The Federal Reserve Bank of New York works to promote sound and well-functioning financial systems and markets through its provision of industry and payment services, advancement of infrastructure reform in key markets and training and educational support to international institutions.
The Outreach & Education function engages, empowers and educates the public in the Second District. Our outreach mission furthers the Bank’s commitment to the region by listening to the communities we serve and developing programs, analysis and sponsored conferences and clinics to help meet their needs. Our education mission aims to advance public knowledge about the Federal Reserve System and its role in the economy.
In this paper, I derive and implement a nonparametric, arbitrage-free technique for multivariate contingent claim (MVCC) pricing. Using results from the method of copulas, I show that the multivariate risk-neutral density can be written as a product of marginal risk-neutral densities and a risk-neutral dependence function. I then develop a pricing technique using nonparametrically estimated marginal risk-neutral densities (based on options data) and a nonparametric dependence function (based on historical return data). By using nonparametric estimation, I avoid the pricing biases that result from incorrect parametric assumptions such as lognormality.
I apply this technique to estimate the joint risk-neutral density of euro-dollar and yen-dollar returns. I compare the nonparametric risk-neutral density with density based on a lognormal dependence function and nonparametric marginals. The nonparametric euro-yen risk-neutral density has greater volatility, skewness, and kurtosis than the density based on a lognormal dependence function. In a comparison of pricing accuracy for euro-yen futures options, I find that the nonparametric model is superior to the lognormal model.