30,130 research outputs found
Martingale Option Pricing
We show that our generalization of the Black-Scholes partial differential
equation (pde) for nontrivial diffusion coefficients is equivalent to a
Martingale in the risk neutral discounted stock price. Previously, this was
proven for the case of the Gaussian logarithmic returns model by Harrison and
Kreps, but we prove it for much a much larger class of returns models where the
diffusion coefficient depends on both returns x and time t. That option prices
blow up if fat tails in logarithmic returns x are included in the market
dynamics is also explained
Sequential Monte Carlo Methods for Option Pricing
In the following paper we provide a review and development of sequential
Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte
Carlo-based algorithms, that are designed to approximate expectations w.r.t a
sequence of related probability measures. These approaches have been used,
successfully, for a wide class of applications in engineering, statistics,
physics and operations research. SMC methods are highly suited to many option
pricing problems and sensitivity/Greek calculations due to the nature of the
sequential simulation. However, it is seldom the case that such ideas are
explicitly used in the option pricing literature. This article provides an
up-to date review of SMC methods, which are appropriate for option pricing. In
addition, it is illustrated how a number of existing approaches for option
pricing can be enhanced via SMC. Specifically, when pricing the arithmetic
Asian option w.r.t a complex stochastic volatility model, it is shown that SMC
methods provide additional strategies to improve estimation.Comment: 37 Pages, 2 Figure
Fractional constant elasticity of variance model
This paper develops a European option pricing formula for fractional market
models. Although there exist option pricing results for a fractional
Black-Scholes model, they are established without accounting for stochastic
volatility. In this paper, a fractional version of the Constant Elasticity of
Variance (CEV) model is developed. European option pricing formula similar to
that of the classical CEV model is obtained and a volatility skew pattern is
revealed.Comment: Published at http://dx.doi.org/10.1214/074921706000001012 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A generalization of Hull and White formula and applications to option pricing approximation
By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock prices. This extension will allow us to construct option pricing approximation formulas. Numerical examples are presented.Continuous-time option pricing model, stochastic volatility, Malliavin calculus
Black-Scholes option pricing within Ito and Stratonovich conventions
Options financial instruments designed to protect investors from the stock
market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton
proposed a very popular option pricing method using stochastic differential
equations within the Ito interpretation. Herein, we derive the Black-Scholes
equation for the option price using the Stratonovich calculus along with a
comprehensive review, aimed to physicists, of the classical option pricing
method based on the Ito calculus. We show, as can be expected, that the
Black-Scholes equation is independent of the interpretation chosen. We
nonetheless point out the many subtleties underlying Black-Scholes option
pricing method.Comment: 14 page
Option Pricing with Delayed Information
We propose a model to study the effects of delayed information on option
pricing. We first talk about the absence of arbitrage in our model, and then
discuss super replication with delayed information in a binomial model,
notably, we present a closed form formula for the price of convex contingent
claims. Also, we address the convergence problem as the time-step and delay
length tend to zero and introduce analogous results in the continuous time
framework. Finally, we explore how delayed information exaggerates the
volatility smile
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