Option Pricing on Backward-Looking Rates

Master thesis (2021)

Authors

L.H.Z. de Miranda Electrical Engineering, Mathematics and Computer Science

Contributors

C.W. Oosterlee Numerical Analysis - EEMCS (supervisor 1)
M. Keijzer Mathematical Physics - EEMCS (supervisor 2)
M. Möller Numerical Analysis - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Lisa de Miranda
Monte Carlo Hull-White model Black-Karasinski model Backward-looking rates Pricing kernel Trinomial trees
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Published Date

19-03-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This thesis is devoted to option pricing on backward-looking rates. For the last decades, interest rate products were often linked to IBOR rates. IBORs are short-term borrowing rates charged between global banks in the unsecured interbank market. The purpose of this thesis is to compare the Hull-White model to the Black-Karasinski model for the pricing of caps/floors on compounded rates. Both models are so-called short-rate models, which are widely used for interest rate modelling. Due to the IBOR reform, new products are expected to appear in the market. One type of these products is caps/floors linked to the new Risk-Free Rate (RFR). The new RFRs will be in-arrears backward-looking rates and, as a consequence, have an impact on the choice of pricing models.
This thesis considers caps/floors on the new compounded RFR rates. For both models various pricing techniques for caps/floors on compounded rates are investigated. For the Hull-White model, the pricing kernel approach and a Monte Carlo simulation are explored. The pricing kernel approach yields an analytic formula for caps/floors on compounded rates. This formula is also used for the comparison. For the Black-Karasinski model, the pricing kernel approach, the trinomial tree method and the Monte Carlo simulation are considered. The pricing kernel approach yields a semi-analytic formula for caps/floors on compounded rates. However, in practice the computation time of this semi-analytic formula turned out to be substantial. Further, despite the fast computation time of the trinomial tree for LIBOR caps/floors, the trinomial tree method is rather slow for the caps/floors on compounded rates. As a result, the Monte Carlo simulation is the most suitable pricing technique, along the three
explored methods, for caps/floors on compounded rates under the Black-Karasinski model. Therefore, the Monte Carlo simulation is used for pricing caps on compounded rates in the model comparison.
Since there exists no liquid market yet for caps/floors linked to the new RFR, the models are calibrated to a proxy market. First, the Black-Karasinski model is calibrated to the proxy market using a heuristic approach. This heuristic approach is chosen as a compromise between computation time and accuracy. Then, the Hull-White model is calibrated to the Black-Karasinski model using the stripping method. Having both models calibrated, the price of caplets/floorlets on compounded rates are calculated. Thereafter, these prices are inverted to Bachelier implied volatilities for a uniform comparison. From the comparison of the two models, a difference in Bachelier implied volatility is observed in a range of 4 to 4 bps. This is of one order less than the volatility itself.