Editor’s Letter

Donald Trump became the 45th President of the United States less than one month ago. The United States and the rest of the world are floundering in a state of massive uncertainty. Major changes are under discussion, including abandonment of trade agreements, abolishing Obamacare (the Affordable Care Act), privatization of Social Security, and many more, but the dimensions of what is to come are as yet quite ill-defined. It is easy to focus just on the United States, but this huge uncertainty is hardly restricted to one country: Brexit launched the United Kingdom onto a path whose endpoint is hard to see. Other European countries are heading into elections that feature strong candidates on the right, who now view victory as more possible than ever before. The chaos in the Middle East is ongoing and continues to generate the largest flow of refugees across Europe since the 1940s. Indeed, it is hard to see stability anywhere.

And yet the U.S. stock market keeps hitting new all-time highs and the VIX (CBOE’s Volatility Index—the market’s “fear gauge”) is at rock bottom, at times falling below 11%. Whatever happened to risk aversion?

The November election featured a stark choice between what appeared to be two maximally different candidates. Clinton was a well-known quantity, with quite possibly the most extensive experience in government of any U.S. Presidential candidate ever. She offered continuity. Trump was primarily known to the public from a long series of debates and a popular television show that portrayed him as a highly skilled manager of major corporate enterprises. But with no experience in government at all, his big appeal to the voters was to be a “disrupter.” He would overturn a dysfunctional Washington establishment full of entrenched politicians and lobbyists who had lost touch with the American public.

The highly dichotomous nature of the choice echoes the increasingly polarized nature of the U.S. population. There is essentially no middle ground any more. Conservatives vote straight Republican and Progressives vote straight Democrat. In Washington, the eight years of the Obama administration featured repeated votes in which all Republicans voted one way and all Democrats voted the opposite. Legislative success largely consisted of blocking the other side’s initiatives, leading to constant stalemate even on things that would normally not be controversial, like raising the federal debt ceiling.

The Republicans’ landslide victory gave them not only the presidency but also control of both houses of Congress and a large majority of state governorships and legislatures. But Trump’s policy statements as a candidate were short on detail and often inconsistent with long-held Republican positions, so the Republicans in Congress have had a hard time agreeing with him, or with each other, and it is very much in question what direction future policy will actually follow. Will Congress be able to raise the debt ceiling by March 15 now that the Republicans have to do it themselves? Who knows?

So, how can the stock market be so upbeat? Well, the theory I have offered before about volatility continues to apply, which is that it is intrinsically different from uncertainty. That is, even though the level of uncertainty may be extreme, volatility refers to day-to-day price changes. Right now, new information flowing into the market is not resolving the uncertainty, so investors are getting no new evidence that they should change their expectations about stock returns. Measured volatility can be low at the same time that uncertainty is high.

But isn’t it a surprise that the stock market keeps going higher? Well, for Democrats and others who believe that a Trump presidency must be disastrous all around, including for the economy, it is a big surprise. With no hard evidence to back this opinion, I hypothesize that the majority of professional economists did not think a Trump victory, with its attendant reductions in taxes, regulations, and spending, would be good for the economy; certainly that was the opinion of many “armchair” economists. But thinking about the overall picture, the Democrat’s platform called for a minimum wage of $15 per hour, tax increases for the wealthy, continued and perhaps accelerated regulation of banking, Wall Street and the environment, and similar progressive policies. At first glance, this certainly suggests that the share of the national economic pie that goes to corporate profits may well increase. Even if the pie itself doesn’t end up growing much over time, with greater wealth flowing to those who own and buy stocks, higher stock prices should not be entirely surprising.

And what about risk aversion? Well, the non-Clinton voters wanted disruption. They demanded a regime shift. That is, a large portion of the electorate became political risk-lovers. Disruption means high volatility, and a regime shift entails a completely new economic and political order. But this means historical experience no longer gives much guidance about the future of the system. As they say in the prospectus: “Past performance is no guarantee of future results.”

Turning to this issue of The Journal of Derivatives, the lead article by Su, Chen, and Newton presents a derivatives valuation methodology that is extremely powerful and flexible but quite straightforward: quadrature. Quadrature starts by setting up a vector of discrete states for the underlying asset for each critical date in an option’s lifetime (or a matrix, when there are two or more stochastic state variables). For a European call, only a single date, expiration, is involved, while a Bermudan option with three early exercise dates would require four price vectors. Discretizing the transition probabilities allows option values at each date to be computed to a high degree of accuracy very efficiently. The authors demonstrate the method and show how to adapt it for option problems ranging from the simplest plain-vanilla Black–Scholes to a Heston jump-diffusion stochastic volatility specification.

In their article, Leblon and Moraux are concerned with modeling interest-dependent derivatives—options on coupon bonds in their case. They show how to extend to quadratic expressions, the closed-form model for coupon bond options when the short-term interest rate is a linear function of the underlying state variables.

Biktimirov and Wang consider model-free implied volatility (MFIV) as a forecast of future realized volatility and compare its performance with that of Black–Scholes IV and a GARCH (generalized autoregressive conditional heteroskedasticity) model. Across an international sample of 13 major stock markets, the best performer turns out to be the trusty Black–Scholes model.

The last two articles are concerned with the effect of counterparty credit risk on derivatives values. Nauta looks at FVA, funding valuation adjustment, which is supposed to adjust the reported value of an asset that is going to be financed in the money market for the expected future cost of funding, assuming the firm must pay a premium over the riskless interest rate. He observes that the proposed accounting treatment makes no distinction between liquid and illiquid assets, even though they have very different exposure in the case of a liquidity stress event. Nauta develops a more appropriate approach that takes into account assets’ different liquidity characteristics and the maturity of the funding versus the length of the expected holding period.

The final article by Escobar, Mahlstedt, Panz, and Zagst develops a general valuation model for a derivative instrument involving two risky counterparties who enter a derivative contract on a portfolio of other assets.

Back in the real world, we await further developments, with or without trepidation depending upon your political preferences. It will certainly be interesting to see what the future brings.

Hail to the Disrupter in Chief! ...and buckle your safety belts.

TOPICS: Options, quantitative methods, credit risk management

Stephen Figlewski

Editor

• © 2017 Pageant Media Ltd