Why XVAs need to be factored into options pricing

Ignoring valuation adjustments could be storing up problems for the future

If you thought derivatives valuation adjustments (XVAs) had become easy, it is time for a new challenge.

So far, much of the discussion around accurately estimating XVAs – reflecting costs associated with funding, counterparty credit risk, capital and initial margin – has centred on swaps, often leaving products such as options on the sidelines because of the sheer complexity of estimating them correctly.

Typically, XVAs are calculated by taking the expected positive exposures of a derivative at future points in time and then applying the relevant costs to that exposure – a funding spread is applied to calculate the funding valuation adjustment (FVA), for instance – and using appropriate discount factors to arrive at a present value.

In the case of products with optionality, this has one serious flaw.

American options and Bermudan swaptions pricing, for instance, is based on payoffs that can be achieved depending on whether the option is exercised at a given date or not. This is reflected in the so-called exercise boundary of the option, which shows the optimal exercise price over time. However, the XVA calculation for these products is applied after the payoff is estimated, therefore leaving a key cost component out of the decision to exercise an option at a given time. In swaptions, for example, the decision to exercise the option to enter into a swap is based on an XVA-free exercise value. 

“Existing models take the exercise decision based on XVA-free underlying and continuation values, where XVA really means portfolio XVA. XVA adjustments to an option portfolio are only applied at a later stage, when the exercise decision is already made. Clearly, there is no established standard to compute option values with XVA-corrected exercise in the market,” says Peter Caspers, a senior quantitative analyst at advisory Quaternion Risk Management in Germany.

This can result in the mispricing of these products, argues Andrew Green, a managing director and lead XVA quant at Scotiabank in London. “XVAs are reflected partially in the price, but unless you reflect it in the exercise boundary you won’t get the correct price.”

In this month’s first technical, XVA at the exercise boundary, Green, and co-author Chris Kenyon, head of XVA quantitative research at Lloyds Banking Group, propose a way to factor XVAs into options exercise values, thereby making the pricing of these products more accurate. 

What we are potentially layering on top is a second regression to determine where the exercise occurs, accounting for the impact of XVAs
Andrew Green, Scotiabank

The quants calculate an adjustment to modify the exercise values of the option so it is part of the pricing of the derivative. The XVA adjustments are calculated using a regression to get their forward conditional expected values at exercise dates. Once these are available, they can be plugged into a backward Monte Carlo simulation – typically used for pricing complex products with optionality – as adjustments to the exercise value. At each exercise date, a decision must be made on whether the option should be exercised or not. If expected XVA costs are added to the exercise value, it influences the exercise decision and in turn, the pricing simulation. 

“What we are potentially layering on top is a second regression to determine where the exercise occurs, accounting for the impact of XVAs. In a sense, it is using elements of both current XVA techniques and the more traditional use of regression to determine exercise boundaries,” says Green.

The only caveat is that they are able to do this for single deals, whereas XVAs are typically calculated at the netting set or portfolio level. For netting sets, one would have to consider the exercise values of all trades; this is not straightforward to simulate, says Scotiabank’s Green. 

Using their technique, Green and Kenyon find the XVAs on an unsecured 5x5 physically settled European swaption can be multiples of the swap delta – or the sensitivity of the derivative to its underlying – which is a key part of pricing and hedging strategy. The implied volatility smile of the swaption also shifts significantly. Below the at-the-money strike, the smile falls to zero, showing there is no possible way of making money from exercising the option at that point if XVAs are accounted for.

The numbers are significant, and show how important it is to factor costs correctly, even if it brings in additional complexity. In the case of credit valuation adjustment (CVA), for instance, which has been around for more than a decade, Standard Chartered took a $712 million loss due to a change in its valuation methodology in 2015.

After years of multi-billion dollar losses and heavy investment in valuation engines and skillsets, dealers might find it impossible to think of more ways to complicate XVAs. However, ignoring a known effect because of its complexity could create problems down the line. Exercising options that are not profitable once XVAs are factored in is one example of that.  

Even if it takes some time to develop fast techniques to accurately price XVAs into options at portfolio or netting set level as opposed to trade-level, Kenyon and Green’s work at least kick-starts the debate on a known problem that has largely been ignored.

Click here to view our second technical paper for February, Identification and capitalisation of non-modellable risk factors.

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