Journal•ISSN: 1945-497X
Siam Journal on Financial Mathematics
Society for Industrial and Applied Mathematics
About: Siam Journal on Financial Mathematics is an academic journal published by Society for Industrial and Applied Mathematics. The journal publishes majorly in the area(s): Stochastic volatility & Computer science. It has an ISSN identifier of 1945-497X. Over the lifetime, 465 publications have been published receiving 10308 citations. The journal is also known as: Society for Industrial and Applied Mathematics journal on financial mathematics & Journal on financial mathematics.
Topics: Stochastic volatility, Computer science, Volatility (finance), Implied volatility, Portfolio
Papers
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TL;DR: A family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion is analyzed, showing that a simple model variant can capture the default clustering implied by index and tranche market prices during September 2008, a month that witnessed significant volatility.
Abstract: This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are self- and cross-exciting and facilitate the description of complex event dependence structures. ODEs characterize the transform of an affine point process and the probability distribution of an integer-valued affine point process. The moments of an affine point process take a closed form. This guarantees a high degree of computational tractability in applications. We illustrate this in the context of portfolio credit risk, where the correlation of corporate defaults is the main issue. We consider the valuation of securities exposed to correlated default risk and demonstrate the significance of our results through market calibration experiments. We show that a simple model variant can capture the default clustering implied by index and tranche market prices during September 2008, a month that witnessed significant volatility.
306 citations
TL;DR: In this article, two projection techniques to derive affine approximations of the original Heston model are presented, which can prescribe a nonzero correlation structure between all underlying processes and can therefore be used for fast calibration of the hybrid model.
Abstract: We discuss the Heston model [Rev. Financ. Stud., 6 (1993), pp. 327-343] with stochastic interest rates driven by Hull-White (HW) [J. Derivatives, 4 (1996), pp. 26-36] or Cox-Ingersoll-Ross (CIR) [Econometrica, 53 (1985), pp. 385-407] processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these approximations we can prescribe a nonzero correlation structure between all underlying processes. The affine approximate models admit pricing basic derivative products by Fourier techniques [P. P. Carr and D. B. Madan, J. Comput. Finance, 2 (1999), pp. 61-73, F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848] and can therefore be used for fast calibration of the hybrid model.
185 citations
TL;DR: In this paper, a new formula for general spread option pricing based on Fourier analysis of the payoff function is introduced, which is easy to implement, stable, efficient, and applicable in a wide variety of asset pricing models.
Abstract: Spread options are a fundamental class of derivative contracts written on multiple assets and are widely traded in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient, and flexible enough to apply in general asset models. The present paper introduces a new formula for general spread option pricing based on Fourier analysis of the payoff function. Our detailed investigation, including a flexible and general error analysis, proves the effectiveness of a fast Fourier transform implementation of this formula for the computation of spread option prices. It is found to be easy to implement, stable, efficient, and applicable in a wide variety of asset pricing models.
184 citations
TL;DR: A Hamilton-Jacobi-Bellman equation is constructed for the optimal cost and strategy of mean-variance optimal agency execution strategies for varying risk aversion and these strategies adapt optimally to the instantaneous variations of market quality.
Abstract: We consider the problem of mean-variance optimal agency execution strategies, when the market li- quidity and volatility vary randomly in time. Under specific assumptions for the stochastic processes satisfied by these parameters, we construct a Hamilton-Jacobi-Bellman equation for the optimal cost and strategy. We solve this equation numerically and illustrate optimal strategies for varying risk aversion. These strategies adapt optimally to the instantaneous variations of market quality.
169 citations
TL;DR: An optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time is constructed, to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency.
Abstract: We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limit-order book that determines the price The limit-order book is permitted to have arbitrary shape The form of the optimal execution strategy is to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency At the end of this period, another lump purchase is made, and following that there is again a period of purchasing continuously at a rate set to match the order book resiliency At the end of this second period, there is a final lump purchase Any of the lump purchases could be of size zero A simple condition is provided that guarantees that the intermediate lump purchase is of size zero
167 citations