Asian option pricing under negative asset price in commodity market

Patrick Ge and Jerry Zhou

International Journal of Financial Markets and Derivatives, 2024, vol. 10, issue 1, 21-34

Abstract: The conundrum of crude oil's futures price plunging below zero thrust the markets into a turbulent period in April 2020. Negative prices have long been seen in commodity markets, such as negative freight rates and electricity prices, etc. Those phenomena led to the failure of the traditional options pricing models, as they cannot accept negative asset prices. In this paper, an analytical pricing formula based on the Bachelier model is derived for Asian options, to replace the well-adopted Turnbull-Wakeman model in the midst of negative asset prices. In practice, the switching of models involves a couple of issues of volatility transformation, valuation changes, etc. A realistic approach is discussed to achieve a smooth model transition and minimise the impact on the market.

Keywords: option pricing; negative price; Bachelier model; commodity; Asian option; model switch. (search for similar items in EconPapers)
Date: 2024
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