Path Dependent Electricity Option Pricing
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Polkuriippuvaisen sähköoption hinnoittelu
This thesis studied hourly electricity spot models and their application in path dependent option pricing. The first goal was to find a suitable hourly spot model that captures the price dynamics and enables risk-neutral pricing of the path dependent electricity spot options. The second goal was to study the pricing consistency of different models. In order to price path dependent options on electricity spot price, spot models obtaining the price dynamics, most importantly the mean-reversion and jumps, and the risk factors are needed. In the first part of this thesis, the literature was studied regarding the main background theory, the stochastic electricity spot models being the main focus area. It was found that there are multiple alternative ways to describe the underlying stochastic process, which is usually assumed to be mean-reverting process with jumps. The most challenging part of the modeling is regarded to be the jumps. In addition, it can be even assumed that the underlying stochastics of the electricity spot price could be presented by more than one stochastic factor. In this thesis, there were four different two-factor models, two jump-diffusion models and two regime-switching models, two of which were actually daily spot models to which the hourly prices were generated by historical profile sampling technique. The second part of the thesis focused on estimating the different models and applying them on pricing Asian options by using Monte Carlo simulation. To obtain the risk-neutrality, all of the models were calibrated with quoted monthly future contracts after estimating the model parameters with the spot data. The models were then used to price quarterly Asian options with different strikes and maturities, and Black-Scholes implied volatilities were calculated. In line with the prior research, it was found that the implied volatilities were affected by the definitions of the model and their parameters: the mean-reversion, jump size, jump volatility and jump intensity have clear implications on the implied volatility. Additionally, this thesis showed that the daily spot models generated consistently lower prices for Asian spot options than the hourly spot models. To validate the resulting implied volatilities of all of the models, they were compared with the prices of corresponding European options on future contracts observed from the markets. It was found that the resulting implied volatilities are in line with the market prices.