Related papers: A fast Fourier transform method for Mellin-type op…
In this paper we derive semi-closed form prices of barrier (perhaps, time-dependent) options for the Hull-White model, ie., where the underlying follows a time-dependent OU process with a mean-reverting drift. Our approach is similar to…
We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are…
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…
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the…
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number…
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation…
The distribution of a time integral of geometric Brownian motion is not well understood. To price an Asian option and to obtain measures of its dependence on the parameters of time, strike price, and underlying market price, it is essential…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential…
Despite significant advancements in machine learning for derivative pricing, the efficient and accurate valuation of American options remains a persistent challenge due to complex exercise boundaries, near-expiry behavior, and intricate…
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian…
We consider the problem of computing upper and lower bounds on the price of a European basket call option, given prices on other similar baskets. Although this problem is very hard to solve exactly in the general case, we show that in some…
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale…
We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a…
We present a generative framework for pricing European-style basket options by learning the conditional terminal distribution of the log arithmetic-weighted basket return. A Mixture Density Network (MDN) maps time-varying market inputs…
In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial…