ORCID Profile
0000-0003-4201-055X
Current Organisation
Western Sydney University
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Publisher: Informa UK Limited
Date: 1984
Publisher: Informa UK Limited
Date: 20-05-2014
Publisher: Hindawi Limited
Date: 26-07-2015
DOI: 10.1155/2015/258217
Abstract: We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate with log-normal jump litudes and the volatility model with log-uniformly distributed jump litudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semianalytical formula for the price of the foreign exchange European call option.
Publisher: Journal of Mathematical Sciences and Modelling
Date: 30-12-2018
DOI: 10.33187/JMSM.432019
Abstract: We examine European call options in the jump-diffusion version of the Double Heston stochastic volatility model for the underlying price process to provide a more flexible model for the term structure of volatility. We assume, in addition, that the stochastic interest rate is governed by the Cox-- Ross -- Ingersoll (CIR) dynamics. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the European call option in the hybrid call option/interest rates model. Numerical results show that the model implied volatilities are comparable for in-s le but outperform out-of-s le implied volatilities compared to the benchmark Heston model[1], and Double Heston volatility model put forward by Christoffersen et al., [2] for calls on the S& P 500 index.
Publisher: Informa UK Limited
Date: 30-06-2014
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2009
DOI: 10.1142/S0219024909005166
Abstract: Forward start options are examined in Heston's (Review of Financial Studies6 (1993) 327–343) stochastic volatility model with the CIR (Econometrica53 (1985) 385–408) stochastic interest rates. The instantaneous volatility and the instantaneous short rate are assumed to be correlated with the dynamics of stock return. The main result is an analytic formula for the price of a forward start European call option. It is derived using the probabilistic approach combined with the Fourier inversion technique, as developed in Carr and Madan (Journal of Computational Finance2 (1999) 61–73).
Publisher: Cambridge University Press (CUP)
Date: 04-1997
DOI: 10.1017/S000497270003389X
Abstract: This paper is concerned with the filtering problem for a nonlinear stochastic system of prey-predator logistic equations. Based on the innovations approach, we establish the Zakai equation for the unnormalised conditional distribution and the adjoint Zakai equation for the unnormalised conditional density of the nonlinear filter. Using a perturbation technique, we obtain the appropriate expressions for the unnormalised conditional distribution and density of stochastic integrals with respect to the observation processes.
Publisher: Informa UK Limited
Date: 06-2013
Publisher: Springer International Publishing
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 02-02-2018
Publisher: Elsevier BV
Date: 05-2010
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2021
DOI: 10.1142/S2424786321500055
Abstract: This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].
Publisher: Cambridge University Press (CUP)
Date: 06-1996
DOI: 10.1017/S0004972700017135
Abstract: Sufficient conditions are obtained for the existence and global asymptotic stability of a periodic solution in Volterra's population system of integrodifferential equations with periodic coefficients. It is shown that if (i) the intraspecific negative feedbacks are instantaneous and dominate the interspecific effects (ii) the minimum possible growth rates are stronger than the maximum interspecific effects weighted with the respective sizes of all species, when they are near their potential maximum sizes, then the system of integrodifferential equations has a unique componentwise periodic solution which is globally asymptotically stable.
Publisher: World Scientific Pub Co Pte Lt
Date: 05-2008
DOI: 10.1142/S0219024908004804
Abstract: In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein–Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein–Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.
Publisher: Cambridge University Press (CUP)
Date: 06-1983
DOI: 10.1017/S0004972700025934
Abstract: Sufficient conditions which are verifiable in a finite number of arithmetical steps are derived for the existence and global asymptotic stability of a feasible steady state in an integro-differential system modelling the dynamics of n competing species in a constant environment with delayed interspecific interactions. A novel method involving a nested sequence of “asymptotic” upper and lower bounds is developed.
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2017
DOI: 10.1142/S242478631750013X
Abstract: We examine currency options in the double exponential jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semi-analytical formula for the price of the European currency call option in the hybrid foreign exchange/interest rates model.
No related grants have been discovered for Rehez Ahlip.