Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre
نویسندگان
چکیده
In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito’s lemma. An integral expression for the general solution of the PDE is presented by using Duhamel’s principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. We solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach is very competitive in terms of accuracy. Keyword: American Options, Fourier Transform, Laplace Transform, Method of Characteristics. JEL Classification: C61, D11 [email protected]; School of Finance and Economics, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia. [email protected]; Actuarial Studies, Australian School of Business, The University of New South Wales, Sydney, NSW 2052, Australia. 1
منابع مشابه
Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre
In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomi...
متن کاملTime-Inconsistent Stochastic Linear-Quadratic Control: Characterization and Uniqueness of Equilibrium
In this paper, we continue our study on a general time-inconsistent stochastic linear–quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward– backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the ...
متن کاملOptimal Stopping under Probability Distortion∗
We formulate an optimal stopping problem where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can t...
متن کاملQuantitative Finance Research Centre
We present the multi-factor quadratic reduced form model for pricing of credit risky securities. We use quadratic Gaussian processes to model the short term interest rate and the intensity of default showing that we get tractable formulas for the price of credit default swaps and credit default swaptions.
متن کامل