Implied Risk-neutral Probability Density Functions From Option Prices: Theory and Application

The pricing kernel puzzle: survey and outlook

“…Rosenberg and Engle (2002), BaroneAdesi, Engle, and Mancini (2008), Barone-Adesi and Dall'O (2010)). Estimation of the riskneutral distribution is by now a well-established field of research and a large literature covers it; see the surveys by Jackwerth (1999), Jackwerth (2004), and Bahra (1997). Given a large enough cross section (more than 10 option strike prices), most methods perform relatively similar and yield the desired risk-neutral distributions where one typically uses the SPX options on the S&P 500 index with typical maturities of 30 to 60 days.…”

“…First, national banks paid already attention to the riskneutral distribution, which can be backed out from index option prices, see e.g. Bahra (1997) for the Bank of England. Under the assumption of a representative investor with a power utility, Sarantopoulou-Chioureaa and Skiadopoulos (2015) back out time-varying riskaversion coefficients from data on S&P 500 index options.…”

Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density

“…Their construction extracts a risk-neutral density from actual option prices. Such a discretized density can be obtained in an involved way from actual market quotes for a set of options with similar strike prices and maturities [Jackwerth and Rubinstein (1996), Bahra (1997), Cakici and Foster(2002), Jackwerth and Rubinstein (2004)]. Some of the features that these implied binomial trees posses are: risk-neutral steps and price dependent local volatilities [we refer to Dumas, Fleming and Whaley (1998) for an empirical study of this latter feature].…”

Option-Implied Risk-Neutral Distributions and Risk Aversion

“…Four articles are available to the reader who wants a deeper understanding of these methods-Cont (1997), Bahra (1997), Jackwerth (1999), and Perignon and Villa (2002). Cont focused on methods for obtaining the riskneutral distributions, whereas the other surveys also covered applications.…”