Firm-specific risk-neutral distributions with options and CDS

BIS Working Papers  |  No 921  | 
19 January 2021



Investors can extract information about future stock returns from options. Unlike those on equity indices, options on individual companies are often illiquid and are typically useful for learning about only the central part of the return distribution. Other derivatives known as credit default swaps (CDS) can shed light on the probability of extreme returns. However, investors have limited insights on the probability of intermediate returns, which are larger (in absolute value) than those for which options are informative but smaller than extreme returns for which CDS are relevant.


We develop a method that combines options and CDS to better characterise the full distribution of expected stock returns. We assess whether investors value the additional information about intermediate returns with a series of asset pricing tests.


Relative to using options only, blending options and CDS can capture important company-specific information more efficiently. Stock portfolios based on differences between options/CDS and options-only estimates of expected returns earn a substantial risk premium. We can conclude that investors value the information we unlock with our methodology.


We propose a method to extract the risk-neutral distribution of firm-specific stock returns using both options and credit default swaps (CDS). Options and CDS provide information about the central part and the left tail of the distribution, respectively. Taken together, but not in isolation, options and CDS span the intermediate part of the distribution, which is driven by exposure to the risk of large but not extreme returns. Through a series of asset-pricing tests, we show that this intermediate-return risk carries a premium, particularly at times of heightened market stress.

JEL Codes: G12, G13, G14

Keywords: risk neutral distributions, investor expectations, CDS spreads