Nonparametric Predictive Inference for Asian options

TL;DR

This paper introduces a nonparametric predictive inference approach to price Asian options, especially arithmetic average options, using limited assumptions and historical data, providing a more uncertainty-aware valuation method.

Contribution

It presents a novel nonparametric predictive inference method for Asian option pricing that reduces reliance on distributional assumptions and incorporates uncertainty in predictions.

Findings

NPI effectively infers future asset prices with limited data.

The method is validated through simulations and empirical energy market data.

A new risk measure for Asian options is proposed.

Abstract

Asian option, as one of the path-dependent exotic options, is widely traded in the energy market, either for speculation or hedging. However, it is hard to price, especially the one with the arithmetic average price. The traditional trading procedure is either too restrictive by assuming the distribution of the underlying asset or less rigorous by using the approximation. It is attractive to infer the Asian option price with few assumptions of the underlying asset distribution and adopt to the historical data with a nonparametric method. In this paper, we present a novel approach to price the Asian option from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is applied to infer the average value of the future underlying asset price, which attempts to make the prediction reflecting more uncertainty because of the limited information. A rational pairwise trading criterion is also proposed in this paper for the Asian options comparison, as a risk measure. The NPI method for the Asian option is illustrated in several examples by using the simulation techniques or the empirical data from the energy market.