In this month’s Quantcast, Thomas Roos, a London-based consultant specialising in derivatives, talks about models that produce arbitrageable swaptions prices and the crude methods firms currently use to fix them.
His new paper, Discrete time stochastic volatility, attempts to eliminate arbitrage by introducing a stochastic volatility model that is better-equipped to capture the dynamics of the underlying volatility at higher strikes.
According to Roos, most firms resort to ad hoc methods that reduce the arbitrage rather than eliminate it completely.
“Quite a few of these methods mitigate the arbitrage rather than remove it completely, and people typically just live with whatever is left over. Some more sophisticated houses use more complex solutions that are guaranteed to be arbitrage-free,” says Roos.
One reason for this might be that existing models that produce arbitrageable prices are faster and easier to implement. However, at a slightly higher cost, one can eliminate arbitrage and obtain more accurate prices, says Roos
“The main problem with arbitrage is not that it is always financially significant, but rather that it creates this nagging doubt at the back of your mind. And the volatility smile is so fundamental and it serves as an input to so many other models that you want it to be rock solid – you don’t want to worry about it,” he adds.
Roos also spoke in favour of benchmark reform, but added that it meant there is a lot of work left for rates quants to adapt their existing models to new rates and conventions.
“It really means one has additional work to do as a quant. One needs to implement the new conventions, and one also has to deal with the bases that arise from the new indices versus the old indices. But overall I think it’s a good thing people are looking at benchmarks that actually have more liquid markets and are more readily traded and observable. It doesn’t make a lot of sense to have a huge derivative market based on benchmarks that are quite thinly traded, if at all,” he added.
1:35 Current projects
3:25 Benchmark reform and impact on pricing
4:18 Motivation behind forthcoming paper
5:38 How existing methodologies fix arbitrage in swaptions prices
7:05 Advantage of new methodology over existing methods
8:41 How significant is arbitrage in swaptions prices?
11:10 Comparison to Heston model
13:38 Computational performance
15:05 Products to which the model can be applied
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