Related papers: Lower Bound Approximation to Basket Option Values …
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas…
This paper addresses the approximation of the local volatility function in the Cheyette interest rate model. Its main contribution is an explicit analytical formula for approximating local volatility, derived by extending the classical…
We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular,…
This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…
This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A…
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by…
The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most…
Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…
A parsimonious generalization of the Heston model is proposed where the volatility-of-volatility is assumed to be stochastic. We follow the perturbation technique of Fouque et al (2011, CUP) to derive a first order approximation of the…
We derive the short-maturity asymptotics for European and VIX option prices in local-stochastic volatility models where the volatility follows a continuous-path Markov process. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics…
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
In this article, we present an approach which allows to take into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associeted options. Specifically, the marginal distribution of…
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is…