Estimation of FX Option Implied Density Functions: Nonparametric-Malz Approach

This paper estimates risk-neutral density (RND) for USD-TRY exchange rate through the nonparametric-Malz approach using European FX options for various tenors and a wide range of tails. FX option implied risk-neutral density is a valuable tool in terms of extraction of market assessment about future exchange rates, valuation of financial derivatives, portfolio risk management and monitoring financial stability. However, RND estimation for FX options requires non-trivial data adjustment due to the fact that these options are traded/quoted as structured products in over-the-counter (OTC) markets and the conventions are in terms of deltas rather than strike prices. In this regard, one of the main contributions of the study is that premium-adjusted delta convention used in the quotation of options on USD-TRY exchange rate is taken into account in the construction of implied volatility-delta space, which has been overlooked in the previous studies. Absence of this adjustment leads to a biased estimation of the implied volatility curve and RND, especially at longer-maturity horizons. Empirical findings provide evidence for the existence of volatility smile for the options on USD-TRY exchange rate. Furthermore, the examination of RND surface in recent periods displays the variation in the dispersion of option implied distributions of USD-TRY exchange rate due to volatility in financial markets.