Related papers: Local Variance Gamma and Explicit Calibration to O…
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the…
We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices.…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. 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 develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time…
This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime…
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a…
The paper builds a Variance-Gamma (VG) model with five parameters: location ($\mu$), symmetry ($\delta$), volatility ($\sigma$), shape ($\alpha$), and scale ($\theta$); and studies its application to the pricing of European options. The…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential…
We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary…
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options…
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…
We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results…
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the…
We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The…