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A market resilient data-driven approach to option pricing

Anindya Goswami, Nimit Rana

TL;DR

A data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing is presented, which provides an advantage over conventional models when predicting atypical out-of-sample test data.

Abstract

In this paper, we present a data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing. Using the theoretical treatment, we derive a common representation space for achieving domain adaptation. The success of an implementation of this idea is shown using some real data. Then we report several experimental results for critically examining the performance of the derived pricing models.

A market resilient data-driven approach to option pricing

TL;DR

A data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing is presented, which provides an advantage over conventional models when predicting atypical out-of-sample test data.

Abstract

In this paper, we present a data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing. Using the theoretical treatment, we derive a common representation space for achieving domain adaptation. The success of an implementation of this idea is shown using some real data. Then we report several experimental results for critically examining the performance of the derived pricing models.
Paper Structure (18 sections, 3 theorems, 31 equations, 7 figures, 3 tables)

This paper contains 18 sections, 3 theorems, 31 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Non-parametric Settings
  4. Parametric Settings
  5. Application of an Implied Volatility Estimate in Domain Adaptation
  6. A Common Representation Space
  7. Discussion on the approximation error
  8. Approach $\mathcal{A}_{DS}$ for Domain Shift
  9. Ensemble Model
  10. Data
  11. Description of Supervised Learning Approach
  12. Model Performance
  13. Performance comparison using RMSE
  14. Performance of multi-source training model
  15. Model performance on synthetic test data
  16. ...and 3 more sections

Key Result

Theorem 2.2

Assume that the market contains two risky assets other than a risk-free asset, whose price processes are modeled by $S_1$ and $S_2$, satisfying (M1)-(M3) with a common auxiliary process $V$. Let $\varphi_i$ denote the European call option price function on the $i$th risky asset. That is, $\varphi_i

Figures (7)

  • Figure 1: Visualization of relative error in the approximation relation \ref{['eqpsi']}
  • Figure 2: Q-Q plot for the log return distributions of the "Close" prices of the BANKNIFTY and NIFTY50 indices for training dataset from January 01, 2015 to August 31, 2019
  • Figure 3: Q-Q plot for the log return distributions of the “Close” prices of NIFTY50 in training and testing data
  • Figure 4: Q-Q plot for the log return distributions of the “Close” prices of BANKNIFTY in training and testing data
  • Figure 5: Histograms of subtraction of predicted from actual 'normalized price' are plotted for models trained on combined N$50$ and BNF training data. Both models with $\mathcal{A}_{HH}$, and $\mathcal{A}_{DS}$ approaches are tested on different indices with both typical and atypical scenarios.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Definition 2.1: Moneyness
  • Theorem 2.2
  • proof : Proof of Theorem \ref{['theo2.2']}
  • Remark 2.3: Homogeneity Hint Approach or $\mathcal{A}_{HH}$
  • Definition 2.4: $\rho$-scaling of a process
  • Lemma 2.5
  • proof
  • Theorem 2.6
  • proof : Proof of Theorem \ref{['theo2.5']}
  • Remark 2.7: Estimation of the volatility scalar $\rho$