We extend back to 1890 the volatility implied by options index (VIX), available only since 1986, using the frequency of words on the front-page of the Wall Street Journal. News implied volatility (NVIX) captures well the disaster concerns of the average investor over this longer history. NVIX is particularly high during stock market crashes, times of policy-related uncertainty, world wars and f...

This note explores the behaviour of the implied volatility of a European call option far frommaturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.

A few recent papers have derived estimates of the representative agent's risk aversion by comparing the statistical density of asset returns and the state-price density. The implied risk aversion estimates obtained in these studies are puzzling, exhibiting (i) pronounced U-shaped patterns (a smile ) and (ii) negative values. This paper analyzes three potential explanations for these phenomena: ...

J ia n Su n is an executive director at a large financial institution in N ew York, NY. [email protected] C onsider a call swaption m aturing at tim e T > 0 w ritten on an underly ing swap m aturing at a later tim e T' > T. Let A t(T,T') be the spot price at time t e [0,T] o f a forward­ starting annuity whose payments begin at T and end at T'. Let F (T ,T ') be the forward swap rate at tim e...