Booth Id:
MATH032
Category:
Mathematics
Year:
2021
Finalist Names:
Sahajpal, Simran (School: Lillestrom High School)
Abstract:
The Black-Scholes formula returns a single price for a European call option such that it allows no risk-free profit for a trader. The formula assumes that returns follow a normal distribution and are statistically independent. This report analyzes how well a data set of 365 daily power prices for Oslo in 2018 satisfies the assumptions of normality and independence of returns of the Black-Scholes formula. The assumption of normality was tested qualitatively and quantitively. The qualitative testing involved visual evaluation of histograms of the returns and the inspection of its normal quantile-quantile plot. It was observed that the returns exhibit high kurtosis and a heavy-tailed nature rather than normality. To quantify the adherence to normality, the carefully chosen Kolmogorov-Smirnov, Anderson-Darling and Shapiro-Wilk statistical tests were conducted. It was found that the assumption of normality was strongly rejected by all three quantitative tests as the p-value yielded was considerably smaller than the significance level. The assumption of independence of returns was tested by executing a sample autocorrelation function to detect any statistically significant correlation between returns under 40 lags. It was found that the returns had autocorrelations higher than that expected by the assumption of independence. Hence, the two important assumptions of the Black-Scholes formula were found to not be satisfied. This is a significant conclusion as the ideal-world assumptions of Black-Scholes are not met and thereby, the option price calculation for power using Oslo, 2018 data, is not truly risk-neutral.