Roland Conybeare
2450ab4ed9
git-subtree-dir: xo-process git-subtree-mainline:abd08e3491git-subtree-split:7cfc560f02
102 lines
3.3 KiB
C++
102 lines
3.3 KiB
C++
/* @file BrownianMotion.cpp */
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#include "xo/reflect/TaggedPtr.hpp"
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//#include "time/Time.hpp"
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#include "BrownianMotion.hpp"
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#include <cmath>
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namespace xo {
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using xo::time::utc_nanos;
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using xo::scope;
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using xo::xtag;
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namespace process {
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double
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BrownianMotionBase::variance_dt(nanos dt) const
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{
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constexpr uint64_t c_sec_per_day = (24L * 3600L);
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constexpr double c_day_per_sec = (1.0 / c_sec_per_day);
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/* time-to-horizon in nanos */
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double dt_sec = std::chrono::duration<double>(dt).count();
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double dt_day = dt_sec * c_day_per_sec;
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return this->vol2_day_ * dt_day;
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} /*variance_dt*/
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double
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BrownianMotionBase::exterior_sample_impl(utc_nanos t,
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BrownianMotionBase::event_type const & lo,
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double x0)
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{
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constexpr bool c_logging_enabled = false;
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scope log(XO_DEBUG(c_logging_enabled));
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/* sample brownian motion starting at t0;
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* offset by lo.second
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*/
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utc_nanos lo_tm = lo.first;
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double lo_x = lo.second;
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nanos dt = (t - lo_tm);
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/* variance at horizon t, relative to value at lo.first */
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double var = this->variance_dt(dt);
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/* scale for variance of B(t) - B(lo) */
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double dx = ::sqrt(var) * x0;
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double sample = lo_x + dx;
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log && log("result",
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xtag("start-time", this->t0()),
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xtag("vol2-day", this->vol2_day()),
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xtag("lo.tm", lo_tm),
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xtag("lo.x", lo_x),
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xtag("dt-us", std::chrono::duration_cast<std::chrono::microseconds>(dt).count()),
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xtag("var", var),
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xtag("dx", dx));
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return sample;
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} /*exterior_sample_impl*/
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// ----- BrownianMotion -----
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#ifdef NOT_IN_USE
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utc_nanos
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BrownianMotion::hitting_time(double const & a,
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event_type const & lo)
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{
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/* (1)
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* probability density function p1(s)
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* giving hitting time for brownian motion starting at 0,
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* first time to reach a constant barrier a:
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*
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* a^2
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* - ---
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* a 2.s
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* p1(s) = ------------- . e
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* sqrt(2.pi.s^3)
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*
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* (2)
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* we also know probability density function p2(s)
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* giving hitting time for brownian motion starting at 0,
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* first time to reach expanding barrier a + ct:
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* (i.e. T2 = inf{t : B(t) = c.t + a, t > 0})
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*
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* (c.s + a)^2
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* - -----------
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* a 2.s
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* p2(s) = -------------- . e
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* sqrt(2.pi.s^3)
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*
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*/
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} /*hitting_time*/
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#endif
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} /*namespace process*/
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} /*namespace xo*/
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/* end BrownianMotion.cpp */
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