Marcos Carreira: Learning Interest Rate Interpolation

FULL TITLE

Learning Interest Rate Interpolation

ABSTRACT

The usual methods for interest rate interpolation consider only the values and time to maturity of spot rates as the inputs, and differ mainly on the continuity of the implied forward rates. We treat the interpolation problem as a replication problem, where a bond (or interest rate future/swap) is priced as a function of the minimum variance replicating portfolio of the traded bonds (or derivatives). In this view, the hedging ratios determined by the interpolation are as important (if not more) than getting the “right” interpolated rate; this is similar to the adjustments to the Black and Scholes delta as a consequence of the joint dynamics of the asset price and volatility in the different volatility models. We show how to learn the parameters of the weight functions and apply this method to the overnight rate indexed interest rates derivatives in Brazil. We then extend the concept from interpolating broken dates to the market references, in order to determine which points are key to the shape and dynamics of the curve and which points can be replicated by these real anchors.

BIO

Marcos C. S. Carreira, a PhD candidate at École Polytechnique, is the co-author of the book "Brazilian Derivatives and Securities: Pricing and Risk Management of FX and Interest-Rate Portfolios for Local and Global Markets". He was Derivative Products Officer and later Technical Modeling Officer at BM&FBovespa, where he contributed to risk management, derivatives pricing, exchange fees, microstructure and HFT functions. At Credit Suisse Brazil, he was a Managing Director in charge of the FX and IR Options desk, after being the Risk Manager responsible for Market, Counterparty and Liquidity Risks. Marcos holds an engineering degree from Instituto Tecnológico de Aeronáutica (ITA) and a Masters in Economics at Insper. Marcos also lectured for the MECAI Professional Masters course in Mathematical Finance at ICMC-USP and is a regular speaker at quantitative finance conferences.