17 research outputs found
Valuing T-year contingent options
Invited speakerWe consider the problem of valuing Guaranteed Minimum Death Benefits (GMDB) in various variable annuity and equity-indexed annuity contracts. We assume that the life contingent options will expire at a fixed time T. By using a discounted density function approach, we provide closed for expressions for the values of the contingent options. In particular we show that the results in Ulm (2008) can be obtained easily using our approach. This talk is based on a joint paper with Hans Gerber and Elias Shiu.postprin
On the distribution of the time-integral of the geometric Brownian motion
We study the numerical evaluation of several functions appearing in the small
time expansion of the distribution of the time-integral of the geometric
Brownian motion as well as its joint distribution with the terminal value of
the underlying Brownian motion. A precise evaluation of these distributions is
relevant for the simulation of stochastic volatility models with log-normally
distributed volatility, and Asian option pricing in the Black-Scholes model. We
derive series expansions for these distributions, which can be used for
numerical evaluations. Using tools from complex analysis, we determine the
convergence radius and large order asymptotics of the coefficients in these
expansions. We construct an efficient numerical approximation of the joint
distribution of the time-integral of the gBM and its terminal value, and
illustrate its application to Asian option pricing in the Black-Scholes model
Simulation schemes for the Heston model with Poisson conditioning
Exact simulation schemes under the Heston stochastic volatility model (e.g.,
Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified
Bessel function evaluations. We propose a new exact simulation scheme without
the modified Bessel function, based on the observation that the conditional
integrated variance can be simplified when conditioned by the Poisson variate
used for simulating the terminal variance. Our approach also enhances the
low-bias and time discretization schemes, which are suitable for pricing
derivatives with frequent monitoring. Extensive numerical tests reveal the good
performance of the new simulation schemes in terms of accuracy, efficiency, and
reliability when compared with existing methods
On an efficient multiple time step Monte Carlo simulation of the SABR model
In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options
A comprehensive literature review on pricing equity warrants using stochastic approaches
Prior literature's revealed that most researchers tend to employ the Black Scholes model to
price equity warrants. However, the Black Scholes model was found deficient by contributing to large
estimation errors and mispricing of equity warrants. Therefore( issues revolving equity warrants are discussed in this paper, by focusing on specific topics and respective stochastic models to provide a basis for improvements in future research. In recent years, stochastic approaches had been used to a great extent among researchers due to the expansive applications in both theoretical and practical sense. Subsequently, this paper provides the results of a comprehensive literature review on various
stochastic modelling methods and its applications for pricing financial derivatives in terms of
applications, modifications of methods, comparisons with other methods, and general related researches. Focus is given on two types of stochastic mod~ls namely stochastic volatility and
stochastic interest rate models; along with the discussions associating these two types of models.
This paper acts as a valuable source of information for academic researchers and practitioners not only for pricing financial instruments, but also in various other fields involving stochastic techniques
Dynamic hybrid pricing formulation for equity warrants
Equity warrants are instruments issued by a company that give the stockholder the privilege of buying a stock at a certain strike price within a particular timeframe. Motivated by empirical studies, the Black-Scholes option pricing model is not suitable to price a warrant since both assumptions of constant volatility and constant interest
rates in the model are incompatible. This study proposed the Heston-Cox-Ingersoll- Ross (Heston-CIR) hybrid model to identify the effects of stochastic volatility and stochastic interest rates in pricing equity warrants. The study constructed new analytical pricing formulas for equity warrants by using Cauchy transformation and partial differential equation approaches. The local optimization method is employed to obtain the estimated parameter values by calibrating the Heston-CIR model. The effectiveness of the proposed model is investigated through the empirical study using the data from
Bursa Malaysia. The proposed model shows significant improvement on the computation time in estimating nine model parameters, ranging from 38.12 to 62.62 seconds compared to the existing models. Moreover, the empirical study suggested that the proposed model is accurate when compared to the real market over five years
period. This model also produced smallest pricing errors among the existing models. The finding also suggested equity warrants in moneyness opportunity, 88.75% of the warrants are profitable. In conclusion, the proposed model performs the best in identifying the effects of stochastic volatility and stochastic interest rates in pricing
equity warrants