 £101.63 £102.88

32 33 34 35 36 37 381.96545024412 2.43436415 -0.67492761 -1.019345864 1.4040164 0.8190923885 0.74611642

4.522125% 5.615061% -1.632017% -2.434781% 3.213546% 1.850216% 1.680125%£104.63 £105.78 £98.38 £97.59 £103.27 £101.87 £101.69

39 40 41 42 43 44 451.8320447216 -0.431463445 -2.61699750621 0.24938993939 0.0134165359 1.07483612 2.4442608224

4.211186% -1.064555% -6.158557% 0.522365% -0.027638% 2.446299% 5.638128%£104.30 £98.94 £94.03 £100.52 £99.97 £102.48 £105.80

46 47 48 49 50-0.4436128103 0.40720946282 0.200006201 0.55473367 0.06647699

-1.092873% 0.890207% 0.407262% 1.234054% 0.096035%£98.91 £100.89 £100.41 £101.24 £100.10