831 research outputs found
Efficient pricing of discrete arithmetic Asian options under mean reversion and jumps based on Fourier-cosine expansions
We propose an efficient pricing method for arithmetic Asian options based on Fourier-cosine expansions. In particular, we allow for mean reversion and jumps in the underlying price dynamics. There is an extensive body of empirical evidence in the current literature that points to the existence and prominence of such anomalies in the prices of certain asset classes, such as commodities. Our efficient pricing method is derived for the discretely monitored versions of the European-style arithmetic Asian options. The analytical solutions obtained from our Fourier-cosine expansions are compared to the benchmark fast Fourier transform based pricing for the examination of its accuracy and computational efficienc
Lower Precision calculation for option pricing
The problem of options pricing is one of the most critical issues and fundamental building blocks in mathematical finance. The research includes deployment of lower precision type in two options pricing algorithms: Black-Scholes and Monte Carlo simulation. We make an assumption that the shorter the number used for calculations is (in bits), the more operations we are able to perform in the same time. The results are examined by a comparison to the outputs of single and double precision types. The major goal of the study is to indicate whether the lower precision types can be used in financial mathematics. The findings indicate that Black-Scholes provided more precise outputs than the basic implementation of Monte Carlo simulation. Modification of the Monte Carlo algorithm is also proposed. The research shows the limitations and opportunities of the lower precision type usage. In order to benefit from the application in terms of the time of calculation improved algorithms can be implemented on GPU or FPGA. We conclude that under particular restrictions the lower precision calculation can be used in mathematical finance.
The Pricing of Asian Options in Uncertain Volatility Model
This paper studies the pricing of Asian options when the volatility of the underlying
asset is uncertain. We use the nonlinear Feynman-Kac formula in the G-expectation theory
to get the two-dimensional nonlinear PDEs. For the arithmetic average fixed strike Asian
options, the nonlinear PDEs can be transferred to linear PDEs. For the arithmetic average
floating strike Asian options, we use a dimension reduction technique to transfer the two-dimensional
nonlinear PDEs to one-dimensional nonlinear PDEs. Then we introduce the
applicable numerical computation methods for these two classes of PDEs and analyze the
performance of the numerical algorithms
Efficient Procedure for Valuing American Lookback Put Options
Lookback option is a well-known path-dependent option where its
payoff depends on the historical extremum prices. The thesis focuses
on the binomial pricing of the American floating strike lookback put
options with payoff at time (if exercise) characterized by
where denotes the price of the underlying stock at time .
Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and
Vorst} (RBCV, 1992) who proposed a transformed binomial lattice
model for efficient pricing of this class of option, this thesis
extends and enhances their binomial recursive algorithm by
exploiting the additional combinatorial properties of the lattice
structure. The proposed algorithm is not only computational
efficient but it also significantly reduces the memory constraint.
As a result, the proposed algorithm is more than 1000 times faster
than the original RBCV algorithm and it can compute a binomial
lattice with one million time steps in less than two seconds. This
algorithm enables us to extrapolate the limiting (American) option
value up to 4 or 5 decimal accuracy in real time
Black-Scholes formulae for Asian options in local volatility models
We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat kernel expansion method in the framework of hypoelliptic, not uniformly parabolic, partial differential equations
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