Upgrade to Pro — share decks privately, control downloads, hide ads and more …

1121

Tomonori Kanno
December 02, 2013
57

 1121

Tomonori Kanno

December 02, 2013
Tweet

Transcript

  1. Context Aim Approach Problems Next Task Price movement in FX

    Market Return / 15min Count 2013೥12݄2೔݄༵೔
  2. Context Aim Approach Problems Next Task Price movement in FX

    Market Count Return / 15min 2013೥12݄2೔݄༵೔
  3. Context Aim Approach Problems Next Task Price movement in FX

    Market The difference between these 2 distribution brew up the CRISIS 2013೥12݄2೔݄༵೔
  4. Target Aim Approach Problems Next Task Stop using the Gaussian

    Assumption of price movement Because it obviously doesn’t work in real market 2013೥12݄2೔݄༵೔
  5. Target Aim Approach Problems Next Task Stop using the Gaussian

    Assumption of price movement Because it obviously doesn’t work in real market Then, what’s the ideal solution? 2013೥12݄2೔݄༵೔
  6. Target Aim Approach Problems Next Task Value-Based Market Model is

    a simple model for price movement 2013೥12݄2೔݄༵೔
  7. Target Aim Approach Problems Next Task Value-Based Market Model Definition

    of Value R : Trading rate between asset i and j at time t V : Value of asset i at time t i j, t i, t 2013೥12݄2೔݄༵೔
  8. Target Aim Approach Problems Next Task Definition of Value R

    : Trading rate between asset i and j at time t i j, t R ~ 100 ˈ ˇ, now V ~ ? ˈ, now V ~ ? ˇ, now V : Value of asset i at time t i, t Value-Based Market Model 2013೥12݄2೔݄༵೔
  9. Target Aim Approach Problems Next Task So, what will happen

    if we use value instead of price(rate)? Value-Based Market Model 2013೥12݄2೔݄༵೔
  10. Target Aim Approach Problems Next Task If value is distributed

    in gaussian, Value-Based Market Model 2013೥12݄2೔݄༵೔
  11. Target Aim Approach Problems Next Task If value is distributed

    in gaussian, The density function of price f(z; S) can be calculated as follows Value-Based Market Model 2013೥12݄2೔݄༵೔
  12. Target Aim Approach Problems Next Task Value-Based Market Model If

    value is distributed in gaussian, ˆ S ≡ ￿ 1 ρ ρ 1 ￿ , ω ≡ ￿ x y ￿ f(z; ˆ S) = ￿ ∞ −∞ dx ￿ ∞ −∞ dyδ(z − x y )f(x, y; ˆ S) = ￿ ∞ −∞ dx ￿ ∞ −∞ dyδ(z − x y )((2π)N | ˆ S|)− 1 2 e− 1 2 ωT ˆ S−1 ω = 1 πγ{(z−z0 γ )2 + 1} (γ ≡ (1 − ρ2)1 2 , Z0 ≡ ρ) The density function of price f(z; S) can be calculated as follows 2013೥12݄2೔݄༵೔
  13. Target Aim Approach Problems Next Task Value-Based Market Model If

    value is distributed in gaussian, ˆ S ≡ ￿ 1 ρ ρ 1 ￿ , ω ≡ ￿ x y ￿ f(z; ˆ S) = ￿ ∞ −∞ dx ￿ ∞ −∞ dyδ(z − x y )f(x, y; ˆ S) = ￿ ∞ −∞ dx ￿ ∞ −∞ dyδ(z − x y )((2π)N | ˆ S|)− 1 2 e− 1 2 ωT ˆ S−1 ω = 1 πγ{(z−z0 γ )2 + 1} (γ ≡ (1 − ρ2)1 2 , Z0 ≡ ρ) Cauchy distribution (a kind of t-distribution) The density function of price f(z; S) can be calculated as follows 2013೥12݄2೔݄༵೔
  14. Target Aim Approach Problems Next Task This model still contains

    many assumptions 2013೥12݄2೔݄༵೔
  15. Target Aim Approach Problems Next Task This model still contains

    many assumptions Real distribution is NOT a Cauchy distribution 2013೥12݄2೔݄༵೔
  16. Target Aim Approach Problems Next Task Checking all assumptions if

    it’s correct or it’s actually needed Prepare some quantitative validation 2013೥12݄2೔݄༵೔
  17. Target Aim Approach Problems Next Task Price movement denominated in

    each currencies in variable clusters gaussian cluster1 (ρ = 0) cluster2 (ρ = 0.7) cluster3 (ρ = 0.9) 2013೥12݄2೔݄༵೔