Related papers: Long-term option pricing with a lower reflecting b…

The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss…

Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process {\xi} with memory as e.g. a L\'evy semi-stationary process.…

We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient…

In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date…

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…

This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional…

Option pricing theory, such as the Black and Scholes (1973) model, provides an explicit solution to construct a strategy that perfectly hedges an option in a continuous-time setting. In practice, however, trading occurs in discrete time and…

Consider an American option that pays G(X^*_t) when exercised at time t, where G is a positive increasing function, X^*_t := \sup_{s\le t}X_s, and X_s is the price of the underlying security at time s. Assuming zero interest rates, we show…

We present a neural-network valuation of financial derivatives in the case of fat-tailed underlying asset returns. A two-layer perceptron is trained on simulated prices taking into account the well-known effect of volatility smile. The…

In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only the absence of arbitrage opportunities. We formulate this as…

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…

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including…

This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…

This paper deals with the problem of discrete-time option pricing by the mixed fractional version of Merton model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option…

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…

We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…

We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…

This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…

We consider approximate pricing formulas for European options based on approximating the logarithmic return's density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as…