This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the...

In this paper, a closed form path-independent approximation of the fair variance strike for a variance swap under the constant elasticity of variance (CEV) model is obtained by applying the small disturbance asymptotic expansion. The realized variance is sampled continuously in a risk-neutral...

In this paper we introduce a new fast and accurate numerical method for pricing exotic derivatives when discrete monitoring occurs, and the underlying evolves according to a Markov one-dimensional stochastic processes. The approach exploits the structure of the matrix arising from the numerical...

The problem of pricing the variance swap when the underlying asset follows the CEV process is considered. A hedging argument is used to replicate the variance swap in part using the log contract. The price of the log contract is shown in practice to provide a fast and accurate pricing method for...

This paper studies the impact of stochastic volatility (SV) on optimal investment decisions. We consider three different SV models: an extended Stein/Stein model, the Heston Model and an extended Heston Model with a constant elasticity variance (CEV) process and derive the the long-term optimal...

We derive a closed-form expression for the stock price density under the modified SABR model [see section 2.4 in Islah (2009)] with zero correlation, for β = 1 and β 1, using the known density for the Brownian exponential functional for μ = 0 given in Matsumoto and Yor (2005), and then...

This paper discusses the pricing of geometric Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price geometric Asian options. We find that the binomial tree method for the...

Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretization is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case...

We apply a singular perturbation analysis to some option pricing models. To illustrate the technique we first consider the European put option under the standard Black-Scholes model, with or without barriers. Then we consider the same option under the constant elasticity of variance (CEV)...