Browsing by Author "Backwell, Alexander"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Open Access
    Covered Interest Parity and XVAs
    (2024) Pavlou, Danae; Backwell, Alexander
    Covered interest parity relies on a traditional no-arbitrage argument and states that the difference in interest rates between two currencies should be linked to the spot and forward exchange rates. One would expect an arbitrage opportunity to be traded away, however, the covered interest parity relationship has been shown to break down with the arbitrage opportunity persisting. This dissertation seeks to show that valuation adjustments can be considered one of the reasons why covered interest arbitrage persists. A classic covered interest parity trade is considered, where we borrow directly from the South African market and simultaneously synthetically lend rand, which involves entering a foreign exchange contract to fix the exchange rate. From this setup, we look to derive, from first principles, the net value of the strategy, highlighting the funding valuation adjustment. Further, the default of both parties within the strategy is considered, which allows us to consider the credit valuation adjustment and the debt valuation adjustment.
  • Thumbnail Image
    Item
    Open Access
    Term structure models with unspanned factors and unspanned stochastic volatility
    (2018) Backwell, Alexander; Ouwehand, Peter
    Certain models of the term structure of interest rates exhibit unspanned stochastic volatility (USV). A model has this property if it involves a source of stochastic variation — called an unspanned factor — that does not affect the model’s interest rates directly, but does affect the extent to which future interests are liable to change (that is, interest-rate volatility). This thesis is concerned with these models, from a variety of perspectives. Firstly, the theoretical foundation of the USV property is addressed. Formal definitions of unspanned factors and USV are developed, generalising ones tentatively proposed in the literature. Several results from these definitions and the accompanying framework are derived. Particularly, the ability to hedge general claims (i.e., the completeness or lack thereof) of these models is examined in detail. Examples are given to illustrate the features of the proposed framework and the necessity of the generalised definitions. Secondly, the empirical issue of whether USV models are necessary to plausibly represent observed interest-rate markets is interrogated. An empirical derivative-hedging approach is adopted, the results of which are contextualised by also treating data simulated from models with USV and non-USV versions. It is shown that hedging effectiveness is relatively robust to the presence of USV, which resolves the apparent conflict between the two studies that have taken a hedging approach to this question. Despite the cross-sectional hedging effects being surprisingly minor, further regression results show that USV models are needed to model the time series of market interest rates. Finally, the thesis addresses a certain class of models that exhibit USV: those with one spanned factor (driving interest-rate variation) and one unspanned, volatility-related factor. Being the simplest non-trivial USV models, these bivariate USV models are fundamental, and — like onefactor models in general settings — are helpful in introducing and comparing higher-factor models when simple ones are insufficient. These models are shown to exist (contradicting a claim in the literature); to share a particular affine form for their bond pricing functions; and to necessarily exhibit a short-term interest rate with dynamics of a certain type. A specific bivariate USV model is then proposed, which is analysed and compared to others in the literature.