The term structure of S&P 100 model-free volatilities

We develop an improved method to obtain the model-free volatility more accurately despite the limitations of a finite number of options and large strike price intervals. Our method computes the model-free volatility from European-style S&P 100 index options over a horizon of up to 450 days, the first time that this has been attempted, as far as we are aware. With the estimated daily term structure over the long horizon, we find that (i) changes in model-free volatilities are asymmetrically more positively impacted by a decrease in the index level than negatively impacted by an increase in the index level; (ii) the negative relationship between the daily change in model-free volatility and the daily change in index level is stronger in the near term than in the far term; and (iii) the slope of the term structure is positively associated with the index level, having a tendency to display a negative slope during bear markets and a positive slope during bull markets. These significant results have important implications for pricing and hedging index derivatives and portfolios.     

Pricing equity options everywhere

Finite difference methods are a popular technique for pricing American options. Since their introduction to finance by Brennan and Schwartz their use has spread from vanilla calls and puts on one stock to path-dependent and exotic options on multiple assets. Despite the breadth of the problems they have been applied to, and the increased sophistication of some of the newer techniques, most approaches to pricing equity options have not adequately addressed the issues of unbounded computational domains and divergent diffusion coefficients. In this article it is shown that these two problems are related and can be overcome using multiple grids. This new technique allows options to be priced for all values of the underlying, and is illustrated using standard put options and the call on the maximum of two stocks. For the latter contract, I also derive a characterization of the asymptotic continuation region in terms of a one-dimensional option pricing problem, and give analytic formulae for the perpetual case.     

Is convexity efficiently priced? Evidence from international swap markets

While it is widely claimed in the literature that convexity is correctly priced, we find evidence in four major swap markets that this is the case only on average and that extended periods occur when convexity-based trading strategies offer economically very significant exceptional returns. These abnormal returns can be reaped with fully no-peek-ahead strategies and after accounting for transaction costs. We find a strong link between the periods of highest profitability and conditions of reduced market liquidity. This suggests that, as observed in recent liquidity studies on US Treasuries, temporary deviations from market efficiency at the long end of the swap curve occur when pseudo-arbitrageurs do not have sufficient capital to correct the mispricings.     

Riding the swaption curve

We conduct an empirical analysis of the term structure in the volatility risk premium in the fixed income market by constructing long-short combinations of two at-the-money straddles for the four major swaption markets (USD, JPY, EUR and GBP). Our findings are consistent with a concave, upward-sloping maturity structure for all markets, with the largest negative premium for the shortest term maturity. The fact that both delta–vega and delta–gamma neutral straddle combinations earn positive returns that seem uncorrelated suggests that the term structure is affected by both jump risk and volatility risk. The results seem robust for macroeconomic announcements and the specific model choice to estimate the risk exposures for hedging.