Page 1

Displaying 1 – 13 of 13

Showing per page

A fuzzy approach to option pricing in a Levy process setting

Piotr Nowak, Maciej Romaniuk (2013)

International Journal of Applied Mathematics and Computer Science

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...

A priori error estimates for reduced order models in finance

Ekkehard W. Sachs, Matthias Schu (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...

Actuarial Approach to Option Pricing in a Fractional Black-Scholes Model with Time-Dependent Volatility

Adrian Falkowski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We study actuarial methods of option pricing in a fractional Black-Scholes model with time-dependent volatility. We interpret the option as a potential loss and we show that the fair premium needed to insure this loss coincides with the expectation of the discounted claim payoff under the average risk neutral measure.

An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model

Xin-Jiang He, Wenting Chen (2019)

Applications of Mathematics

We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown “no default” probability is derived first. It is shown that the “no default” probability is equivalent to the price of a down-and-out binary...

Analytical approximation of the transition density in a local volatility model

Stefano Pagliarani, Andrea Pascucci (2012)

Open Mathematics

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.

Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance

Łukasz Delong (2012)

Applicationes Mathematicae

We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target...

Asymptotics of riskless profit under selling of discrete time call options

A. V. Nagaev, S. A. Nagaev (2003)

Applicationes Mathematicae

A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.

Currently displaying 1 – 13 of 13

Page 1