Related papers: Remark on repo and options
We consider options that pay the complexity deficiency of a sequence of up and down ticks of a stock upon exercise. We study the price of European and American versions of this option numerically for automatic complexity, and theoretically…
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival'…
Presented is intuitive proof of Black-Scholes formula for European call options, which is based on arbitrage and properties of lognormal distribution. Paper can help students and non-mathematicians to better understand economic concepts…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
Prices of European call options in a regime-switching local volatility model can be computed by solving a parabolic system which generalises the classical Black and Scholes equation, giving these prices as functionals of the local…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning…
We study some properties of the American option price in the stochastic volatility Heston model. We first prove that, if the payoff function is convex and satisfies some regularity assumptions, then the option value function is increasing…
This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but…
We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE…
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 consider arbitrage free valuation of European options in Black-Scholes and Merton markets, where the general structure of the market is known, however the specific parameters are not known. In order to reflect this subjective uncertainty…
This work illustrates how several new pricing formulas for exotic options can be derived within a Levy framework by employing a unique pricing expression. Many existing pricing formulas of the traditional Gaussian model are obtained as a…
In the paper, the pricing of Quanto options is studied, where the underlying foreign asset and the exchange rate are correlated with each other. Firstly, we adopt Bayesian methods to estimate unknown parameters entering the pricing formula…
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 give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…