Learning From Interest Rate Implied Volatilities: A Relative Value Analysis of Swaptions

Johan Jørgensen

Student thesis: Master thesis


No previous research has firmly been conducted on relative value analysis on longer expiry European swaptions. This paper conducts an empirical analysis underpinning the concept of relative value analysis for ATM European swaptions on EUR and USD market by studying time series dataset of implied volatilities. We investigate the EUR and USD market for 2010-2017 by applying a principal component analysis (PCA) framework.
The thesis investigates longer expiry swaption straddles. All with a low exposure towards changes in the underlying swap rate. This gives the opportunity to focus on hedging implied volatility level rather than delta hedging. In the analysis we have found three significant dynamics represented on the implied volatility surface. The first dynamic are interpreted as an overall implied volatility level factor. The two other dynamics captures the implied volatility curves, each specifying a dimension on the implied volatility surface. Also, we give evidence that these three dynamics on the implied volatility surface explain over 95 % of the total variance for both USD and EUR markets. This is a consistent result over the entire period from 2010-2017. Furthermore, an investigation of the linkage between principal component scores and economic variables shows a high correlation between the first principal component (PC) and the US stock market.
To put these result into perspective, an unorthodox multiple regression model for hedging PC’s are introduced. The model is constructed by different very liquid asset classes as a cheap and effective hedge. Results show that this hedging strategy is only efficient during subperiods when using a rolling 30 week data window. Furthermore, an example of a relative value trade is illustrated. However relative value trading opportunities are difficult to spot as these seems to occur rarely between 2010 and 2017.
Lastly, modelling with PCA on implied volatility surface is discussed. Here we introduce the major pitfalls of a PCA setup.

EducationsMSc in Business Administration and Mathematical Business Economics, (Graduate Programme) Final Thesis
Publication date2017
Number of pages85
SupervisorsSøren Bundgaard Brøgger