Related papers: Digital double barrier options: Several barrier pe…
For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as…
It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
In this paper, we price American-style Parisian down-and-in call options under the Black-Scholes framework. Usually, pricing an American-style option is much more difficult than pricing its European-style counterpart because of the…
We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multi-variate generalization of the Black-Scholes model. While there is no gap…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
In this paper we present a very simple way to price a class of barrier options when the underlying process is driven by a huge class of L\'evy processes. To achieve our goal we assume that our market satisfies a symmetry property. In case…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
Option written on several foreign exchange rates (FXRs) depends on correlation between the rates. To evaluate the option, historical estimates for correlations can be used but usually they are not stable. More significantly, pricing of the…
In this paper we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage…
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…
Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. A better understanding of these fluctuations can greatly benefit crypto…
The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we…
In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…