Related papers: Pricing under the Benchmark Approach
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…
This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
Optimal pricing of European call option is described by linear stochastic differential equation. Trading strategy given by a twin of stochastic variables was integrated w.r.t. Black-Scholes formula to adopt optimal pricing to tarading…
We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices.…
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C…
This paper presents a framework of imitating the principal investor's behavior for optimal pricing and hedging options. We construct a non-deterministic Markov decision process for modeling stock price change driven by the principal…
We present an approach for pricing European call options in presence of proportional transaction costs, when the stock price follows a general exponential L\'{e}vy process. The model is a generalization of the celebrated work of Davis,…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…
We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark's, subject to a…
A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted…
This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional…