Efficient Pricing of Path Dependent Options with Low Volatility

Abstract

In this chapter, we develop a new option pricing model based on the modal average of the underlying asset. Financial derivatives have developed rapidly over the past few decades due to their risk-averse nature, with options being the preferred financial derivatives due to their flexible contractual mechanisms, particularly Asian options. The underlying stock's geometric or arithmetic averages are typically used to price Asian options. These techniques, however, are not appropriate for equities with very little volatility. We propose the use of the modal average as the measure of the underlying stock price. We implement the suggested approach to price options traded on certain exchange equities using data from the Ghana Stock Exchange. The outcomes consistently demonstrate that the modal average model beats the current option pricing algorithms for underlying equities with less than 3% volatility. We proceed to show that theoretically this assertion is indeed true.