Related papers: Black-Scholes without stochastics or PDEs
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally…
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…
We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment…
In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below…
Economists often estimate models using data from a particular domain, e.g. estimating risk preferences in a particular subject pool or for a specific class of lotteries. Whether a model's predictions extrapolate well across domains depends…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
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…
Traders and investors involved in an option contract having the underlying stock in range bound are likely to lose their initial investment. Timing in buying an option contract is of capital importance. In a recent article [1] the…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask…
This paper examines a class of barrier options-multi-step barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression of option prices of this type under the Black-Scholes model.…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our…
The Black-Scholes theory of option pricing has been considered for many years as an important but very approximate zeroth-order description of actual market behavior. We generalize the functional form of the diffusion of these systems and…
We present a new high-order compact scheme for the multi-dimensional Black-Scholes model with application to European Put options on a basket of two underlying assets. The scheme is second-order accurate in time and fourth-order accurate in…
This paper studies the entropy of tree-shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree-shift of finite type is equivalent to solving a system of nonlinear recurrence equations.…