Date Thesis Awarded

5-2024

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Ed Chadraa

Committee Members

Gregory Hunt

Narayani Sritharan

Abstract

The variance swap has recently gained popularity as a financial instrument with considerable value in hedging volatility risk. This is due to its payoff being purely derived from the underlying asset’s volatility. In this thesis, estimations of variance swap payoffs are conducted using the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Continuous Generalized Autoregressive Conditional Heteroskedasticity (COGARCH) model. Namely, we investigate the GARCH(1,1) model and the COGARCH(1,2) model. The former is widely used as a result of its mathematical comprehensibility. The latter is a relatively recent and less studied model conceived by Brockwell, Chadraa, and Lindner (2006). An Autoregressive Moving Average (ARMA) process is applied to obtain the squared residuals that are then used to fit the GARCH(1,1) and COGARCH(1,2) models. Our aim is to provide insight into which model outperforms the other, and whether there is a practical use for either with respect to variance swaps. A derivation of the fair strike of a variance swap is provided for each model in order to estimate payoffs. Ultimately, we analyze the models’ payoff estimations for three-year variance swap contracts using past closing prices of the S&P 500 as the underlying asset.

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