Abstract
The article investigates the effects played on options pricing by negative risk-free rates when the underlying is an equity with null dividends. In such anomalous conditions, in fact, the fair value at early exercise of the American Call would not match the value of the European Call with the same financial features. We originally motivate this assumption with theoretical arguments. We then move to an empirical investigation where we put at work some quasi-closed formulas for pricing an American option and the stochastic trinomial trees algorithm. We then draw the conclusion that from a numerical viewpoint, the bias between the fair value of the American Call and the value of the corresponding. European Call is mainly due to approximation errors, which can be mitigated when Trinomial Stochastic Trees are used.
Highlights
As outlined in a recent note from the Actuarial Association of Europe [1], nowadays negative nominal interest rates for long term maturities are observable in both European and American financial markets
We move to an empirical investigation where we put at work some quasi-closed formulas for pricing an American option and the stochastic trinomial trees algorithm
We examined how the existing numerical schemes react in the pricing of an American Call option, in presence of anomalous conditions
Summary
As outlined in a recent note from the Actuarial Association of Europe [1], nowadays negative nominal interest rates for long term maturities are observable in both European and American financial markets. It is necessary to check to what extent the existing pricing models can be adapted to incorporate negative nominal. This aspect has been already investigated in some research papers: [3] and [4] discuss the issue for options written on interest rates, both from the practical and the theoretical viewpoint; [5], focusing on foreign exchange and index options investigate whether the use of models allowing for negative interest rates can improve option pricing and implied volatility forecasting; [6], discusses a new closed form for option pricing that leads to sensitively lower the error in European options pricing. The Hull and White model [9], has been recently adapted to calibrate in a more proper way when the underlying is a negative interest rate [10]; to the best of our knowledge, much less efforts have been devoted to model the effects of negative nominal interest rates in option pricing for other types of underlying
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