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riow1983 / Kaggle-Optiver-Realized-Volatility-Prediction

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社内論文発表 #3

Open riow1983 opened 3 years ago

riow1983 commented 3 years ago

"Incorporating Prior Financial Domain Knowledge into Neural Networks for Implied Volatility Surface Prediction" について発表する.

URL: https://arxiv.org/pdf/1904.12834.pdf

riow1983 commented 3 years ago

[選定理由]

[Background] Pro:

Con:

提案手法:

[ブラック-ショールズ方程式] input file image input file image

[Implied Volatilityとは]

input file image input file image

[3種類のVolatility]

Historical volatility, or realized volatility, is a volatility measure calculated using past price movement in an underlying. Implied volatility is an estimate of future volatility derived from current option prices. ... The historical volatility might act as a guide, but an option’s implied volatility is where the rubber meets the road for what the market is actually demanding and predicting for the future.

https://doughtrading.squarespace.com/blog/volatility-skew

riow1983 commented 3 years ago

[ブラック-ショールズ方程式の限界]

そのような批判にこたえる形でブラック–ショールズモデルが持つ仮定を緩めたものとして:

[関連手法] ボラティリティモデルは２グループに分けられる:

直接法は更に２グループに分かれる:

直接staticモデル:

riow1983 commented 3 years ago

[Model]

input file image

[prior financial domain knowledge] IVが持つ8つの性質:

  1. Positivity
  2. Twice Differentiation
  3. Monotonicity
  4. Absence of Butterfly Arbitrage
  5. Limiting Behaviour
  6. Right Boundary
  7. Left Boundary
  8. Asymptotic Slope

条件1-5は無裁定条件を, 条件6-7は境界条件を, 条件8は漸近線の存在, をそれぞれ規定している.

[smile関数 (& sigmoid関数)] mにsmile関数を, tauにsigmoid関数をそれぞれ適用することで 条件1 Positivityと条件2 Twice Differentiationが満たされるように保証.

[incorporated conditions in loss functions] 損失関数 l = l_0 + \gamma l_1 + \delta l_2 + \ita l_3 + \rho l_4 + \omega l_5 の内, l_1 - l_4に反映. l_1: 条件3 Monotonicity l_2: 条件4 Absence of Butterfly Arbitrage l_3: 条件6-7 Left and Right Boundary l_4: 条件8: Asymptotic Slope

[Training w/ synthetic data] It is worth mentioning that the values of 𝑚 and 𝜏 in ℓ1, · · · , ℓ4 can also be sampled from the training data. However, the trained neural network may fail to meet those conditions when the given values of 𝑚 and 𝜏 for prediction are out of the scope of the training data. If the training data have limited observations of input variables, creating synthetic data by sampling values from their domains is an effective way to train the model with good generalization capabilities

[Experiments]

input file image

riow1983 commented 3 years ago

[Conclusion]

riow1983 commented 3 years ago

[論文]

[Wikipedia]

[その他Webページ]

[文献]