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We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We propose a robust hypothesis testing procedure for the predictability of multiple predictors that could be highly persistent. Our method improves the popular extended instrumental variable (IVX) testing (Phillips and Lee, 2013; Kostakis…
We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the…
We present an agent behavior based microscopic model that induces jumps, spikes and high volatility phases in the price process of a traded asset. We transfer dynamics of thermally activated jumps of an unexcited/ excited two state system…
In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when…
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
In this three-part series of papers, we argue that the conventional spread measures are not well defined for credit-risky bonds and introduce a set of credit term structures which correct for the biases associated with the strippable cash…
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula.…
We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for…
We study the behavior of the critical price of an American put option near maturity in the Jump diffusion model when the underlying stock pays dividends at a continuous rate and the limit of the critical price is smaller than the stock…
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…
The paper uses functional auto-regression to predict the dynamics of interest rate curve. It estimates the auto-regressive operator by extending methods of the reduced-rank auto-regression to the functional data. Such an estimation…
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We…