3,123 research outputs found
Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps
In this paper we present some results on Geometric Asian option valuation for
affine stochastic volatility models with jumps. We shall provide a general
framework into which several different valuation problems based on some average
process can be cast, and we shall obtain close-form solutions for some relevant
affine model classes.Comment: 20 page
Pricing Exotic Options in a Path Integral Approach
In the framework of Black-Scholes-Merton model of financial derivatives, a
path integral approach to option pricing is presented. A general formula to
price European path dependent options on multidimensional assets is obtained
and implemented by means of various flexible and efficient algorithms. As an
example, we detail the cases of Asian, barrier knock out, reverse cliquet and
basket call options, evaluating prices and Greeks. The numerical results are
compared with those obtained with other procedures used in quantitative finance
and found to be in good agreement. In particular, when pricing at-the-money and
out-of-the-money options, the path integral approach exhibits competitive
performances.Comment: 21 pages, LaTeX, 3 figures, 6 table
Approximating stochastic volatility by recombinant trees
A general method to construct recombinant tree approximations for stochastic
volatility models is developed and applied to the Heston model for stock price
dynamics. In this application, the resulting approximation is a four tuple
Markov process. The first two components are related to the stock and
volatility processes and take values in a two-dimensional binomial tree. The
other two components of the Markov process are the increments of random walks
with simple values in . The resulting efficient option pricing
equations are numerically implemented for general American and European options
including the standard put and calls, barrier, lookback and Asian-type
pay-offs. The weak and extended weak convergences are also proved.Comment: Published in at http://dx.doi.org/10.1214/13-AAP977 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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