Monte Carlo Option Pricer

xxxxx x xxxxxxxx xxxx xx xxxxx xxxxx xxxxx xxxxxxxxx xxxxxxxx xxxxxx. xxxx xx xxx "xxxxx xxxxx" xx xxxxxxxxxxx xxxxxxx, xxx xxxxxxxxxx xxx xx xxxxxxx xx xxxxxx xxxxx xxxxxx xx xxxx: xxx xxxx xxx xxxx-xxxxxxx xxxxx, xxx xxx xxxx xx xxxx xxxxxxx xxxx, xxx xxx xxxxxxxxxx xxxx x xxxxxxxxxx xxxx xx xxxxxxxxxxxx xx xx xxxxxxxx.

xxxxx xxx xxxx-xxxxxxx xxxxxxx, xxx xxxxxxxx xxxxx xx

[ x_x = x_x xxx!xxxx(xxxx(x - xxxxx{x}{x}xxxxx^xxxxxx) x + xxxxx xxxx{x}, xxxxxx), xxxxx x xxx xxxxxxx{x}(x, x) ]

xxx xxx xxxx xxxxx xx (x^{-xx}, xxxxxx{x}[xxx(x_x - x, x)]).

xxxxxxxxx xxxxx_xxxxxxxx_xxxx(xx, x, x, x, xxxxx, x_xxxxx, xxxx) xxxxxxxxx xxx xxxxxxxxxx xxxxxxx xxxxxx xxxx x_xxxxx xxxxxxxxx xxxxxxxx xxxxxx, xx x xxxxx.

xxxxxxxxxxx xx xxxxxxxxxx xxxxxxx; xxxxxx xx xx xxx xxxxx xxxxxx xxxxx:

• xxxxxx xxx xxxxxxxxx xxxx: xxx = xxxxxx.xxxxxx(xxxx);
• xxxx xxxxxxx xxx xxxxxxxx xxxxxx xxx xxxx xxxx xxx.xxxxx(x, x) (xxx xxxxxxxxxxxxx, xxx xxxxx), xx xxxx xxxxx, xxxxxx xx xxxxx xxxxx xx xxx xxxxxxxxx;
• xxxxxxx xxx xxxxxxx xx xxxx xxxxx xxx xxxxxxxx xx xxxx.xxx(-x * x).

xxxxxxxx

xxx(xxxxx_xxxxxxxx_xxxx(xxx.x, xxx.x, x.x, x.xx, x.x, xxxxx, x) - xx.xxxx) < x.xxxx
# xxxx

xxx(xxxxx_xxxxxxxx_xxxx(xx.x, xxx.x, x.x, x.xx, x.xx, xxxxx, xxx) - x.xxxx) < x.xxxx
# xxxx

xxxxxxxxxxx

• x <= x_xxxxx <= xxxxxx; xxxxx >= x (xxxx xxxxx = x xxx xxxx xx xxxxx xxxx, xxx xxxx, xxxx xxxxxx xx xx xxxxxx xxxxx xxx xxxxx).
• x xxxxx xxxxxx xxxx xx xxxx xxxxxx; xxxxx xx xxxxxxx xxxxxx xxx xxxxxxxxx xxxx.
• xxx xxxxxx xxxx xxxx xxx,xxx xxxxx xxx xxxxxx xxxx xxxxxxxx xxxxx xxxxxx x.x xx xxx xxxxx-xxxxxxx xxxxxx xxxx: x xxxxxxx xxxxxxxxx xxxxxxxxx, x xxxxxx xxxxx xxx (xxxxx xxxxxxx xxx (-xxxxx^x/x), xxxxxxxxx xxxxxxxx, xxxxx (xxxx{x})) xxxxxx xx xxx xxxx xxxx xxx xxxxx xxxxx xxxxx.