Dilemmas when valuing swaptions
Persistently low interest rates are presenting financial institutions with challenges when valuing and managing the risks on interest rate options. The limitations of traditional valuation models are being exposed. Increasingly, they do not offer a solution and are no longer suitable for calculating interest rate sensitivities. But why is that? And what can be done about it?
Valuation models for swaptions – options that allows the owner the right but not the obligation to enter into an underlying swap – actually model the distribution of the forward rates. The traditional Black model works on the assumption that the volatility of these interest rates is proportionate to their level. Because of this, the model’s volatility parameter is known as ‘relative volatility’. When interest rates are low, the implications of this are twofold.
Firstly, the implicit volatility – the volatility that equates the model value to the market value – increases exponentially the closer the interest rate moves towards zero. Secondly, the volatility is not defined for negative forward rates. In this case, as we are already witnessing with short-term interest rate options, the model is unsuitable.
Interest rate sensitivities
Clearly, both implications are undesirable. This has less to do with the valuation of swaptions than with the measurement of interest rate sensitivities. When revaluing swaptions, the question arises of how the volatility will behave in the wake of an interest-rate shock. In many cases, there is no direct market quote available for this. And, particularly with the current interest rates, interpolation does not always yield a reliable picture either. In order to get around this problem, financial institutions have embarked on a quest for alternative models. Two models are frequently used in practice. These are based on what are known as ‘shifted Black’ and ‘Normal’ volatilities. Choosing either one of these entails a number of fundamental choices and practical considerations.
In the shifted Black model, the volatility curve – the connection between the forward rate and the implicit volatility for a given swaption – is shifted in such a way that it is also defined for negative forward rates. Provided this shift is sufficiently large, the model will generate a market value. This model also provides an insight into market value sensitivity. But the question is how representative this picture is, given that the sensitivities will change due to the shift. The practical considerations involve deciding how large the shift should be, as there is no market consensus on this. Furthermore, this parameter has bearing on issuing a quote, and adjusting these aspects in existing systems may prove problematic.
In the Normal model, volatilities are defined in absolute rather than relative terms. The volatility is thus also defined for negative forward rates. The question is whether this choice is made on a permanent basis or must be reversed when interest rates are higher. Moreover, it is by no means clear that the Normal model is an improvement in all interest rate environments and countries. After all, in countries with high(er) interest rates, this transition is not an issue – or at least, not yet. Consequently, a policy must be formulated, approved and implemented for all these issues. There’s also the fact that not all systems are suited to dealing with Normal volatilities. A seemingly simple switch to illustrating volatilities in basis points rather than percentages can mean a substantial change to existing systems and processes.
All in all, choosing one of the above models is a complex and fundamental choice that involves more than just adjusting formulas. It is a choice that must be supported and properly documented by several stakeholders in the organization. Although the ultimate choice can be seen as an agreement or consensus, it is important to ensure that it is a well-informed choice.