2,543 research outputs found
Pricing volatility derivatives under the modified constant elasticity of variance model
© 2015 Elsevier B.V. All rights reserved. This paper studies volatility derivatives such as variance and volatility swaps, options on variance in the modified constant elasticity of variance model using the benchmark approach. The analytical expressions of pricing formulas for variance swaps are presented. In addition, the numerical solutions for variance swaps, volatility swaps and options on variance are demonstrated
Pricing Derivatives Securities with Prior Information on Long- Memory Volatility
This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochastic volatility (LMSV) model, constructed by including an autoregressive fractionally integrated moving average (ARFIMA) process in a stochastic volatility scheme. Under this framework, we work up maximum likelihood spectral estimators and bootstraped confidence intervals. In the light of the empirical findings, we develop a Bayesian model for pricing derivative securities with prior information on long-memory volatility.contingent pricing, econometric modeling
PRICING EUROPEAN OPTION UNDER A MODIFIED CEV MODEL
A financial derivative is an instrument whose payoff is derived from the behavior of another underlying asset. One of the most commonly used derivatives is the option which gives the right to buy or to sell an underlying asset at a pre-specified price at (European) or at and before (American) an expiration date. Finding a fair price of the option is called the option pricing problem and it depends on the underlying asset prices during the period from the initial time to expiration date. Thus, a “good” model for the underlying asset price trajectory is needed. In this work, we are interested in European call options. We propose a new Constant Elasticity of Variance (CEV) model that covers the post-crash situations. First, we set up the modified CEV model for markets with high volatility. Then we find a numerical solution for the stochastic differential equation of the underlying price. The risk-neutral valuation method shows that the option price can be written as an expected value of the discounted underlying asset price at maturity. Then we use Monte Carlo methods for finance this to find a numerical solution for the price of a European option under a CEV model with high volatility. Keywords
A Closed-Form Approximation of Likelihood Functions for Discretely Sampled Diffusions: the Exponent Expansion
In this paper we discuss a closed-form approximation of the likelihood
functions of an arbitrary diffusion process. The approximation is based on an
exponential ansatz of the transition probability for a finite time step , and a series expansion of the deviation of its logarithm from that of a
Gaussian distribution. Through this procedure, dubbed {\em exponent expansion},
the transition probability is obtained as a power series in . This
becomes asymptotically exact if an increasing number of terms is included, and
provides remarkably accurate results even when truncated to the first few (say
3) terms. The coefficients of such expansion can be determined
straightforwardly through a recursion, and involve simple one-dimensional
integrals.
We present several examples of financial interest, and we compare our results
with the state-of-the-art approximation of discretely sampled diffusions
[A\"it-Sahalia, {\it Journal of Finance} {\bf 54}, 1361 (1999)]. We find that
the exponent expansion provides a similar accuracy in most of the cases, but a
better behavior in the low-volatility regime. Furthermore the implementation of
the present approach turns out to be simpler.
Within the functional integration framework the exponent expansion allows one
to obtain remarkably good approximations of the pricing kernels of financial
derivatives. This is illustrated with the application to simple path-dependent
interest rate derivatives. Finally we discuss how these results can also be
used to increase the efficiency of numerical (both deterministic and
stochastic) approaches to derivative pricing.Comment: 28 pages, 7 figure
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