deep learning statistical arbitrage

• empirial
• stanford
• Jorge guijarro
• markus

Motivation

• Pair trading
• GM and Ford
• Assumption
  • prices are on average similar
• Exploit temporal price different between similiar seests

Three components of statisical arbitarge

• contrict protolio
• trading signal

Foundational problem

Research question

• arbitrage portolios
• arbitarge signals

Contributions

• Novel conceptual framework
• Unified framework
• To compare different statistical arbitrage methods
  • Portolio generation
  • signal extraction
  • allocation decision
• Study each component and compare with conventional models

Novel methods

• statistical factor
• Convolution neural network

Empirical

• substantially outperforms
• sharpe ratios

Parametric models

• PCA
• cOINTEGRATION
• STOCHASTIC CONTROL
• SIMPLE PAIRS TRADING
• INTRACTABLE PARAMETRIC MODELS WITH ml

Model

$$R_{n,t}={\beta }_{n,t-1}^T{F}_t+\epsilon$$

$$x:={\epsilon }_t^L:=({\epsilon }_{n,t-L})$$

$$w_{t-1}^{\epsilon }=w^{\epsilon }(\theta ({\epsilon }_{t-1}^L))$$

$$w_{t-1}^R=\frac{}{}$$

$$d{X}_t=\kappa (\mu -X_t)$$

$${\theta }_i=\sum _{j=1}^L{W}_j^{filter}{X}_j$$

$$W^{}$$

$${\theta }^{CNN+Trans}(X)$$

$$y_I^{(0)}=\sum _{m=1}^{D_{size}}{W}_m^{local}X$$

$$h_i=\sum _{I=1}^L{\alpha }_i,I\widetilde{x_I}$$

$$Fama-FrenchFactor$$

$$CNN+Transform$$

$$\alpha ,t_{\alpha },R^2$$

$$t_{\mu }$$

$$w_{t-1}=\frac{w_{t-1}^{}}{}$$

$$L=60$$

$$FFN$$

$$<1\%$$

$$T_{train}=4$$

$$fast-reversal$$

• fast reversal
• early momemtum
• low frequency downturn
• low frequency momentum

---

• smooth trends or local curvature
• most recent 14 days get more attention for trading decision

---

• more complex than simple reversal patterns

$$cost(w_{t-1}^R,w_{t-2}^R)=0.0005||w_{t-1}$$

$$B=7$$

$$SR=1$$

$$arbitrage$$

$$mean$$

$$\Delta P=P_2-P_1$$

$$V=\sum$$

$$V=|{\beta }_0+{\beta }_1\Delta P|$$

$${\beta }_0=c({\mu }_A-{\mu }_B)$$

$${\beta }_1=f(risk)$$

$$E(V)=E[|{\beta }_0+{\beta }_{1\sigma P}Z|]$$

$$Z$$

$$N(0,1)$$

$$E(V)=constant$$

$$\frac{1}{1+\varphi (\frac{h|{\beta }_0|}{{\beta }_1})}$$

$$K>S_T$$

$$K\le S_{\tau }$$

$$K-S_{\tau }$$

$$K>S_0,k=S_0$$

$$moneyness=\frac{log(\frac{K}{S_0})}{\sigma \sqrt{\tau }}$$

$$longdated=large\tau$$

$$Moneyness=\frac{log(\frac{K}{S_0})}{\sigma \sqrt{\tau }}$$

$$SPX$$

$$3billion$$

$$R{V}_t^{option}=\sum _i(r_{i,t}^{option}{)}^2$$

realized variance
$$R{V}_t^{option}=\sum _i(r_{i,t}^{option}{)}^2$$