Pricing Interest Rate Derivatives in a Negative Yield Environment

Abstract: The main purpose of this thesis is to price interest rate derivatives in the today negative yield environment. The plain vanilla interest rate derivatives have now negative strikes and negative values of the underlying asset, the forward rate. The Black’76 model fails because of its assumption of log-normal distribution of the underlying that does not allow the underlying to be negative. The normal model gives a solutions to this problem since it assumes the underlying being normally distributed and then it can takes every value also negative. The shifted Black model has the same hypothesis of the Black-Scholes model but it adds a shift value in order to overcome the issue generated by the negativity of the strike values and of the current forward rate, with the only restrictions that the sum of the shift and the strike and the sum between the underlying value and the strike are positive. The shifted SABR model is used to find the shifted black volatilities for different strikes to plug later on the shifted Black formula to price interest rate derivatives. A comparison between the models and a brief analysis on delta hedge strategies are made.