In this paper, we present a new strategy for pricing average value options, i.e. options whose payoff depends on the average price of the underlying asset over a fixed period leading up to the maturity date. Such options are of particular interest and importance for thinly-traded assets (e.g. crude oil), since price manipulation is inhibited, and both the investor and issuer enjoy a welcome degree of protection from the vagaries of the market. These options are often implicit in a bond contract, although they also appear in a straightforward form. Our results suggest that the price of an average-value option will always be lower than that of a standard European option. Our pricing strategy involves Monte Carlo simulation with variance reduction elements and offers an enhanced pricing method to both arbitragers and hedgers, as well as to the issuers of such bonds.

A Pricing Method for Options Based on Average Asset Values

In this paper, we study Heston-CIR model with the double exponential jumps. We first verify the existence and uniqueness of the solution related to the price process of the model. Next, we calibrat...

Pricing multi-asset American option under Heston-CIR diffusion model with jumps

‎The Black-Scholes equation is one of the most important mathematical models in option pricing theory, but this model is far from market realities and cannot show memory effect in the financial market. This paper investigates an American option based on a time-fractional Black-Scholes equation under the constant elasticity of variance (CEV) model, which parameters of interest rate and dividend yield supposed as deterministic functions of time, and the price change of the underlying asset follows a fractal transmission system. This model does not have a closed-form solution; hence, we numerically price the American option by using a compact difference scheme. Also, we compare the time-fractional Black-Scholes equation under the CEV model with its generalized Black-Scholes model as α = 1 and β = 0. Moreover, we demonstrate that the introduced difference scheme is unconditionally stable and convergent using Fourier analysis. The numerical examples illustrate the efficiency and accuracy of the introduced difference scheme.

https://cmde.tabrizu.ac.ir/article_10335_264b729cd71d9f412f817b6d5634349e.pdf

A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options

CEV model equipped with the long-memory

In this paper, we propose an approximation method based on Picard iterations deduced from the Doleans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g. solutions to non-Lipchitz SDEs. An application to the pricing of Asian-style contingent claims in the CEV model is presented and compared to other methods of the literature.

/pdf/approximation-of-non-lipschitz-sdes-by-picard-iterations-3p4an8l7fe.pdf

Approximation of non-Lipschitz SDEs by Picard iterations

One of the financial model with nonconstant volatiltiy is the constant elasticity of varinace model, or CEV model for short. The CEV model is an altrnative to the Black–Scholes model of stock price movements. In this diffusion process, unlike the Black–Scholes model, the volatility is a function of the stock price and involves two parameters. In this article, we propose an efficient Monte-Carlo algorithm for pricing arithmetic Asian option under CEV model. In an earlier work by Mehrdoust, an efficient Monte Carlo simulation algorithm for pricing arithmetic Asian options under Black–Scholes model is proposed. The proposed algorithm has proved extremely successful in decreasing the standard deviation and the error of simulation in pricing of the arithmetic Asian options. In this article, we find that the proposed algorithm under the geometric Brownian motion assumption in the Black–Scholes model can effectively apply for pricing arithmetic Asian options when the stock price process follows the CEV m...

Efficient Monte Carlo option pricing under CEV model

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Efficient Monte Carlo option pricing under CEV model