9,482 research outputs found
Option Valuation using Fourier Space Time Stepping
It is well known that the Black-Scholes-Merton model suffers from several
deficiencies. Jump-diffusion and Levy models have been widely used to partially
alleviate some of the biases inherent in this classical model. Unfortunately,
the resulting pricing problem requires solving a more difficult partial-integro
differential equation (PIDE) and although several approaches for solving the
PIDE have been suggested in the literature, none are entirely satisfactory. All
treat the integral and diffusive terms asymmetrically and are difficult to
extend to higher dimensions. We present a new, efficient algorithm, based on
transform methods, which symmetrically treats the diffusive and integrals
terms, is applicable to a wide class of path-dependent options (such as
Bermudan, barrier, and shout options) and options on multiple assets, and
naturally extends to regime-switching Levy models. We present a concise study
of the precision and convergence properties of our algorithm for several
classes of options and Levy models and demonstrate that the algorithm is
second-order in space and first-order in time for path-dependent options
Pricing and Hedging Basket Options with Exact Moment Matching
Theoretical models applied to option pricing should take into account the
empirical characteristics of the underlying financial time series. In this
paper, we show how to price basket options when assets follow a shifted
log-normal process with jumps capable of accommodating negative skewness. Our
technique is based on the Hermite polynomial expansion that can match exactly
the first m moments of the model implied-probability distribution. This method
is shown to provide superior results for basket options not only with respect
to pricing but also for hedging.Comment: 35 pages, 10 table
Gibbs sampler with jump diffusion model: application in European call option and annuity
In this paper, we are presenting a method for estimation of market parameters
modeled by jump diffusion process. The method proposed is based on Gibbs
sampler, while the market parameters are the drift, the volatility, the jump
intensity and its rate of occurrence. Demonstration on how to use these
parameters to estimate the fair price of European call option and annuity will
be shown, for the situation where the market is modeled by jump diffusion
process with different intensity and occurrence. The results is compared to
conventional options to observe the impact of jump effects.Comment: 15 pages, 5 figures, Submitted to IJTA
Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes
Fast pricing of American-style options has been a difficult problem since it
was first introduced to financial markets in 1970s, especially when the
underlying stocks' prices follow some jump-diffusion processes. In this paper,
we propose a new algorithm to generate tight upper bounds on the Bermudan
option price without nested simulation, under the jump-diffusion setting. By
exploiting the martingale representation theorem for jump processes on the dual
martingale, we are able to explore the unique structure of the optimal dual
martingale and construct an approximation that preserves the martingale
property. The resulting upper bound estimator avoids the nested Monte Carlo
simulation suffered by the original primal-dual algorithm, therefore
significantly improves the computational efficiency. Theoretical analysis is
provided to guarantee the quality of the martingale approximation. Numerical
experiments are conducted to verify the efficiency of our proposed algorithm
Exchange Options Under Jump-Diffusion Dynamics
Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated Wiener components. Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. We use Mertonās analysis to extend Margrabeās results to the case of exchange options where both stock price processes also contain compound Poisson jump components. A Radon-NikodĀ“ym derivative process that induces the change of measure from the market measure to an equivalent martingale measure is introduced. The choice of parameters in the Radon-NikodĀ“ym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic intepretation of the early exercise premium.American options; exchange options; compound Poisson processes; equivalent martingale measure
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
European options can be priced by solving parabolic partial(-integro)
differential equations under stochastic volatility and jump-diffusion models
like Heston, Merton, and Bates models. American option prices can be obtained
by solving linear complementary problems (LCPs) with the same operators. A
finite difference discretization leads to a so-called full order model (FOM).
Reduced order models (ROMs) are derived employing proper orthogonal
decomposition (POD). The early exercise constraint of American options is
enforced by a penalty on subset of grid points. The presented numerical
experiments demonstrate that pricing with ROMs can be orders of magnitude
faster within a given model parameter variation range
The History of the Quantitative Methods in Finance Conference Series. 1992-2007
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.
A Review of Volatility and Option Pricing
The literature on volatility modelling and option pricing is a large and
diverse area due to its importance and applications. This paper provides a
review of the most significant volatility models and option pricing methods,
beginning with constant volatility models up to stochastic volatility. We also
survey less commonly known models e.g. hybrid models. We explain various
volatility types (e.g. realised and implied volatility) and discuss the
empirical properties
On the value of being American
The virtue of an American option is that it can be exercised at any time.
This right is particularly valuable when there is model uncertainty. Yet almost
all the extensive literature on American options assumes away model
uncertainty. This paper quantifies the potential value of this flexibility by
identifying the supremum on the price of an American option when no model is
imposed on the data, but rather any model is required to be consistent with a
family of European call prices. The bound is enforced by a hedging strategy
involving these call options which is robust to model error
Option prices with call prices
There exist several methods how more general options can be priced with call
prices. In this article, we extend these results to cover a wider class of
options and market models. In particular, we introduce a new pricing formula
which can be used to price more general options if prices for call options and
digital options are known for every strike price. Moreover, we derive similar
results for barrier type options. As a consequence, we obtain a static hedging
for general options in the general class of models. Our result can be utilised
in several significant applications. As a simple example, we derive an upper
bound for the value of a general American option with convex payoff and
characterise conditions under which the value of this option equals to the
value of the corresponding European option.Comment: 10 page
- ā¦