Calibration of pricing models to bitcoin options
Saarilahti, Aleksi (2023)
Saarilahti, Aleksi
2023
Tuotantotalouden DI-ohjelma - Master's Programme in Industrial Engineering and Management
Johtamisen ja talouden tiedekunta - Faculty of Management and Business
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Hyväksymispäivämäärä
2023-05-23
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-202305195943
https://urn.fi/URN:NBN:fi:tuni-202305195943
Tiivistelmä
A type of derivatives, which use crpytocurrency as an underlying asset has become more popular during the past years as they offer alternative solutions to traditional financial instruments. Even though the dynamics and pricing principles of different financial derivatives have been rather popular subjects in quantitative finance, the literature on crypto derivatives has been rather scarce. The calibration of the pricing model is often considered an essential part of the derivative pricing, aiming to find the optimal parameters of a certain model through the pricing data available. This is typically done by using the quoted market prices or quoted implied volatilities. Even though the obtained parameters are primarily for pricing purposes, they also give valuable information about the characteristics of the underlying asset.
The purpose of this thesis is to conduct a calibration of asset pricing models to the European-style call options, which use the bitcoin as an underlying asset. The option data involved was acquired from the Deribit cryptocurrency exchange from the review period of September 30th 2021 to October 31st 2021. With respect to the model calibrations, the stochastic volatility models of Heston and Bates are applied here. The calibrations of both models are carried out once per day across the review period by applying implied volatilities. With each calibration, a quoted implied volatility surface is established to which the model is calibrated. The study aims primarily at analysing the calibrated parameters and their development throughout the review period. On top of that, this study aims at answering what kind of implied volatility surfaces European-style bitcoin call options develop, and how these change across the review period.
Based on the calibration results both models produce relatively good implied volatility surface fits, especially for short maturities. The obtained parameters support the volatile behaviour of bitcoin and the positive correlation between returns and volatility, which is not uncommon in the crypto markets. The results also show that certain parameters have a more significant impact on the final outcome. Despite a few exceptions, the parameters remain rather stable across the review period. Based on the established implied volatility surfaces, the variation throughout the review period is relatively large. However, when comparing the formed implied volatility surfaces to the ones found in previous studies and literature, many similarities can be found. During the review period, each IV surface provides a rather clear smile effect at short time to maturities, but there is a tendency of a forward skewed shape when maturities increase. This also highlights the growing demand of OTM- options in order to better hedge the price risk of bitcoin.
The purpose of this thesis is to conduct a calibration of asset pricing models to the European-style call options, which use the bitcoin as an underlying asset. The option data involved was acquired from the Deribit cryptocurrency exchange from the review period of September 30th 2021 to October 31st 2021. With respect to the model calibrations, the stochastic volatility models of Heston and Bates are applied here. The calibrations of both models are carried out once per day across the review period by applying implied volatilities. With each calibration, a quoted implied volatility surface is established to which the model is calibrated. The study aims primarily at analysing the calibrated parameters and their development throughout the review period. On top of that, this study aims at answering what kind of implied volatility surfaces European-style bitcoin call options develop, and how these change across the review period.
Based on the calibration results both models produce relatively good implied volatility surface fits, especially for short maturities. The obtained parameters support the volatile behaviour of bitcoin and the positive correlation between returns and volatility, which is not uncommon in the crypto markets. The results also show that certain parameters have a more significant impact on the final outcome. Despite a few exceptions, the parameters remain rather stable across the review period. Based on the established implied volatility surfaces, the variation throughout the review period is relatively large. However, when comparing the formed implied volatility surfaces to the ones found in previous studies and literature, many similarities can be found. During the review period, each IV surface provides a rather clear smile effect at short time to maturities, but there is a tendency of a forward skewed shape when maturities increase. This also highlights the growing demand of OTM- options in order to better hedge the price risk of bitcoin.