Most interest rate models in mathematical finance are based on stochastic calculus.
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Improving the accuracy by capturing more information from data and simulating interest rates by using the powerful tools of quantum field theory are the main advantages of quantum finance. Coupon bond and forward interest rates have been extensively studied in Ref. Numerical simulations of forward interest rates and pricing European and barrier options are studied in this paper using the approach of quantum finance. As shown in Eq.
The exact price of the zero-coupon barrier option is given by Ref. Simulation of coupon bond European and barrier options in quantum finance. Jan The sensitivity analysis of propagator for path independent quantum finance model. Mar Fuel Energ Abstr. Sep J Chem Phys. Get access to 30 million figures. Join for free.
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This is an asset class distinct from the existing coupon bonds. The index-linked coupon bond is an example of a sukuk, which is an instrument that implements one of the cornerstones of Islamic finance Askari et al.
The index-linked coupon bond is defined using the mathematical framework of quantum finance Baaquie, , The coupons are stochastic, with the quantum of coupon payments depending on a publicly traded index that is chosen to reflect the primary drivers of the revenues of the issuer of the bond.
The index ensures there is information symmetry — regarding the quantum of coupon being paid — between issuer and investor. The dependence of the coupon on the index is designed so that the variation of the index mirrors the changing fortunes of the issuer, with the coupon's quantum increasing for increasing values of the index and conversely, decreasing with a fall of the index. Option price and market instability. An option pricing formula, for which the price of an option depends on both the value of the underlying security as well as the velocity of the security, has been proposed in Baaquie and Yang The FX foreign exchange options price was empirically studied in Baaquie et al.
The option price proposed in Baaquie and Cao Yang did not fit the data during the crisis of — The market prices of the FX option for various currencies are studied in the light of our hypothesis. Jan The economic crisis of 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.
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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, 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. Pricing American put option on zero-coupon bond in a jump-extended CIR model. Full-text available. This paper presents a jump extension to the CIR model of the short interest rate with exponential distribution jumps. We derive an approximated price of an American put option on a defaultable-free, zero-coupon bond using the two-GJ approach based on combining an European put option and a Bermudan option with two possible exercise dates.
Closed-form solutions for both the European put option and the Bermudan option are obtained by using multivariate Fourier transforms and characteristic functions. The accuracy and efficiency of the approximation are examined using the least-square Monte Carlo simulation as the benchmarks. Finally several numerical examples illustrating the results have been presented and the prices have been compared to the corresponding prices for American option in the pure diffusion model.
The sensitivity analysis of propagator for path independent quantum finance model. Mar Fuel Energ Abstr.
- Pricing American options for interest rate caps and coupon bonds in quantum finance | Request PDF.
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Quantum finance successfully implements the imperfectly correlated fluctuation of forward interest rates at different maturities, by replacing the Wiener process with a two-dimensional quantum field. Interest rate derivatives can be priced at a more realistic value under this new framework.
Pricing American options for interest rate caps and coupon bonds in quantum finance
The quantum finance model requires three main ingredients for pricing: However, the hedging strategy only focused on fluctuation of forward interest rates. This hedging method is based on the assumption that the propagator, the covariance of forward interest rates, has an ergodic property. Since inserting the propagator is the main characteristic that distinguishes quantum finance from the Libor market model LMM and the Heath, Jarrow and Morton HJM model, understanding the impact of propagator dynamics on the price of interest rate derivatives is crucial.
This research is the first step in developing a hedge strategy with respect to the evolution of the propagator. We analyze the dynamics of the propagator from Libor futures data and the integrated propagator from zero-coupon bond rate data. Then we study the sensitivity of the implied volatility of caplets and swaptions according to the three dominant dynamics of the propagator, and the change of the zero-coupon bond option price according to the two dominant dynamics of the integrated propagator.
Dynamics of implied volatility surfaces from random matrix theory. We analyze the dynamics of the implied volatility surface of KOSPI futures options from random matrix theory. To extract the informative data, we use random matrix criteria. Implied volatility data have a colossal eigenvalue, and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction. We discern the marketwide knowledge of the implied volatility surface movement such as the level, skew, and smile effect. These dynamics has the ergodic property and long range autocorrelation.
We also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics, and confirm the existence of leverage effect even in the short time interval. Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet. The industry standard for pricing an interest-rate caplet is Black's formula. Another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates.
An empirical study is carried out to compare the two caplet pricing formulae. Historical volatility and correlation of forward interest rates are used to generate the field theory caplet price; another approach is to fit a parametric formula for the effective volatility using market caplet price.
The study shows that the field theory model generates the price of a caplet and cap fairly accurately. Black's formula for a caplet is compared with field theory pricing formula. It is seen that the field theory formula for caplet price has many advantages over Black's formula. An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of options, including those with path-dependent and early exercise features.
As examples, the application of the method to European and American options in the Black-Scholes model is illustrated.
A particularly simple and fast semi-analytical approximation for the price of American options is derived. The results of the algorithm are compared with those obtained with the standard procedures known in the literature and found to be in good agreement. The main result of this paper is that a martingale evolution can be chosen for LIBOR such that, by appropriately fixing the drift, all LIBOR interest rates have a common market measure.
LIBOR is described using a quantum field theory model, and a common measure is seen to emerge naturally for such models. To elaborate how the martingale for the LIBOR belongs to the general class of numeraires for the forward interest rates, two other numeraires are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale.