Interest Rates and Coupon Bonds in Quantum Finance

Abstract

The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing on interest rates and coupon bonds, this book does not employ stochastic calculus – the bedrock of the present day mathematical finance – for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry.

Empirical analysis of quantum finance interest rates models

“…The quantum finance Libor Market Model of the Libor forward interest rates f L (t, x) and log Libor φ(t, x) are defined as follows [9,10] ∂f…”

“…Libor and Euribor give quite distinct values for the parameters; interest caplets yield parameters different than those obtained from the Libor data or from swaption data [9]. For hybrid instruments that straddle many instruments and markets, one needs to further develop the models considered so far.…”

“…The scaling factor is chosen to make σ (t, x) equal to the empirical volatility σ E (t, x) and yields, from Eq. (9) κ(θ ) = D(θ , θ )…”

Simulation of coupon bond European and barrier options in quantum finance

“…Quantum finance refers to the application of the theoretical and mathematical formalism of quantum mechanics and quantum field theory to problems arising in finance [3]. Models based on quantum finance are able to incorporate subtle correlations between interest rates for different maturities.…”

“…Coupon bond and forward interest rates have been extensively studied in Ref. [3], and the Hamiltonian formulations of European and barrier bond options have been studied in detail in Ref. [1].…”